Pipeline Design for Water Engineers

PIPELINE DESl6N fOR WATER EN6IMEERSTHIRD REVISED AND UPDATED EDITION DEVELOPMENTSIN WATER SCIENCE, 40 OTHER TITLES IN THIS SERIES VOLUMES 7 3 ARE OUT OIF PRINT 4 J.J. FRIED GROUNDWATER POLLUTION 5 N. RAJARATNAM TURBULENT JETS 6 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS 7 v. HANK AND J. SVEC GROUNDWATER HYDRAULICS 8 J. BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL AFRICA 9 T.A. McMAHON AND R.G. MElN RESERVOIR CAPACITY AND YIELD 10 G. KOVACS SEEPAGE HYDRAULICS 1i w.n. GRAF AND C.H. MORTIMER (EDITORS) HYDRODYNAMICSOF LAKES: PROCEEDINGS OF A SYMPOSIUM 12-13 OCTOBER 1978. LAUSANNE, SWITZERLAND 12 W. BACK AND D.A. STEPHENSON (EDITORS) CONTEMPORARY HYDROGEOLOGY: THE GEORGE BURKE MAXEY MEMORIAL VOLUME 13 M.A. MARlfJO AND J.N. LUTHIN SEEPAGE AND GROUNDWATER 14 D. STEPHENSON STORMWATER HYDROLOGY AND DRAINAGE 15 D. STEPHENSON PIPELINE DESIGN FOR WATER ENGINEERS (completely revised edition of Vol. 6 in the series) 16 W. BACK AND R. LETOLLE (EDITORS) SYMPOSlClM ON GEOCHEMISTRY OF GROUNDWATER 17 A.H. EL-SHAARAWI (EDITOR) IN COLLABORATION WITH S.R. ESTERBY TIME SERIES METHODS IN HYDROSCIENCES 18 J.BALEK HYDROLOGY AND WATER RESOURCES IN TROPICAL REGIONS 19 D. STEPHENSON PIPEFLOW ANALYSIS 20 I. ZAVOIANU MORPHOMETRY OF DRAINAGE BASINS 21 M.M.A. SHAHIN HYDROLOGY OF THE NILE BASIN 22 H.C.RIGGS STREAMFLOW CHARACTERISTICS 23 M. NEGULESCU MUNICIPAL WASTEWATER TREATMENT 24 L.G.EVERETT GROUNDWATER MONITORING HANDBOOK FOR COAL AND OIL SHALE DEVELOPMENT 25 W. KINZELBACH GROUNDWATER MODELLING: AN INTRODUCTION WITH SAMPLE PROGRAMS IN BASIC 26 D. STEPHENSONAND M.E. MEADOWS KINEMATIC HYDROLOGY AND MODELLING 27 A.M. EL-SHAARAWI AND R.E. KWIATKOWSKI (EDITORS) STATISTICAL ASPECTS OF WATER CIUALITY MONITORING - PROCEEDINGS OF THE WORKSHOP HELD AT THE CANADIAN CENTRE FOR INLAND WATERS, OCTOBER 1985 28 M.JERMAR WATER RESOURCES AND WATER MANAGEMENT 29 G.W. ANNANDALE RESERVOIR SEDIMENTATION 30 D.CLARKE MICROCOMPUTER PROGRAMS IN GROUNDWATER 31 R.H. FRENCH HYDRAULIC PROCESSES IN ALLUVIAL FANS 32 L. VOTRUBA, 2. KOS. K. NACHAZEL, A. PATERA ANDV. ZEMAN ANALYSIS OF WATER RESOURC_ESYSTEMS 33 L. VOTRUBA AND V. BROZA WATER MANAGEMENT IN RESERVOIRS 34 D. STEPHENSON WATER AND WASTEWATER SYSTEMS ANALYSIS 35 M.A. CELlA ET AL. COMPUTATIONAL METHODS IN WATER RESOURCES, VOLUME 1 MODELING SURFACE AND SUB-SURFACE FLOWS. PROCEEDINGS OF THE VII INTERNATIONAL CONFERENCE, MIT. USA, JUNE 1988 36 M.A. CELIA ET AL. COMPUTATIONAL METHODS IN WATER RESOURCES, VOLUME 2 NUMERICAL METHODS FOR TRANSPORT AND HYDROLOGICAL PROCESSES. PROCEEDINGS OF THE V11 INTERNATIONAL CONFERENCE, MIT, USA, JUNE 1988 37 D.CLARKE GROUNDWATER DISCHARGE TESTS: SIMULATION AND ANALYSIS THIRD REVISED AND UPDATED EDITION DAVID STEPHENSON Department of Civil Engineering University of the Witwatersrand Johannesburg, South Africa ELSEVlER Amsterdam - Oxford - N e w York - Tokyo 1989 ELSEYIER SCIENCE PUBLISHERS B.V. Sara Burgerhartstraat 25 P.O. Box 2 1 1, 1000 A€ Amsterdam, The Netherlands Distributors for the United States and Canada: ELSEVIER SCIENCE PUBLISHINGCOMPANY INC. 655, Avenue of the Americas New York, NY 10017, U.S.A. ISBN 0-444-87373-2 0 Elsevier Science Publishers B.V., 1989 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher, Elsevier Science Publishers B.V./ Physical Sciences & EngineeringDivision, P.O. Box 330, 1000 AH Amsterdam, The Netherlands. Special regulations for readers in the U.S.A. - This publication has been registered with the Copyright Clearance Center Inc. (CCC), Salem, Massachusetts. Information can be obtained from the CCC about conditions under which photocopies of parts of this publication may be made in the USA. All other copyright questions, including photocopying outside of the USA, should be referred t o the publisher. No responsibility is assumed by the Publisher for any injury and/or damage t o persons or property as a matter of products liability, negligence or otherwise, or from any use or operation of any methods, products, instructions or ideas contained in the material herein. Printed in The Netherlands V PREFACE TO FIRST EDITION Pipelines lengths are for has and are being constructed in ever-increasing and rational diameters, bases have work of working to pressures. Accurate and design essential years achieve economic to done safe designs. Engineers Much resorted been semi-empirical design formulae. the recently in an effort to r a t i o n a l i z e design pipelines. This as well book as col lates pub1 ished some material new on rational and design methods data. the to Although aim of presenting techniques in many retaining the or oook conventional is to bring approaches instances, techniques an the most modern design It is suitable the as most the c i v i l to hydraulic but engineer. also contains introduction the in will Many subject the a l so of d a t a on advanced techniques the book field. be i3ecause of useful to the sound theoretical and background under-graduate post-graduate students. the s u b j e c t s , and the such as mathematical optimization, book may provide for leads for are s t i l l in t h e i r infancy methods modern graphs The planning ancillary with codes design piping at in further bear and research. in The the the of solution proposed of many and problems mind of acceptance in the book half computers calculators many were of prepared with book the is the assistance of with computers. and and first of this In concerned half, book hydraulics design in pipelines. are second The structural does not features discussed. deal detail manufacture, of of practice large are l a y i n g a n d operation, from the engineer's as in opposed other will nor should desk. to i t replace design is Emphasis on the Pipelines covered industrial and domestic directed which pub1 ications. Although the water the It engineer, of be be many t h i s book other that by be of use to engineers i n v o l v e d as of well the as solids and and gases. piping should may fluids some noted designs techniques of pre- described stressed covered pipes, patents. of These include pipes types and concrete methods stiffening branches and v a r i o u s coatings. VI The S . I . system of metric u n i t s i s preferred i n i n brackets the book although Most g r a p h s Worked to imperial u n i t s a re g i ve n a n d equations examples work in in many instances. a r e represented i n uni versa1 dimensionless form. for as many they problems a n d the reader are given these The the i s advised through the text. at often elaborate on symbols chapter used ideas not in each with highlighted chapter are and algebraic end summarized general chapter. of that in together the specific references a r r a n g e d The appendix data. the order of further subject matter i n the and standards and gives references other useful PREFACE TO SECOND EDITION The gratifying response to the f i r s t e d i t i o n of t h i s book resulted in small ations The replaced amendments to the second impression, a n d some major a l t e r - i n t h i s new edition. chapters by data on transport relevant of to solids water and sewers have Thus a been new more engineers. chapter on the effects of a i r i n water pipes i s included, chapter on pumping systems for water pipelines. as well as a latter was The reviewed by B i l l Glass who added many of h i s own ideas. There are additions and u p d a t i n g throughout. There is additional information on p i p e l i n e economics and optimum diameters i n Chapter 1 . A comparison of currently sections are used friction formulae is now made in Chapter and 2. The flow on non-circular These are are pipe and p a r t l y largely in of the full pipes to the book basic water sewer omitted. as and hammer interest drainage engineer and such covered author’s ‘Stormwater introduction Hydrology to water Drainage’ theory (Elsevier, preceeds the 1981). design A of hammer protection of pumping a n d g r a v i t y l i n e s i n Chapter 4 . flexible pipes are brought limit The together. sections An on structural section design on of enlarged soil-pipe interaction and states of f l e x i b l e pipes preceeds the design of s t i f f e n e d pipes. Although recognised needs some of the new edition is now fairly basic, it is that this i s d e s i r a b l e for both the p r a c t i c i n g engineer who the student who comes across refreshing and the problem of p i p e l i n e design f o r the f i r s t time. VIII PREFACE TO THIRD E D I T I O N Recent research i n c a v i t a t i o n a n d flow control h a s prompted a d d i t i o n a l sections on pipes a n d make up this. There a r e also new sections on references in supports and a to new exposed layout secondary this edition. stress. Some Additional sections appearing p r e v i o u s editions, noteably on p i p e network systems a n a l y s i s a n d o p t i m i z a t i o n have been ommitted as they were considered more appropriate in the alJthOr’S p a r a l l e l book ‘Pipeflow A n a l y s i s ’ b y the same p u b l i s h e r . IX ACKNOWLEDGEMENTS The b a s i s for course of and my t h i s book was d e r i v e d from my experience a n d i n the with the Hand Water Engineers. may Board a n d Stewart, S v i r i d o v extensive be knowledge reflected of duties 0 iver, 1 in Consulting these The Engineers although I the organizations therefore herein I am solely to blame f o r any inaccuracies o r misconceptions. to my wife Lesley, am g r a t e f u l twins during who, i n a d d i t i o n to looking a f t e r assiduously typed the first many a lost weekend, d r a f t of t h i s book. David Stephenson X CONTENTS CHAPTER 1 ECONOMIC PLANNING lntroduct ion P i p e l i n e Economics B a s i c s of E c o n o m i c s M e t h o d s of Ana I y s i s Uncertainty in Forecasts Balancing Storage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 9 10 11 14 CHA?TER 2 HYDRAULICS The F u n d a m e n t a l E q u a t i o n s of F l u i d F l o w F l o w H e a d Loss R e l a t i o n s h i p s . . Empirical Flow Formulae 2 a t i o n a l Flow Formulae C o m p a r i s o n of F r i c t i o n F o r m u l a e M i n o r Losses . . P r e s s u r e and F l o w C o n t r o l i n P i p e s lntroduct ion T y p e s of V a l v e s I so l a t i n g V a Iv e s Control Valves C a v i t a t i o n in C o n t r o l V a l v e s . . I n t e r a c t i o n b e t w e e n C a v i t a t i o n a n d W a t e r Hammer P r e s s u r e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 18 18 19 24 26 28 28 28 29 29 32 34 CHAPTER 3 P I P E L I N E SYSTEM ANALYSIS AND DESIGN Network A n a l y s i s E q u i v a l e n t P i p e s for P i p e s in S e r i e s o r P a r a l l e l Loop Flow Correction Method The Node H e a d C o r r e c t i o n M e t h o d A l t e r n a t i v e M e t h o d s of A n a l y s i s iqetwork A n a l y s i s b y L i n e a r T h e o r y O p t i m i z a t i o n of P i p e l i n e Systems D y n a m i c P r o g r a m m i n g f o r O p t i m i z i n g Compound P i p e s T r a n s p o r t a t i o n P r o g r a m m i n g for L e a s t - c o s t A1 l o c a t i o n o f Resources L i n e a r P r o g r a m m i n g f o r D e s i g n of l e a s t - c o s t Open N e t w o r k s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 37 38 40 41 43 44 45 48 52 . . . . . . . . . . . . XI CHAPTER 4 WATER HAMMER AND SURGE R i g i d Water Column Surge Theory M e c h a n i c s o f W a t e r Hammer E l a s t i c W a t e r Hammer T h e o r y Method o f A n a l y s i s Effect of F r i c t i o n Protection of Pumping Lines Pump I n e r t i a Pump B y p a s s R e f l u x V a l v e Surge Tanks Discharge Tanks A i r Vessels In-Line Reflux Valves Release V a l v e s Choice o f P r o t e c t i v e D e v i c e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 60 64 64 68 69 73 76 77 79 85 89 91 93 CHAPTER 5 AI3 IN P I P E L I N E S Introduction Problems of A i r Entrainment A i r I n t a k e a t Pump Sumps A i r Absorption a t Free Surfaces H y d r a u l i c Removal of A i r H y d r a u l i c Jumps Free F a l l s A i r Valves Head Losses in P i p e l i n e s W a t e r Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 97 99 101 102 102 104 105 108 109 CHAPTER 6 EXTERNAL LOADS Soil Loads Trench conditions Embankment Conditions Superimposed Loads T r a f f i c Loads Stress Caused b y Point Loads Uniformly Loaded Areas . Effect o f R i g i d Pavements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 113 116 120 121 121 122 123 XI1 CHAPTER 7 CONCRETE PIPES The Effect of B e d d i n g Prestressed Concrete Pipes Circumferential Prestressing C i r c u m f e r e n t i a l P r e s t r e s s a f t e r Losses Circumferential Stress u n d e r F i e l d Pressure L o n g i t u d i n a l Prestressing L o n g i t u d i n a l Stresses A f t e r L o s s e s P r o p e r t i e s o f Steel and C o n c r e t e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 129 131 131 133 134 136 136 CHAPTER 8 STEEL AND F L E X I B L E P I P E I n t e r n a l Pressures Tension R i n g s to Resist I n t e r n a l Pressures D e f o r m a t i o n of C i r c u l a r P i p e s u n d e r E x t e r n a l L o a d Effect of L a t e r a l Support S t r e s s d u e to C i r c u m f e r e n t i a l B e n d i n g More General Deflection Equations S t i f f e n i n g R i n g s to R e s i s t B u c k l i n g w i t h no side support Tension R i n g s Stiffening Rings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 143 146 149 151 152 156 156 156 CHAPTER 9 SECONDARY STRESSES Stresses a t Branches Crotch Plates Internal Bracing Stresses a t Bends T h e P i p e a s a Beam Longitudinal Bending Pipe Stress a t Saddles . . Ring Girders Temperature Stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 162 165 172 173 173 174 175 176 CHA?TER 10 P I PES. F I TT I NGS AND APPURTENANCES ?ipe M a t e r i a l s Steel P i p e Cast I r o n P i p e Asbestos Cement P i p e Concrete P i p e Plastic Pipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179 179 179 180 180 180 L i n e Val ves Sluice Valves B u t t e r f l y Valves Globe Valves Needle a n d Control Valves Spherical Valves Reflux Valves A i r Valves A i r Vent Valves A i r Release Valves Thrust Blocks Forces Induced by Supports . L o n g i t u d i n a l Stress Temperature Stresses Forces at Bends L a t e r a l Movement Forces on Supports Unbalanced Forces Flow Measurement Venturi Meters Nozz I es Orifices Bend Meters Mechanical Meters Electromagnetic I n d u c t i o n Mass a n d Volume Measurement Te I erne t ry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 182 183 184 184 185 186 186 186 188 190 194 195 195 196 196 197 197 198 198 199 1 99 200 200 201 201 201 CHAPTER 1 1 L A Y I NG AND PROTECTION Selecting a Route L a y i n g a n d Trenching Thrust Sores Pipe Bridges Underwater Pipelines Joints a n d Flanges Coatings Linings Cat hod i c Prot ec t ion Galvanic Corrosion Stray Current E l e c t r o l y s i s Thermal I n s u l a t i o n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 206 208 208 210 212 2 6 1 2 7 1 218 21a 222 223 XIV CHAPTER 12 PUMP I NG I NSTALLAT I ON5 I n f l u e n c e of Pumps in P i p e l i n e Design T y p e s of P u m p s P o s i t i v e Displacement Types C e n t r i f u g a l Pumps T e r m s and D e f i n i t i o n s Head Total Head Net P o s i t i v e S u c t i o n Head S p e c i f i c Speed Impeller Dynamics Pump C h a r a c t e r i s t i c C u r v e s ivto t o r s Pumpstat ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228 228 228 229 231 23 1 231 232 233 234 236 239 240 GENERAL REFE2ENCES AND STANDARDS . . . . . . 242 BOOKS FOR FURTHER READING . . . . . . . . . 250 APPEND I X Symbols for p i p e f i t t i n g s Properties of p i p e shapes P r o p e r t i e s of w a t e r P r o p e r t i e s of p i p e m a t e r i a l s Conv ers i o n f a c t o r s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252 253 254 255 256 AUTHdR SUBJECT INDEX INDEX . . . . . . . . . . . . . . . . . . . . . . . . 258 260 1 CHAPTER 1 ECONOMIC PLANNING I NTRODUCT ION Pipes have been used for many c e n t u r i e s for transporting fluids. and lead pipes iron, was pipes The Chinese f i r s t u s e d bamboo p i p e s t h o u s a n d s o f y e a r s ago, p i p e s were were used unearthed a t in Pompeii. It was In only later with c e n t u r i e s wood-stave the advent of Cast cast iron England. pressure in however, used that pipelines 19th were manufactured. and is still extensively the Century used. Steel were f i r s t introduced towards small and t h e e n d of t h e l a s t c e n t u r y , The facilitating c o n s t r u c t i o n of high grade large bore pipelines. i n c r e a s i n g use o f pipelines 10 Newtons have with per been or steels a n d large r o l l i n g m i l l s has enabled and working pressure over Welding diameters square over 3 metres to be millimetre manufactured. and techniques perfected spiral enabling longitudinally circumferentially P i p e l i n e s a r e now welded welded p i p e s to b e m a n u f a c t u r e d . a l s o made plastics formulae thereby in r e i n f o r c e d concrete, p r e - s t r e s s e d concrete, varying design conditions. of asbestos cement, Reliable this flow and claywares, available to suit the became for pipelines century, a l s o p r o m o t i n g t h e use of p i p e s . Prior fluids common to this century by water a n d sewage Nowadays gases and were p r a c t i c a l l y pipelines oils over are long the o n l y the most transported means for pipeline. transporting solids distances. are also Liquid chemicals and in slurry form or in containers being pumped t h r o u g h p i p e l i n e s on ever kilometres of i n c r e a s i n g scales. There a r e the now o v e r world. two m i l l i o n pipelines i n service throughout The g l o b a l e x p e n d i t u r e on p i p e l i n e s i n 1974 was p r o b a b l y o v e r 5 5 000 m i l l i o n . There are many advantages rail, the of pipeline transport compared with o t h e r methods s u c h a s r o a d , waterway most and air:form of transport (1) Pipelines are often economic ( c o n s i d e r i n g e i t h e r c a p i t a l costs, r u n n i n g costs o r o v e r a l l c o s t s ) . susceptible to fluctuations in (2) Pipelining costs are not very 2 prices, since the major cost i s the c a p i t a l o u t l a y and subsequent o p e r a t i n g costs are r e l a t i v e l y small. Operations are not susceptible to labour disputes as little attendance i s r e q u i r e d . Many modern systems operate automatical- lY. Being hidden beneath the ground a pipeline will not mar the n a t u r a l environment. A b u r i e d p i p e l i n e i s reasonably secure against sabotage. A pipeline is independent of external influences such as traffic congestion and the weather. There is normally no problem of r e t u r n i n g empty containers to the source. It is relatively easy to increase the c a p a c i t y of a pipeline by i n s t a l l i n g a booster pump. A b u r i e d p i p e l i n e w i l l not d i s t u r b surface t r a f f i c a n d services. ( 1 0 ) Wayleaves for pipelines are usually easier to obtain than for roads and r a i l w a y s . (11) The accident rate per ton - km is considerably lower than for other forms of t r a n s p o r t . (12) A pipeline can cross rugged terrain difficult for vehicles to cross. There are of course disadvantages associated w i t h p i p e l i n e systems:The initial capital in the expenditure demand i s often large, of so i f there i s any uncertainty necessary. There is some degree speculation may be often a high cost involved in filling a pipeline ( e s p e c i a l l y long fuel Pipelines (although bases). cannot there be are lines). used for more than one m a t e r i a l operating at on a time batch multi-product pipelines There solids, are operating problems associated with the pumping of such as blockages on stoppage. to locate leaks o r blockages. I t i s often d i f f i c u l t P I PEL I NE ECONOM I CS The main cost of a p i p e l i n e system i s u s u a l l y that of the p i p e l i n e 3 itself. gravity The pipeline cost is in fact practically the only cost for and systems b u t as the adverse head increases so the power pumping s t a t i o n costs increase. Table p i p e l i nes. With the time 1.1 indicates some relative costs for typical installed the of economic writing relative instability pipeline costs of and rates of may inflation prevailing at by 20% o r more per will as vary. PVC In may costs for increase year, and different materials particular increase the cost than petro-chemical of concrete materials for such faster those instance, so these f i g u r e s should be inspected w i t h caution. TABLE 1 . 1 Relative P i p e l i n e Costs Bore mm Pipe M a t e r i a l 150 450 1 500 PVC Asbestos cement Reinforced concrete Prestressed concrete M i l d steel High tensile steel Cast i r o n <:,,-s, 6 7 10 11 25 23 23 23 33 28 25 80 90 100 - 150 90 75 - 180 - 120 - indicates not r e a d i l y a v a i l a b l e . i n 1974 under average conditions 1 u n i t = d;/metre The components m a k i n g up the cost of a p i p e l i n e v a r y widely from situation to situation but for water pipelines in open country and t y p i c a l conditions are as follows:Supply of p i p e - 55% - 20% may (may reduce as new m a t e r i a l s a r e developed) Excavation (depends reduce as on terrain, mechanical im- excavation prove) L a y i n g and j o i n t i n g techniques - 5% (may increase w i t h bour costs) la- F i t t i n g s a n d specials Coating and w r a p p i n g Structures ( v a l v e chambers, anchors) - 5% - 2% - 2% 4 L 10 a L 0 r m ._ U 5 Water hammer protection access roads, cathodic structures, fences - 1% . Land acquisition, protection, security - 1% - 5% - 1% - 3% For water from It is Engineering and survey costs Admi n i s t r a t i ve costs Interest d u r i n g construction Many factors have to be considered in s i z i n g a p i p e l i n e : pumping mains the flow to velocity at on the optimum diameter flow and working varies 0.7 m/s 2 m/s, depending pressure. about 1 m/s for for low pressure of heads and a flow and of 100 C/s increasing to 2 m/s of water, factor a flow 1 000 C / S pressure heads at about 400 m The c a p a c i t y optimum Fig. flow and may be even h i g h e r f o r h i g h e r pressures. power and cost structures also for influence any the v e l o c i t y o r conversely the diameter p a r t i c u l a r flow. 1.1 i l l u s t r a t e s the optimum diameter of water mains f o r t y p i c a l conditions. I n planning scale costs. of By a p i p e l i n e system i t should be borne i n mind that of a pipeline diameter has of considerable pipe, effect on the such the unit as operation doubling the the other factors head remaining constant, hand the cost the c a p a c i t y increases six-fold. doubles the lines. main so that It it is the is On the other per unit effect approximately to cost delivered which to decreases 1/3 of original. Whether at the this scale justifies a multi-product large diameter i n fact economical on the install outset depends f o l l o w i n g factors as well as scale:Rate of low growth i n demand ( i t may be uneconomical factors during initial years). to operate a t factor is capacity (Capacity the r a t i o of a c t u a l average discharge to design c a p a c i t y ) . Operating to factor (the ratio of average the throughput period), can be at any time maximum on throughput the rate of during same and which improved will by depend draw-off i n s t a l l i n g storage a t Reduced power costs the consumer's end. due to low friction losses while the p i p e l i n e i s -not o p e r a t i n g a t f u l l c a p a c i t y . C e r t a i n t y of f u t u r e demands. V a r y i n g costs w i t h time ( b o t h c a p i t a l and o p e r a t i n g ) . (6) Rates of interest and c a p i t a l in availability. a second pipeline i f (7) Physical d i ffi cu l ti e s required. The optimum not cost design the construction of p e r i o d of a p i p e l i n e depends on a number of factors, rate of least b e i n g the r a t e of inflation, in interest on c a p i t a l to the r a t e of loans and the scale and addition growth, c e r t a i n t y of f u t u r e demands In waterworks for practice up (Osborne a n d James, it to has been to 1973). economic hence. to size large found years pipelines throughput size of demands 10 30 For and h i g h growth rates, so that technical c a p a b i l i t i e s may l i m i t the the p i p e l i n e , Longer supplementation may stages are normally be r e q u i r e d w i t h i n justified for small 10 years. planning bores and low pressures. It Where may not always are be economic it is to lay to a uniform bore pipeline. and pressures high economic reduce the diameter consequent1 y the wal I thickness. In there planning may be a a trunk main of be with progressive decrease of on i n diameter diameters. the most number should possible compared combinations before deciding Alternative economic. layouts Systems a n a l y s i s techniques such as l i n e a r programming and dynamic programming are i d e a l l y suited f o r such studies. Booster pumping high to pump a stations may be installed along lines instead of high pressure head a t the i n p u t end and m a i n t a i n i n g a along the entire line. By providing for intermediate pressure booster at the pumps a t input end, the design stage instead of pumping to a h i g h head and consequently the p i p e w a l l the pressure heads thicknesses may b e minimized. even though additional There may be a s a v i n g i n o v e r a l l cost, stations are required. pumping The booster stations may not be r e q u i r e d f o r some time. The c a p a c i t y booster this is pumps not at of the p i p e l i n e may often be increased b y i n s t a l l i n g should losses the a later stage although The it be r e a l i s e d that a pipeline always economic. with friction of along flow, increase approximately the square consequently power losses increase considerably The diameter be selected cost by of an a f o r h i g h e r flows. pumping main economic with to convey a known discharge can of alternative whereas sizes. The comparison increasing pipeline increases diameter, power cost 7 TOTAL COST 5 DIAMETER Fig. 1.2 O p t i m i z a t i o n of d i a m e t e r of a p u m p i n g p i p e l i n e . C COST I N CENTS P E R m3 Cl c2 C 4 = 0, + 0; 0 01 02 Q3 Discharge Fig. 7 -3 Optirriization of throughput for certain diaweters 8 in overcoming costs by friction reduces as correspondingly. the p i p e l i n e On the other hand power Thus costs, increase steeply i s reduced in d i a m e t e r . adding together a pipeline and such as An the present Figure example v a l u e of from operating which the one obtains system curve be 1.2, least-cost chapter. rate. If at can selected. is given later in the There will b e a h i g h e r cost the g r e a t e r the design d i s c h a r g e some of a stage pumping as later it is it desired to increase to the throughput capacity diagram different kilolitre system, 1.2 i s convenient the form of replot d a t a from a 1.3. Thus for such Figure in Figure possible or throughputs, is plotted the cost, now e x p r e s s e d i n c e n t s p e r (real) similar, a s the ordinate w i t h a l t e r n a t i v e pipe diameter a parameter. It any can be demonstrated is is a minimum twice the that when the the cost per unit of throughput for an pipeline basis) p i p e l i n e cost of (expressed on annual friction. annual cost the power in o v e r c o m i n g T h u s t h e cost C,(P) c = C, - in cents p e r c u b i c metre of water is + C2(d) 61 wHQ + C 2 ( d ) Q 2gdA (1.1) = c,w + Hs) + CZ(d)/Q 2C1 wHf/Q minimum C i.e. P of - C2(d)/Q2 C Z ( d ) = 2 C,(P) i s power H is is requirement, the total proportional subscript C2(d) of power is to wHQ. s (1.2) w i s the u n i t weight to static a and f to of water, head, rate, refers cost friction, diameter Q d, pumping is the of pipeline C,(P) t h e cost ( a l l costs converted to a u n i t time b a s e ) . (In a given similar manner penstock friction it c a n b e shown supplying head loss that the power o u t p u t of a station the total is a diameter a is hydroelectric one third of maximum if the head a v a i table). 9 R e t u r n i n g to F i g u r e 1.3, the f o l l o w i n g w i l l Q, there be observed: is a c e r t a i n diameter at (1) At any particular throughput w h i c h o v e r a l l costs w i l l b e a m i n i m u m ( i n t h i s case D 2 1. (2) At t h i s d i a m e t e r t h e c o s t p e r ton of if throughput was increased. throughput could be reduced Costs would be a minimum is further at not some the t h r o u g h p u t Q2. same as the Thus a p i p e l i n e ' s optimum throughput throughput for which it is the optimum diameter. (3) If Q Q4 1 were increased by an a m o u n t Q3 so t h a t not but to to total install throughput = Q1 + Q3 i t m a y b e economic optimum diameter diameter a second flow pipeline through (with D3 ) increase the the p i p e w i t h D2, i.e. Q4C4 i s l e s s t h a n QIC1 + Q3C3. (4) At a later the stage when it is justified the to construct line a second be pipeline reduced. The power throughput through overloaded could cost per unit so of the additional throughput decreases of it with being line increasing most pipe diameter to corresponding likelihood an economic increase throughput through existing increases w i t h size (White, 1969). B A S I C S OF ECONOMICS Economics designs. some is used a s a b a s t s f o r c o m p a r i n g a l t e r n a t i v e schemes o r schemes m a y have different cash flows necessitating Different rational is form of the on comparison. rate The c r u x o f a l l methods o f economic which may funds. be in comparison interest discount loans or the form of the may to rate redemption from National projects r e q u i r e a discount reflect b e more a time rate r a t e different of preference, the p r e v a i l i n g interest r a t e , private organizations whereas will interested in the a c t u a l c a s h flows, a n d consequently use the real borrowing The cash compared basis. interest rate. i.e. of payments another may and returns, of one scheme may b e to a common time flows, those with by bringing them Thus a l l one cash flows be discounted next it year is to t h e i r p r e s e n t the same as value. For instance pound this received year fl/l.05 invested ( i t s present value) if could earn 5% i n t e r e s t if 10 this a year. It is usual t o meet capital interest expenditure rate. from a loan over definite period at load by annual a certain paying Provision i s made f o r r e p a y i n g the interest. to amount into a at s i n k i n g fund w h i c h a l s o c o l l e c t s the e n d of each year required The repayments to a71 in n y e a r s i s where r i s the i n t e r e s t r a t e on t h e p a y m e n t s i n t o t h e s i n k i n g f u n d . i s R, then the t o t a l a n n u a l payment i s If t h e i n t e r e s t r a t e o n t h e toan R(l+r)"+ r-R (1.4) ( 1+ r ) n-t Normally the interest rate on the loan i s equal to the interest rate e a r n e d b y t h e s i n k i n g fund so t h e a n n u a l p a y m e n t on a l o a n of El (1.5) is Conversely the present IS v a l u e of a p a y m e n t of S1 a t t h e e n d o f each year over n years The p r e s e n t v a l u e of a s i n g l e amount of f l i n n y e a r s i s Interest on loans, tables are available for determining annual the a n n u a l payments for and the present rates and v a l u e s of redemption payments o r (lnstn. of returns, Civil various 1962) interest periods Engs., Methods of A n a l y s i s Different engineering may and b e compared incomes for schemes r e q u i r e d in a to meet t h e same o b j e c t i v e s economically with n u m b e r of ways. If a l l to payments associated a scheme a r e d i s c o u n t e d is termed a t h e i r present value or value comparison, the analysis present 11 discounted cash flow analysis. On the other this hand if annual net incomes of d i f f e r e n t return method. schemes a r e compared, latter tax is most and i s termed used the r a t e of by private In The frequently profits o r g a n i s a t ions where returns feature priminently. such cases i t i s suggested that i s obtained. u t i I i t ies. Present value the assistance of q u a l i f i e d accountants are most common for public comparisons A form of economic analysis popular in the United to a l l is States is benefit/cost of a analysis. for An economic benefit a certain i s attached value products to scheme, instance economic attached the water supplies, although t h i s is difficult to e v a l u a t e in case of values domestic supplies. a r e attached Those schemes w i t h priority. Where the highest schemes are benefit/cost mutually highest exclusive the such as i s u s u a l l y the case w i t h p u b l i c u n t i l i t i e s the scheme w i t h largest present value a of net benefit is adopted. It the the total water supply requirements of town f o r instance were f i x e d , least-cost scheme would be selected f o r construction. Uncertainty i n Forecasts Forecasts of demands, whether they be f o r water, risk. o i l o r gas, a are i n v a r i a b l y clouded w i t h uncertainty and Strictly i.e. probability benefit of a n a l y s i s i s r e q u i r e d f o r each possible scheme, a n y p a r t i c u l a r scheme w i l l by their probability for a be the sum of number of the net the net benefits mul t i pl i ed demands. Berthouex possible (1971) recommends under-designing for uncertain forecasts, but his b y 5 to analysis 10% f o r p i p e l i n e s to a l l o w does not account for cost inflation. An a l t e r n a t i v e method of a l l o w i n g f o r discount or interest scheme, rate: increasing uncertainty rate will i s to a d j u s t favour future a the low the c a p i t a l cost which would be p r e f e r a b l e i f the demand were uncertain. Example A consumer r e q u i r e s 300 P/s of increase economic his consumption to 600 water P/s for a 5 years further then plans to for 25 years (the l i f e of h i s f a c t o r y ) . 12 He draws for 75% of the time every day. Determine the most economic diameter and the number of p i p e l i n e s r e q u i r e d . i s s u p p l i e d b y a p u b l i c body p a y i n g no t a x . Power for The water a flat and costs 0.5 p/kWhr, which includes an allowance operating maintenance. The interest r a t e on loans ( t a k e n over 20 y e a r s ) a n d a n d the is rate of p.a. kW, inflation in Pump and on a s i n k i n g f u n d i s 10% p e r annum, cost of pipelines, pumps and power 6% pumpstations costs amount to 5300 p e r incremental (including a n allowance f o r standby p l a n t ) a n d pump e f f i c i e n c y i s 70%. The effective discount r a t e may be taken the r a t e of i n f l a t i o n , x i.e. as the interest rate less 4% p.a., since E l t h i s year i s worth f l 1.10/1.06 + 51 x 1.04 next year. be made t h r o u g h one or The s u p p l y could large pipeline each capable of h a n d l i n g 600 O/s, one P/s, two smaller after pipelines the delivering comparison a 300 of installed five years other. A a l t e r n a t i v e diameters pipeline. Similarly i s made i n the f o l l o w i n g was made f o r table for two single each an a n a l y s i s This pipelines d e l i v e r i n g 300 P / s . for i n d i c a t e d an optimum diameter of 600 mm total present value for both p i p e l i n e s of w i l l be the each p i p e l i n e a n d a 5 7 500 p e r 100 m. Thus one p i p e l i n e , 800 mm diameter, most economic solution. Note pipeline, that the analysis it was is independent that of the length such Water cost of that the a although assumed pressure was continuous low-pressure p i p e was a l l t h a t was r e q u i r e d . protection costs a r e assumed incorporated in hammer The the p i p e here. a n a l y s i s i s also independent o f the c a p i t a l loan period, a l t h o u g h the r e s u l t s would be s e n s i t i v e to change i n the interest o r i n f l a t i o n rates. Discount factors were obtained years periods. from present v a l u e tables was not for 4% over for but 5, 25 and 30 Uncertainty allowed would f a v o u r the two smaller p i p e l i n e s . Another i n t e r e s t i n g p o i n t emerged from installed from initially, due to the a n a l y s i s : a high then the I f a 600 mm of the did and p i p e l i n e was demand increase, uncertainty if the increasing it 300 to 600 P/s, to demand head would be more economic boost pumping 13 Sol u t i o n : 1. I n s i d e D i a .mm FIOW 2. 3. 4. e/s N O 0.14 600 _ _ _ _ ~ 600 700 600 300 800 300 600 900 300 0.02 600 H e a d loss m/100 m loss kw/100 m = (3.)xQ/70 0.55 0.06 0.24 0.03 0.12 0.07 Power 0.60 4.,72 0.26 2.06 0.13 1.03 0.09 0.60 5. Energy requirem e n t s kW h r / y r / 100 m = (4.1~8760 x 0.75 3900 31000 1700 13500 850 6600 590 3900 6. Annual cost pumping silo0 m 7. Equiv.Capita1 c o s t of p u m p i n g over 5 years = (6Jx4.452 Equiv .capital c o s t of p u m p i n g o v e r 25 y e a r s . = 20 155 e 67 4 33 3 20 90 -- 40 - 20 - 10 - e. ( 6 . )x15.622 - 24-30 - 1060 - 520 - 310 9. P r e s e n t v a l u e of p u m p i n g cost = (8.)/1.170 2 070 900 440 260 10. Cost of p u m p s etc. f/100 11. m : = ( 4 . ) x300 180 1410 80 620 40 310 30 180 Present v a l u e of pump cost = (10.,)/1.170 for second s t a g e P i p e l i n e cost f/100 m TOTAL COST 180 1200 80 530 40 260 30 150 12. 3600 4200 4800 5400 13. f / 1 0 0 m f o r 300 G 600 e / s 7. '9. + 1 1 . t i 2 7140 5750 5560 :: (least cost) 5850 14 Rate - _ - - m’ls Reservoir empty cumulative demand =/Qdt Reservoir f u l l = c a p a c i t y required 24h I Fig. 1.4 Graphical c a l c u l a t i o n of r e s e r v o i r capacity pump the total rather by a flow than through provide of a the one existing 600 mm diameter This is pipeline indicated one second present with 600 mm of pipeline. comparison the value pumping through value of pumping 600 mm line (57 140/100 m ) the present through two 600 m m lines ( 5 7 500/100 m). BALANCING STORAGE An system aspect is which deserves storage. close a t t e n t i o n in p l a n n i n g the p i p e l i n e reservoir water Demands such as those f o r the season, the day of domestic the week twice and and the industrial time mean may of fluctuate with day. Peak-day demands a r e sometimes peak draw-off for a day. the It i n excess of annual be six demand whereas times the mean to from r e t i c u l a t i o n systems would be uneconomic rates, to provide pipeline capacity meet peak draw-off and b a l a n c i n g r e s e r v o i r s are the head of n o r m a l l y constructed at the consumer end ( a t system) to meet these peaks. The storage the r e t i c u l a t i o n c a p a c i t y r e q u i r e d v a r i e s i n v e r s e l y w i t h the p i p e l i n e c a p a c i t y . The b a l a n c i n g storage and pipeline capacity requirement for any known draw-off pattern diagram: may be determined w i t h a mass flow 15 Plot curve cumulative plot a draw-off with line over slope down a period to versus time, and a b o v e t h i s of the line this equal till the discharge capacity just touches the pipeline. period. Move Then it the mass draw-off lines represents the maximum o r d i n a t e between 1.4). two the b a l a n c i n g storage r e q u i r e d (see F i g . An storage economic capacity comparison for is necessary to determine the optimum a n y p a r t i c u l a r system (Abramov, 1969) b y adding t h e cost o f r e s e r v o i r s and p i p e l i n e s and c a p i t a l i z i n g running c o s t s f o r different cost is c o m b i n a t i o n s and c o m p a r i n g them, selected. It is found that the system w i t h least total t h e most economic storage capacity v a r i e s f r o m one d a y ' s s u p p l y b a s e d o n t h e mean a n n u a l r a t e f o r s h o r t pipelines Slightly than to more mm two day's supply for long pipelines small-bore (over 60 km). (less storage may b e economic for pipelines of 450 diameter). should be In a d d i t i o n provided; a up certain to amount emergency reserve storage 12 h o u r s d e p e n d i n g u p o n the a v a i l a b i l i t y of maintenance f a c i l i t i e s . REFERENCES A b r a m o v , N., 1969. M e t h o d s o f r e d u c i n g p o w e r c o n s u m p t i o n in p u m p i n g w a t e r . I n t . W a t e r S u p p l y Assn. C o n g r e s s , V i e n n a . Berthouex, P.M., 1971. Accommodating u n c e r t a i n forecasts. J. Am. W a t e r Works Assn., 66 ( 1 ) 14. I n s t n . o f C i v i l Engs., 1962. A n I n t r o d u c t i o n t o E n g i n e e r i n g Economics, London. and James, L.D., 1973. M a r g i n a l economics a p p l i e d t o Osborne, J.M. p i p e l i n e d e s i g n . P r o c . Am. SOC. C i v i l E n g s . , 99 ( T E 3 ) 637. W h i t e , J.E., 1969. Economics o f l a r g e d i a m e t e r l i q u i d p i p e l i n e s . P i p e l i n e News, N.J. L I S T OF SYMBOLS C D n - cost p e r u n i t o f t h r o u g h p u t diameter number of y e a r s throughput i n t e r e s t r a t e o n s i n k i n g fund i n t e r e s t r a t e on loan Q r R - CHAPTER 2 HYDRAULICS THE FUNDAMENTAL EQUATIONS OF FLUID FLOW The three most important equations in fluid mechanics are the continuity For tion the flow' with equation, the momentum equation a n d one-dimensional equating flow t h e energy equation. equato steady, is flow is incompressible, obtained at another there by the c o n t i n u i t y any simply rate meant the flow the rate at section By section is no flow no along stream in that tube. at 'steady point a of that variation implies flow velocity the any time. tube 'One-dimensional' and there is flow the is along stream lateral across boundaries stream tubes. The and I t also implies that equation the of stems in the flow from i s irrotational. basic law of motion sections For momentum that sum Newton's states the change forces momentum f l u x the fluid between the two equals steady, the on causing change. one-dimensional flow t h i s i s AFx where = pQAVx (2.1 p i s the f l u i d 1 F i s the force, i s velocity energy of mass density, Q i s the volumetric 'x' direction. done the flow r a t e , V The basic a n d s u b s c r i p t x r e f e r s to the is equation by d e r i v e d b y e q u a t i n g the work and pressure transfer forces to on an element in fluid gravitational change from tion for energy. Mechanical a n d heat energy a r e excluded the equation. and this. In most systems there i s energy loss due to f r i c - turbulence and a t e r m i s included i n the equation to account The resulting equation for steady flow of incompressible f l u i d s i s termed the B e r n o u l l i equation and i s conveniently w r i t t e n a s : where V V2/2g 9 = = = = mean velocity velocity at a section length) head ( u n i t s of g r a v i t a t iona I acce I e r a t ion pressure P 17 p/y Y = pressure head ( u n i t s of length) = u n i t weight of f l u i d Z = e l e v a t i o n above an a r b i t r a r y datum = he The sum of head loss due to friction or turbulence between sections 1 G 2 the velocity head plus pressure head p l u s e l e v a t i o n is termed the total head. Strictly the v e l o c i t y head should be m u l t i p l i e d b y a coefficient to account f o r the v a r i a t i o n in v e l o c i t y across the section of the conduit. The average v a l u e of the coefficient f o r t u r b u l e n t flow laminar uniform variation conduit. For i.e. the Bernoulli should be equation no change to apply in the flow at should be steady, flow or in it is i s 1.06 and f o r termed there along either is 2.0. Flow through on a conduit or is non-uniform the depending whether not a the cross-sectional velocity distribution there velocity any p o i n t w i t h time. The f l u i d applied to The flow should i s assumed to be one-dimensional incompressible, although the and i r r o t a t i o n a l . may be be equation 1960). i n Fig. gases w i t h reservations (Albertson et a l . , The tical respective heads are illustrated 2.1. For most p r a c - cases the v e l o c i t y head i s small compared w i t h the other heads, and i t may be neglected. ENERGY LINE ENTRANCE LOSS FRICTION L O S S COtiTRACTION L O S S FRICTION LOSS I PRESSURE H E A D P/ x E L E \ A T ION Fig. 2.1 Energy heads along a p i p e l i n e 18 F L O W HEAD LOSS RELAT I ONSH I PS Empirical Flow Formulae The throughput o r c a p a c i t y of a p i p e of f i x e d dimensions depends T h i s head i s consumed on the t o t a l head difference between the ends. b y f r i c t i o n and other ( m i n o r ) losses. The first friction head loss/flow relationships were derived from in f i e l d observations. waterworks developed. These e m p i r i c a l although loss/flow ,+- relationships are rational stil I popular have are form practice The head more formulae thus been termed of the formulae established conventional type formulae a n d a r e u s u a l l y i n an exponential v = K R~ sY or s = K*Q"/D~ where V the i s the mean v e l o c i t y of flow, radius and (cross-sectional for a circular K and area K' a r e coefficients, R i s of flow divided full, by the one equals hydraulic wetted perimeter, pipe flowing q u a r t e r of per m the diameter) a n d S of pipe). Some of i s the head g r a d i e n t ( i n m head loss length the equations more f r e q u e n t l y a p p l i e d a r e l i s t e d below: Basic Equation Hazen -Wi I I iams Manning Chezy Darcy S=K1 ( V / C w ) 1.85 SI units f.p.s. units (2.3) (2.4) (2.5) (2.6) /D 1.167 = 6.84 1 K2= 6.32 K =3.03 1 S=K2(nV)2/D 1.33 K2=2.86 K =4.00 s=K~(v/c~)~/D S= X V /~2 g ~ K 3=13.13 DimensionI ess 3 Except f o r the Darcy formula the above equations a r e not u n i v e r s a l a n d the form of the equation depends on the u n i t s . I t should be borne i n m i n d t h a t the formulae were d e r i v e d f o r normal waterworks p r a c t i c e a n d take no account liquid. friction of p i p e . of variations in gravity, temperature o r type of The They a r e f o r t u r b u l e n t flow coefficients vary i n pipes over 50 mm diameter. type of w i t h p i p e diameter, f i n i s h a n d age 1 9 The conventional do not involve fluid formulae a r e comparatively viscosity. They simple to use as they may be solved d i r e c t l y as they do not r e q u i r e an i n i t i a l estimate of Reynolds number to determine the friction solved diameter rule, paper. pipe factor directly or (see next for flow. section). Solution The of rational the equations for cannot be formulae velocity, a slide log-log flows to in be friction head g r a d i e n t i s simple w i t h or graphs use for the a i d of p l o t t e d on analysing have calculator, The computer, are the nomograph of equations where particular networks flow/head loss equations i t e r a t i v e l y solved many times. The most popular formula. flow formula in waterworks for practice is the Hazen-Williams are tabulated solution with F r i c t i o n coefficients use in t h i s equation i n Table 2.1. the aid of I f the formula i s to be used f r e q u e n t l y , most efficient way. Many plotted As the a use chart is the of waterworks organizations graphs head loss gradient a g a i n s t flow f o r v a r i o u s p i p e diameters, v a l u e of a n d v a r i o u s C values. C decreases w i t h age, type of p i p e a n d p r o p e r t i e s of water, f i e l d tests a r e d e s i r a b l e f o r an accurate assessment of C. TABLE 2.1 Hazen-Williams f r i c t i o n coefficients c Badly corroded 130 100 Type of Pipe New Cond i t ion 25 years 50 years old old 140 130 130 110 100 140 120 100 PVC: Smooth concrete, AC: Steel, bitumen I ined, ga I vanized : Cast i r o n : Riveted steel, v i t r i f i e d woodstave: 150 150 150 130 120 60 50 90 80 ( 1 - Dmm 45 ) C For diameters less than 1 000 mm, subtract 0.1 1 000 Rational F l o w Formulae Although use for the conventional more flow formulae are likely to remain in many years, rational formulae are gradually gaining acceptance fic amongst engineers. The new formulae have a sound scientiare uni v ers al l y b a s i s backed b y numerous measurements a n d they 20 applicable. Any consistent units of measurements may be used and I i q u i d s of v a r i o u s viscosities a n d temperatures conform to the proposed formulae. The for inal of flow rational past flow formulae for flow plates i n pipes a r e s i m i l a r to those bodies o r over was on flat ( S c h l i c h t i n g 1960). The o r i g roughness. Lack research smal I-bore pipes w i t h a r t i f i c i a l d a t a on roughness f o r l a r g e pipes has been one deterrent to use of the r e l a t i o n s h i p s i n waterworks practice. The v e l o c i t y maximum in in a full p i p e v a r i e s from zero on the boundary to a the centre. layer Shear forces on the w a l l s oppose the flow and w i t h each a n n u l u s of f l u i d i m p a r t i n g concentric annulus. The a boundary a shear i s established an inner motion flow force to onto neighbouring of it resistance viscosity, relative in the is fluid imparted is by termed kinematic mixing and turbulent turbulent w i t h t r a n s f e r of p a r t i c l e s of d i f f e r e n t momentum between one l a y e r and the next. A this point boundary layer i s established expands until The at it the entrance to a conduit and Beyond t h i s layer gradually the f l o w reaches the centre. becomes uniform. length of pipe required for f u l l y established flow i s g i v e n by S c h l i c h t i n g , (1966). D X = 0.7 Re'"for Reynolds t u r b u l e n t flow. number (2.7) VD/V v The Re = is a dimensionless number i n c o r p o r a t i n g the f l u i d viscosity flow formulae. which i s absent i n t h e conventional than Flow i n a p i p e i s l a m i n a r f o r for higher Re is low R e !less 2 000) and becomes t u r b u i e n t The shear basic force head over loss ( n o r m a l l y the case by to setting the loss i n practice!. the in boundary pressure equation length of derived equal a pipe m u l t i p l i e d by the a r e a : TnDL = v h f nD2/4 = L X E vz 29 21 Fig. 2.2 Moody r e s i s t a n c e d i a g r a m for u n i f o r m f l o w i n conduits 22 where X is the = ( 4 7 / y ) ( V Z / 2 s ) ( r e f e r r e d to stress, a as the Darcy and friction factor), hf is the !he friction relative i.e. X shear D is the pipe diameter head loss over length L . X i s a f u n c t i o n of Re and roughness e/D. F o r l a m l n a r flow, Poiseuille found that L a m i n a r flow zone but X = 64/Re i s independent of the r e l a t i v e roughness. i n normal and engineering flow is practice. complex The and will not occur laminar of little transition undefined between turbulent is also ivterest i n practice. flow conditions The may occur for with Turbulenr rough either a smooth for or a boundary. are in equations from the the friction equation which factor for is the both conditions distribution derived a general velocity turbulent boundary layer, derived from m i x i n g l e n g t h theory: Integrating, w i t h k = 0.4 a n d c o n v e r t i n g logs to base 10, where v is the velocity at a distance y is from a the boundary. sub-layer, For a and hydrodynamical l y smooth b o u n d a r y there y‘= v / m s o that laminar Nikuradse found that /+= The constant 5.5 Where Thus V /%= 5.75 log Y m V + 5.5 (2.10) was found e x p e r i m e n t a l l y . i s r o u g h the l a m i n a r sub-layer = e/30 the boundary y’ i s affected and Nikuradse found that where e i s the boundary roughness. 5.75 log + 8.5 a n d 2.11 and expressing v (2.11) i n terms of Re-arranging equations 2.10 the average v e l o c i t y V b y means of the equation Q = 1 vdA w e get J-T = 210g Re fl - 0.8 layer, smooth b o u n d a r y ) a n d (2.12) ( t u r b u l e n t boundary Jf ~ 2 log - D + 1.14 rough boundary) (2.13) (turbulent boundary layer, 23 Notice tive that for a smooth boundary, a very A is independent of it is the r e l a - r o u g h n e s s e/D and for rough boundary independent o f t h e R e y n o l d s n u m b e r Re f o r a l l p r a c t i c a l p u r p o s e s . Colebrook and White combined E q u a t i o n s 2.12 a n d 2.13 to p r o d u c e a n e q u a t i o n c o v e r i n g b o t h smooth a n d r o u g h b o u n d a r i e s a s w e l l a s t h e t r a n s i t i o n zone; 1 = 1.14 - 2 l o g (D +Rx e 9.35) reduces rough for to E q u a t i o n 2.12 pipes. various This for smooth pipes, (2.14) and to Their Equation equation 2.13 for semi-empirical equation pipes. yields Nikurough- satisfactory results commercially available radse's original ness. h!atural experiments used s a n d as a r t i f i c i a l boundary r o u g h n e s s i s e v a l u a t e d a c c o r d i n g to t h e e q u i v a l e n t s a n d g i v e s v a l u e s of e f o r v a r i o u s s u r f a c e s . ( H y d r a u l i c s Research station, unles? otherwise stated Average roughness. TABLE T a b l e 2.2 2.2 Roughness of p i p e m a t e r i a l s c l e a n surface Smooth 1969) V a l u e o f e ~n mm f o r n e w , Finish: Glas?, d r a w n metals S t e r l , DVC or AC 0 0.015 Coat?(( strel 0.03 GaIvnr>cze-d, v i t r i f i e d c l a y 0.06 Cast i r c r o r cement l i n e d 0.15 Spun concrete or wood s t a v e 0 . 3 R i v e t e d steel 1.5 F o u l sewers, t u b e r c u l a t e d 6 water mains Ur,Iinrd rock, e a r t h 60 _-__. 0.003 0.03 0.06 0.15 0.3 0.6 _____ 0.006 Rough 0.06 0.15 0.3 0.6 I .5 3 15 6 30 300 150 __- Fortunately A increases constant linearly i s not v e r y with age sensitive for to t h e v a l u e o f e assumed. pipes, There may the e water proportionality be reduction d e p e n d i n g on local conditions. also i n c r o s s s e c t i o n w i t h age. The v a r i o u s r a t i o n a l f o m u l a e f o r ::J A were as p l o t t e d on a Fig. 2.2. are single The graph Moody and of this water graph at is presented kinematic in viscosities Apprndix. various temperatures listed the The Moody d i a g r a m pipe velocity or i s useful for calculating manually rate is known. the Unfortunately i.e. is for head is loss if flow it not very given guess amenable head loss, to d i r e c t and a solution for trial and convrse, approach veloc:ity, i.e. A error necessary read off velocity to calculate Reynolds number, then , then r e c a l c u l s t e v e l o city etc. Convergence i s f a i r l y r a p i d however. 24 The Colebrook W h i t e e q u a t i o n i s e a s i e r to use i f h e a d loss i s g i v e n and velocity loss or i s to b e c a l c u l a t e d . velocity It i s not however. so e a s y to solve f o r head X at given or flow The the Hydraulics variables Research Station Wallingford equation to re-arranged produce in the 1055 Cclebrook-White graphs simple explicit flow/head ( H y d r s u l i c Research S t a t i o n , 1969): i n t h e form- E q u a t i o n 2.14 may b e a r r a n g e d (2.15) Thus e, a for any f l u i d at a certain temperature a n d defined roughness and S. g r a p h may water b e p l o t t e d in terms of V,D at 15OC a n d e = 0.06. graphs for Fig. 2.3 i s such a graph for The H y d r a u l i c Research S t a t i o n conditions. The graphs are has plotted similar various sections, also a v a i l a b l e for a step further, non-circular the b y r e p l a c i n g D b y 4R. Station re-wrote Going the Hydraulics in but terms o f Research Colebrook-Whi te e q u a t i o n tional and to dimensionless for parameters viscosity, they propor- V, R a n d S, Using including factors form roughness a gravity. this of the equation produced This universal was also resistance diagram published with in dimensionless parameters. graph is their charts. Fig. 2.3 as an example d e r i v e d on a s i m i l a r b a s i s (VVatson, 1979). Comparison of F r i c t i o n F o r m u l a e Diskin (1960) p r e s e n t e d a useful comparison of the f r i c t i o n f a c t o r s f r o m t h e Hazen-Will iams a n d D a r c y e q u a t i o n s : The D a r c y e q u a t i o n may b e w r i t t e n a s or v v cz The =JTprn = (2.16) (2.17) c Z &R w h i c h i s termed t h e Chezy e q u a t i o n a n d t h e Chezy c o e f f i c i e n t i s = & p equation may be rewritten for (2.18) Hazen-Wi I I iams a I l practical purposes in the f o l l o w i n g dimensionless form: S = 5 1 5 ( V / C W ) * (Cw/Re) this with 0.15 /gD (2.19) equation (2.16) i t may By c o m p a r i n g be deduced t h a t t h e Darcy-Weisbach 26 The and 2.2). Hazen-Williams and will values be coefficient be Cw is a 2.2 therefore Moody that a functionof (see X Re It may p l o t t e d on from Fig. with diagram lines for Fig. observed constant Hazen-Wi I I iams coefficient coincide in the t r a n s i t i o n zone. the Colebrook-Whi te I ines o n l y I n the completely t u r b u l e n t zone f o r non-smooth wi II pipes number with the coefficient one actual l y reduce the greater the Reynolds i .e. cannot associate a c e r t a i n Hazen-Wil I iams coefficient i t v a r i e s depending on the flow rate. The a p a r t i c u l a r p i p e as Hazen-Will iams equation should therefore be used w i t h c a u t i o n f o r h i g h Reynolds numbers and r o u g h pipes. of C w above approximately practice ( R The around 10 ) . equation is widely used for open channel flow and It will also be noted that values 155 a r e impossible t a t t a i n in water-works o 6 Manning p a r t f u l l pipes. The equation i s (2.21 where K is 1.00 in SI u n i t s and 1.486 in ft I b units, and R i s the h y d r a u l i c r a d i u s A/P where A i s the cross-sectional for area of flow and P the wetted perimeter. for non-circular R is D/4 a c i r c u l a r p i p e , a n d i n general sections, 4 R may be substituted f o r D. TABLE 2.3 Values of M a n n i n g ' s ' n ' 0.010 Smooth glass, p l a s t i c Concrete, steel ( b i tumen I i n e d ) galvanized Cast i r o n Slimy or greasy sewers Rivetted steel, v i t r i f i e d wood-stave Rough concrete 0.01 1 0.01 2 0.013 0.015 0.017 MINOR LOSSES method of expressing head loss through f i t t i n g s and changes often Modern used when the con- One i n section ventional press i s the e q u i v a l e n t friction loss l e n g t h method, are used. formulae p r a c t i c e i s to exhe = loss losses through f i t t i n g s where in terms of the v e l o c i t y head i.e. Table 2.4 gives typical KV2/2g K is the loss coefficient. 27 coefficients plementary opening. although data and valve manufacturers coefficients may also provide vary with supgate loss to K which will The v e l o c i t y V use i s n o r m a l l y the mean t h r o u g h the f u l l bore of the p i p e o r f i t t i n g . TABLE 2.4 Loss coefficients f o r p i p e f i t t i n g s Bends hBKBV2/ 2 g Bend a n g l e Sharp r/D=l 2 0.07 0.10 0.12 0.13 6 0.06 0.08 0.08 0.08 30" 45" 60 O 90 1 80° 90" w i t h g u i d e vanes r = 0.16 0.32 0.68 1.27 2.2 0.07 0.13 0.18 0.22 0.2 r a d i u s of bend to centre of p i p e reduction in bend loss A significant i s possible if the r a d i u s i s f l a t t e n e d i n the p l a n e o f the bend. Valves Type: SLuice Butterf I y Globe Needle Ref I u x hv = KvV2/2g Opening: 1/ 4 24 120 4 1 /2 3/4 Ful I 0.2 5.6 7.5 1 1 .o 1.2 0.3 10 0.6 0.5 1-2.5 Contractions a n d expansions in cross-section Contract ions : hc= KcVJ29 Expansions h = K V 2/2g c c l Wal I-Wal I Angle ___ 0 - A 2 4 0.2 __ __ - 0.4 0.6 0.8 1.0 - Al /A2 0 .13 .32 .78 1 .O 0 2 0 4 06 08 10 . . . . . .08 .24 .45 .64 7.5" 150 30 O 180" .5 .37 .25 .15 .07 0 .05 .15 .27 .36 .02 .08 .13 .17 0 0 .02 0 .03 0 -04 0 28 Entrance and e x i t losses: he = KeV2/2g Entrance Exit Protruding Sharp Bevel l e d Rounded 0.8 0.5 0.25 0.05 1 .o 1 .o 0.5 0.2 PRESSURE AND F L O W CONTROL IN PIPES I ntroduct ion Valves the is and other vapour fittings in pipes which reduce the When h e a d may the be cause of reduced rise et bubble formation The downstream. may pipe the pressure collapse water to al, vaporizes. bubbles to the of subsequently or valve as giving Knapp cavitation damage (Ball; well as and 1970, the flow 1961). The geometry valve valve the upstream and downstream pressure, degree of as well as closure r a t e affec? the c a v i t a t i o n p o t e n t i a l the fluid. to The as conditions critical. and under vapour p r e s s u r e of are flow which cavitation damage commences as referred velocity The as cavitation ratio of increases to increases the upstream downstream p r e s s u r e increases. A of number of empirical control of relationships for identifying the s a f e zone operation popular of v a l v e s h a v e been p r o p o s e d b y v a l v e s u p p l i e r s . potential cavitation problem is the pressure Many for The measure i.e. reduction ratio, r a t i o of u p s t r e a m to d o w n s t r e a m p r e s s u r e s . are said to commercially available ratios valves less operate efficiently pressure reducing to of work the than 3 or 4. It i s h o w e v e r more l o g i c a l Since t h e geometry the or application of is w i t h a c a v i t a t i o n index a s indicated valve types influences of valves the for critical Jater. conditions, reducing various pressure flow control described. TYPES OF VALVES Valves are used for two aistinct purposes in pipelines, namely i s o l a t i n g o r flow control. 29 I s o l a t i n g Valves Isolating They only. i.e. and gate should They valves be are used in to the close fully off the or flow fully through closed a pipe. operated open position h a v e poor flow c h a r a c t e r i s t i c s i n the p a r t l y open position. the flow i s l a r g e l y the exposed area of a gate flow control is until the and the o b s t r u c t i o n to there is is often l i t t l e pressure reduction o r shut. and At that stage practically to cavitation possible damage not the seat to v a l v e body may r e s u l t . T h i s type of v a l v e i s i.e. it i s designed designed reduce the pressure a p p r e c i a b l y . to pass the f u l l flow when f u l l y open w i t h minimal head loss. Such spherical designed valves valves. to close include These as gate valves, are butterfly generally valves operated and by r o t a r y or hand valves and are valves rapidly with as possible. threads, Although butterfly gate operated b y spindles screw valves and rot ary v a l v e s can be operated b y t u r n i n g a h a n d l e t h r o u g h 90" to f u l l y close the valve from the fully open position. I n order to overcome high seating these pressures however a n d sometimes to control may have from reduction the gear boxes in the r a t e of closure order to drive the and valves spindle indirectly handwheel. Alternatively electrical pneumatic control systems can be used to operate these valves. Typical i!lustrated open sl(iice in valves, butterfly valves and The spherical valves are Figs. 10.1, 10.2 and 10.4, relationship is between generally that This the is bore area a n d degree of t u r n i n g of the handwheel the gate of non l i n e a r , area I t can be observed i n the case of valve reduces rapidly in to the final stages closure. as the u n f a v o u r a b l e w i t h respect i s reduced r a p i d l y rise to water hammer pressures closure tne of velocity gives of d u r i n g the f i n a l hammer in the stages of than and this higher in water pressures pipe. The uniform rate reduction velocity problems cavitation are g e n e r a l l y avoided w i t h such \ ~ a l \ / e s as they a r e not operated i n p a r t l y closed c o v d i t i o n s except i n emergencies. Control Valves Various water types of v a l v e s h a v e been designed to control linearly the flow of i n pipelines b y r e d u c i n g the open a r e a a n d to c o n t a i n the c a v i t a t i o n effect due to reduction of pressure through the v a l v e . A 30 typical valve). 2.4) valve in common use is illustrated in Fig. 10.3 ( a needle Diaphram type valves, type control slotted r a d i a l flow sleeve v a l v e s ( F i g . is and plunger v a l v e s a r e also employed a n d there valve which and a v a r i a t i o n of slots. control Multiple valves the r a d i a l flow expansion (Fig. type are has a piston covering the basket type high duty valves even 2.5) types more appropriate for pressure and reducing. any have The former r e l y on a s i n g l e increase i n velocity head d i s s i p a t i o n due to expansion whereas the l a t t e r types which variable resistance trim rings or layered baskets reduce the pressure damage i n a number of as a result. stages a n d a r e s a i d to s u f f e r less c a v i t a t i o n is largely because it This the pressure reducing r a t i o i s l i m i t e d at It each stage b u t o v e r a l l these v a l v e s a r e may be r e l a t i v e l y h i g h . less noisy when reducing i s a l s o recognised that h i g h pressures. The needle v a l v e was once used widely i n power s t a t i o n p r a c t i c e as at or COI it was recognised as a streamlined v a l v e which could control flow a l l stages of opening. the initial opening. I t often h a d a p i l o t needle f o r f i n a l seating The valve i s however expensive owing to its struction and i s now replaced to a materials such as l a r g e extent by simpler valves elastometers ( t h e sleeve type using valve) (e.g. sophisticated or by pistons o r diaphrams i n the case of latter type of valve low pressure valves to Dvir, 1981). as On The the the i s not sensitive ingress of cannot poor into quality the water f l e x i b l e d i a p h r a m prevents other hand the diaphram dirt workings. accommodate h i g h pressure d i f f e r e n t i a l s and s u f f e r s wear a f t e r prolonged operation. It may also be subject to vibration and instability as a venturi action i s caused d u r i n g the l a s t stages of closing. Piston is type v a l v e s can b e accurately the exposed face of the c o n t r o l l e d p r o v i d e d the flow piston. to In some types the towards downstream or face of the p i s t o n i s exposed the downstream pressure the atmosphere face of and i s supported by a spring. to I n others the down- stream on the p i s t o n can be subject of a p i l o t control that is off f l u i d pressure depending Such p i l o t systems can be pressure. tubes I n t h i s case blocking. or The a the operation system. operated strainers system hydraulically, the water a r e often r e q u i r e d to prevent also be operated off the p i l o t can electrical solenoids from 31 Fig. 2.4 F l e x f l o Sleeve v a l v e f o r f l o w control ~ i 2.5 ~ , . i g h d u t y control i reduction v a l v e n i t n t r i p l e aasi(ets foi' heao p n e u m a t i c s u p p o r t system. The sure to control system c a n be designed to limit t h e downstream pres- a c e r t a i n maximum f i g u r e . d o w n s t r e a m senses means o f As t h e u p s t r e a m p r e s s u r e b u i l d s UP an i n c r e a s i n g p r e s s u r e i t w i l l open a n d t h e sensor a pilot valve held b y a spring and this pilot valve will in t u r n p e r m i t a b i g g e r p r e s s u r e f r o m u p s t r e a m t o come b e h i n d t h e p i s t o n and partly flow or the close rate venturi the in is ports. which Alternatively case the The the valve may b e u s e d to side of an turn control orifice controls get p r e s s u r e on pressure either measured. difference in p i l o t v a l v e w h i c h w i l l e i t h e r p e r m i t a g r e a t e r p r e s s u r e to the piston to close the valve or exhaust the pressure behind b e h i n d t h e p i s t o n to open t h e v a l v e d e p e n d i n g on w h i c h i s r e q u i r e d . CAVITATION IN CONTROL VALVES The mechanism valve velocity as whereby is by flow is reduced o r the p r e s s u r e i s reduced upstream is in a control high converting and then into pressure energy velocity open energy into a in jet it the the dissipated The turbulence from emerges pipe again. conversion statical pressure energy to v e l o c i t y e n e r g y i s obtained from the Bernoul I i e q u a t i o n ; (2.22) Here that P is the is upstream the pressure, head, W is is Thus the the if unit weight of water a so P/W pressure Z elevation above fixed datum a n d V velocity be V = i s the w a t e r velocity. 2 i s a c o n s t a n t then t h e p o s s i b l e assuming t h e p r e s s u r e h e a d i s r e d u c e d to z e r o w o u l d This however n e g l e c t s u p s t r e a m v e l o c i t y the latter can for be accounted f o r b y velocity in w h e r e H = P/W. a n d downstream p r e s s u r e a l t h o u g h replacing coefficient velocity v = c where the the h is by often ah. To account in the upstream and head a introduced equation fact the p i p e i s often given in t h e f o l l o w i n g f o r m d JzsnF; Cd is (2.23) discharge Apart the coefficient the f a c t which that may vary depending on the v a l v e opening. valve affects from t h e d e g r e e of o p e n i n g o f even if the discharge discharge coefficient, 33 coefficient to v a r y open. The only be actual found i.e. stage of from the i.e. throttling at which c a v i t a t i o n has been commences can classified as was separated from the degree of opening i t would be found to the d i f f e r e n t contraction r a t i o as a d i f f e r e n t area i s owing experiment. which Cavitation vapour incipient p o i n t at bubbles commenced to form, the a n d choking valve stream. and a is the stage a t affected which by the d i s c h a r g e coefficient o f of the water appreciably vaporization down- The v a p o r i z a t i o n occurs because the pressure head i s reduced i s transformed i n t o k i n e t i c energy which impinges i n t o downstream. been in the energy pressure have low A number (Winn of of parameters and Johnson, is for assessing The cavitation significant index. proposed 1970). the factor the indication cavitation cavitation (2.24) where P is the pressure a n d s u b s c r i p t d r e f e r s to downstream, u to upstream a n d v to vapour pressure. For tation streamlined index valves low at cavitation as 0.1 a may not occur until the cavi- drops as occurs whereas f o r index p o o r l y designed v a l v e s nearer cavitation case i t w i l l often higher i.e. 1.0. In any be found on inspection that most control v a l v e s experience at normal o p e r a t i n g pressure r a t i o s . index reduced ratio that by if a the c r i t i c a l factor with a degree of c a v i t a t i o n Pv it Neglecting index nearly i s seen from the c a v i t a t i o n the the pressure pressure can be is 10 0.1 then of whereas reduction possible unstreaml ined index of 0.33 pressure, v a l v e s i s much lower. the pressure reducing For an average c r i t i c a l c a v i t a t i o n ratio i s from 2.24 neglecting vapour 4.0. Various forms of 1970). Very little the c a v i t a t i o n is however index have been proposed ( T u l l i s , the scaling down of the known about c a v i t a t i o n index and much work T h e method of Various velocity quantitatively has to be done i n t h i s f i e l d yet. assessing c a v i t a t i o n i s a l s o d i f f i c u l t . estimation of the increase of volume caused by bubble due to methods have been attempted i.e. owing to the increase in bulk format ion, photographic methods, pressure measurements collapse of the bubbles and sonic- methods. Fig. 2.6 shows the v a r i a t i o n i n noise measured on a r a d i a l flow sleeve v a l v e at d i f f e r e n t c a v i t a t i o n indices f o r a f i x e d degree of opening. I n t e r a c t i o n between C a v i t a t i o n and Water Hammer Pressures It is recognised that the collapse of vapour bubbles when the pressure subsequently the accompanying increases may cause erosion of steel. the symptoms of a poorly T h i s and selected noise a r e often valve. There hammer is wave the however celerity an and interesting the relationship between As a the water is cavitation increases potential. valve closed so b u b b l e formation a n d t h i s reduces the water hammer wave c e l e r i t y downstream (Ch. 4 a n d 5 ) . If which then the it the in free turn gas is a fraction can be related to the cavitation index f u n c t i o n of the upstream or downstream pressure i s possible to solve sirnuttaneously the water hammer equation, cavitation release to valve discharge the equation and the gas index equation index, together with equation relating cavitation f o r free gas volume downstream, mer of wave c e l e r i t y . the cavity the It downstream pressure a n d water hamhowever b y the fact that p a r t turns into l i q u i d gas the may drop If be in i s made d i f f i c u l t i s not gas b u t vapour again bubbles may increases. as they which r a p i d l y Small when pressure in The are the q u a n t i t i e s of due to contained pressure. equations pressure are released bubbles solved therefore not then drop collapse it will completely. be found the the the is (iteratively) would initially that valve downstream to rapidly as closed due begin to the the water hammer deceleration effect. wave c e l e r i t y reduces r a p i d l y the flow and so Then as bubbles form and the consequent pressure This lowering i s reduced so that wave reflections cavitation reduces more s t e a d i l y . on study neglects but it does hold promise f o r the p o t e n t i a l of to effect better control of flow as a v a l v e closes especially this theory indicates that d u r i n g the i n i t i a l stages of closure where flow reduction is more rapid than was previous1 y considered the case. 35 REFERENCES 1960. F l u i d M e c h a n i c s A l b e r t s o n , M.L., B a r t o n , J.R. a n d Simons, D.B., f o r E n g i n e e r s . P r e n t i c e H a l l , N.J. B a l l , J.W., 1970. C a v i t a t i o n d e s i g n c r i t e r i a . I n T u l l i s (1970). Proc. I n s t . Colorado State Univ. D i s k i n , M.H., Nov. 1960. The l i m i t s o f a p p l i c a b i l i t y o f t h e HazenW i l l i a m s f o r m u l a e . L a H o u i l l e B l a n c h e , 6. D v i r , Y., 1981. P r e s s u r e r e g u l a t o r s in w a t e r s u p p l y systems. Water a n d I r r i g a t i o n Review, Water Works A s s o c i a t i o n o f I s r a e l . H y d r a u l i c s Research S t a t i o n , 1969. C h a r t s f o r t h e H y d r a u l i c Designs o f C h a n n e l s a n d PiDes. 3 r d E d n . . H.M.S.O., London. K n a p p , R., D a i l y , 'J.W. a n d Hammitt, F.G.',1961. C a v i t a t i o n . McGrawHill. S c h l i c h t i n g , H., 1960. B o u n d a r y L a y e r T h e o r y . 4 t h E d n . , McGraw-Hill N.Y. T u l l i s , J.P., 1970. Control o f f l o w i n c l o s e d c o n d u i t s . Proc. I n s t . Colorado State U n i v e r s i t y . Watson, M.D., J u l y 1979. A s i m p l i f i e d a p p r o a c h t o t h e s o l u t i o n o f p i p e f l o w p r o b l e m s u s i n g t h e Colebrook-White method. C i v i l Eng. in S.A., 2 1 ( 7 ) , p p 169-171. Winn, W.P. a n d Johnson, D.E. December 1970. C a v i t a t i o n p a r a m e t e r s f o r o u t l e t v a l v e s . Proc. ASCE, HY12. LIST O F SYMBOLS A C - cross-sectional a r e a of flow Hazen-Will iams f r i c t i o n f a c t o r friction factor Chezy f r i c t i o n f a c t o r d e p t h o f water diameter N i k u r a d s e roughness Darcy f r i c t i o n factor ( e q u i v a l e n t to A ) C' Cz d - D e f Fx g he - force gravitational h e a d loss f r i c t i o n h e a d loss loss c o e f f i c i e n t acceleration hf K L n - length of c o n d u i t Manning friction factor wetted p e r i m e t e r pressure P p 36 Q R - flow rate hydraulic radius Reynolds number h y d r a u l i c gradient mean velocity across a section Re S v V X velocity a t a point distance along conduit distance from boundary elevation specific weight Y 2 Y P T V mass density shear stress k i n e m a t i c viscosity Darcy f r i c t i o n f a c t o r - ( f i n USA) x F i g . 2.6 Noise output from a control valve 37 CHAPTER 3 PIPELINE SYSTEM ANALYSIS AND DESIGN NETWORK ANALYSIS The flows by through the the flow a system of interlinked pipes or networks a r e the input controlled points difference between residual pattern pressure will the pressure heads a t heads at the in a drawoff network and points. A steady-state be established such that the f o l l o w i n g two c r i t e r i a a r e satisfied:- (1) The net flow towards any j u n c t i o n or node i s zero, i.e., inflow must equal outflow, and around any closed loop is zero, i.e., only (2) The net head loss one head can e x i s t at any point a t any time. The and loss h l i n e head losses a r e u s u a l l y methods the o n l y based on significant this head Losses Head form € the I most of for h analysis pipes is the are assumption. to be of the relationships where are usually assumed = K?Qn/Dm head loss, P i s the p i p e length, flow and D the i n t e r n a l diameter of the pipe. The calculations are simplified if the friction factor K can be assumed t h e same f o r a l l p i p e s i n the network. E q u i v a l e n t Pipes f o r Pipes i n Series o r P a r a l l e l It the in of i s often head or useful loss to and know flow the e q u i v a l e n t p i p e which a number pipe of may would g i v e same series as interconnected pipes be used in place parallel. The equivalent the compound pipes to perform f u r t h e r flow c a l c u l a t i o n s . The of equivalent diameter and of a compound in p i p e composed of may be sections by different the diameters total lengths for series flow to calculated loss equating head loss any the head through the e q u i v a l e n t p i p e of length equal to the l e n g t h of compound pipe:- K ( Z P ) Q ~ / D ~ K~P Q " / D ~ = z .. De = (3.1) 38 ( m i s 5 i n the Darcy f o r m u l a a n d 4.85 in the Hazen-Williams f o r m u l a ) . Similarly, the e q u i v a l e n t diameter of a system of pipes i n p a r a l l e l total flow through the equivalent pipe ' e ' i s derived by equating the to the sum of the flows through the i n d i v i d u a l pipes ' i ' i n p a r a l l e l : Now h = h. i.e. KP Q " / D ~ = K P ~ Q ~ ~ / D ~ ~ ~ e So Q. = and Q = So cance l i n g out Q , a n d b r i n g i n g D and P e to the l e f t h a n d side, and i f each P i s the same, (3.2) De = [ C ( D i m / n ) ] n / m The equivalent diameter could also be d e r i v e d u s i n g a flow/head loss c h a r t . For pipes flow in parallel, each assume a reasonable head loss and pipe from the read off the through chart. Read o f f the e q u i v a l e n t diameter which would g i v e the total flow a t the same head loss. For p i p e s i n series, head assume a reasonable flow a n d c a l c u l a t e the the c h a r t . Read off the equivalent with the total total pipe loss w i t h assistance of diameter which would discharge the assumed flow head loss across i t s length. I t often speeds network analyses to s i m p l i f y p i p e networks as much as possible Of using equivalent course be the diameters for minor pipes in series or parallel. could this methods of to network a n a l y s i s described below compound pipes and than always is in used the a n a l y s e flows through fact p r e f e r r e d method f o r more complex systems those discussed above. Loop F l o w Correction Method The both loop method and the node method of approximations a n a l y s i n g p i p e networks by a mathematical involve successive speeded technique developed b y Hardy C r o s s (1936). 39 The steps are: Draw all ent). If there is more than one constant head node, connect pairs the pipe network schematically fixed heads to a clear booster scale. pumps Indicate (if presi n ba ancing the flows i n a network b y the loop method inputs, drawoffs, and of constant head nodes or r e s e r v o i r s b y dummy pipes represented by the dashed flow lines. Assume to pipe a diameter head and length In n and calculate flow head corresponding omit this fixed but loss. it subsequent calculating corrections, include I osses. Imagine the network as a of form of pattern of the closed some loops of i n any major order. pipes of To may speed be convergence assumed a are series to solution the loops large side superimposed by side. each instead as at assuming loops as loops to Use pipe only is in many least needed ensure that one loop. Starting with the any pipe assume a flow. Proceed i n each at around a loop sub- containing tracting flows one a t as to a pipe, calculating flows to the flow other pipe by nodes. drawoffs other time, and if loops to Assume loops on unknown. Proceed n e i g h b o u r i n g loops a s i m i l a r basis. as there I t w i l l be necessary to make loops. The more accurate many assumptions are each assumption the speedier w i l l be the solution. Calculate formula the head as loss in each or pipe use a in any loop using loss a such h = Kk'Qn/Dm flow/head chart ( p r e f e r a b l e i f the a n a l y s i s Calculate around arriving the ing loop the the net head i s to be done b y h a n d ) . around t h e loop, i.e., proceeding loss the at loop, the add head starting losses and s u b t r a c t head g a i n s u n t i l point. If the net head the loss around i s not zero, following correct the flows in arol;nd the loop b y adddirection that increment flow in same head losses were c a l c u l a t e d : (3.3) T h i s equation i s the f i r s t o r d e r approximation to the differen- t i a l of the head loss equation and i s d e r i v e d as follows:- 40 Since h = KEQn/Dm dh = KtnQn-'dQ/Dm = (hn/Q)dQ Now t h e t o t a l head loss around each loop should be zero, i.e., c ( h + dh) = 0 C h + x (hn/Q)dQ = 0 The v a l u e of h/Q i s a l w a y s p o s i t i v e ( o r zero i f h a n d Q a r e z e r o ) . (7) I f there is a booster pump i n any loop, subtract the generated head from equations. C before m a k i n g the flow h correction u s i n g the above (8) (9) The flow around each Steps 5-8 loop i n t u r n i s corrected thus (steps 5-71. loop balances a r e repeated u n t i l the head arourld each to a s a t i s f a c t o r y amount. The Node Head Correction Method With loops, the initial node method, are instead of at assuming each node. initial flows around heads assumed Heads a t nodes a r e corrected b y flows were successive approximation for the loop i n a s i m i l a r manner to the way corrected method. The steps in an a n a l y s i s a r e as follows:- (1) Draw all the pipe network schematically to a clear scale. Indicate inputs, drawoffs, f i x e d heads a n d booster pumps. heads at The be each node more the (except i f the head the the initial solu- (2) Assume at that initial node arbitrary is fixed). will accurate assignments, tion. the speedier convergence of (3) Calculate head the flow in each pipe to any node or with a a variable flow/head using the formula Q = (hDm/Kt)'/" using loss c h a r t . (4) Calculate zero, the net inflow to the specific node a n d if this i s not correct the head b y a d d i n g the am'ount *" = C(Q/nh) -Q (3.4) 41 T h i s equation i s d e r i v e d as follows:- dQ = Qdh/nh W require e c ( Q + dQ) = 0 But dH = -dh so F l o w Q a n d head loss h a r e node. considered positive if towards the H i s the head a t the node. i n p u t s ( p o s i t i v e ) a n d drawoffs ( n e g a t i v e ) a t the node should be i n c l u d e d i n E Q . (5) Correct i.e. the head a t each variable-head node in s i m i l a r manner, repeat steps 3 a n d 4 f o r each node. the procedure degree of a pipe (steps 3 accuracy. at to 5 ) until a l l flows balance to a (6) Repeat sufficient ends of I f the head difference between the any stage, omit the pipe from the i s zero p a r t i c u l a r b a l a n c i n g operation. A l t e r n a t i v e Methods of A n a l y s i s Both the loop method and the node method of a computer b a l a n c i n g flows in networks can networks. tables space. or If be done m a n u a l l y b u t done manually, i s preferred for be if set out large in calculations should well even on the pipework layout drawing there i s sufficient Fig. 3.1 i s an example analysed m a n u a l l y b y the node method. There a r e s t a n d a r d computer programs a v a i l a b l e f o r network a n a l y s i s , most of which use the loop method. The main advantage of the node method i s that more i t e r a t i o n s a r e required especially than if for the the loop method is very to achieve the same convergence, to start with. It is system unbalanced n o r m a l l y necessary f o r a l l pipes to h a v e the same o r d e r of head loss. There are a number of methods in some for speeding or the convergence. using a second These order include overcorrection cases, approximation to the d i f f e r e n t i a l s f o r ca I cu I at i n g correct ions. The node head correction method i s slow to converge on account of 42 the fact time. that corrections d i s s i p a t e through equation the network one p i p e a t a has an amplification factor Also the head correction ( n ) a p p l i e d to the correction which causes overshoot. 60m h *26 3Oomm x 2OOOm s/h 0.7 !a lQIh 1140 1 7 0 0 0,7 0.7 97 0.7 N + 0 .1.7 *0,7 0 0 +5s 80 1.5 + 5 4 80 1.5 tS2.7 80 1,s 0 6 5,3 9 NOTES Heads i n metres, flows i n l i t r e s per second, diameters i n millimetres, lengths i n metres. Arrows i n d i c a t e p o s i t i v e d i r e c t i o n of h C Q ( a r b i t r a r y assumption). Blackened c i r c l e s i n d i c a t e nodes w i t h f i x e d heads, numbers in circles indicate order i n which nodes were corrected. Head losses evaluated from F i g . 2.3. H = 1.85 Q in Q/ h Fig. 3.1 Example of node method of network flow a n a l y s i s 43 The loop flow correction be method assumed has the disadvantage in data are in preparation. defined data gence. with Flows must in and around pipe loops, The and drawoffs added e f f o r t indirectly the assumed flows. preparation This data interpretation often offsets the q u i c k e r conver- i s so because of assembly. Trial relatively and error low computing costs compared design is also cumbersome if loop flows h a v e to b e changed each time a new p i p e i s added. Network A n a l y s i s b y L i n e a r Theory The ual in Hardy Cross methods of solution but network a n a l y s i s a r e s u i t e d to manin the effort required The latter methods of comparison the suffer drawbacks w i t h computer o r i e n t a t e d numerical simul taneous balance. solution of sets of methods. equations has the involve flow very with describing effect that and few the head Simultaneous solution iterations are required number of iterations to balance a network when compared the loop flow correction a n d node a l a r g e numrequires for head correction methods. ber of simul taneous O n the other h a n d solution of even if rendered equations, linear, a l a r g e computer memory a n d many i t e r a t i o n s . Newton-Raphson linear equations becomes techniques for successive approximation of non- a r e mathematically subordinate to sophisticated b u t mathematics. the engineering Thus Wood and problem the Charles (1972) approximation l i n e a r i z e d the head loss equation, at each step and establishing i m p r o v i n g the l i n e a r equations for head balance around loops. Isaac and M i l l s (1980) s i m i l a r l y l i n e a r i z e d the head loss equation as follows f o r flow between nodes i and j : 8.. IJ = C..+(H.-H.) IJ I J //m the square (3.5) sign is where the term in root assumed a constant for each i t e r a t i o n . If the Darcy f r i c t i o n equation is employed, Substitute node : equation 3.5 into the equation for flow balance at each EQ.. i IJ = Q. J where Q. J is j, the drawoff if at node j j and i to node negative from to i. Q.. i s the flow from node iJ There i s one such equation f o r each node. If has be a each set Q.. 'J is replaced by the l i n e a r i z e d expression (one for each is node) to i n 3.5, one of for simultaneous equations node. The which can solved node H at each then procedure estimate H at each initially, solve f o r new H ' s . The procedure i s repeat- ed u n t i l s a t i s f a c t o r y convergence i s obtained. OPTIMIZATION O F PIPELINE SYSTEMS The in pipe previous networks section with described or without methods closed the for calculating the flows loops. flow nodes For any particular pipe to network layout or and diameters, at pattern could corresponding be calculated. fixed drawoffs a new inputs various To design sary be to network a if to meet c e r t a i n drawoffs, of possibilities. flows A i t would be neceswould meet compare and number proposed layout just layout sufficient would to analysed and If corresponding were the to demands table. for pressures were s a t i s f a c t o r y , it be accepdiameters not, would be necessary flows try alternative pipe sizes a n d a n a l y s i s of is for at hand. This i s repeated u n t i l a satisfactory would final then be solution repeated trial and error Each process of that the another then possible layout. networks least so d e r i v e d would have to b e costed a n d network w i t h cost selected. A out technique recourse to of determining and the least-cost would be network desirable. directly, No direct of withand trial is error, positive with technique loops. flows, possible for general optimization networks closed T h e problem head losses i s that costs the r e l a t i o n s h i p between p i p e i s not linear and most rourelation- diameters, tine ships. tion and mathematical There a r e a optimization number of be used techniques require linear s i t u a t i o n s where mathematical optirnizato optimize The l a y o u t s a n d these cases a r e are normally confined to techniques and can discussed described below. cases 45 single mains or is tree-like optimize a networks network for which the flow loops, in each b r a n c h known. To with closed random search t e c h n i q u e s o r s u c c e s s i v e a p p r o x i m a t i o n t e c h n i q u e s a r e needed. Mathematical analysis design optimization (which not a is techniques an are also known as as systems they are techniques techniques (again incorrect nomenclature or analysis name techniques), not really will operations research The name Such techniques mathematical techniques a descriptive). be retained optimization techniques here. include simulation technique such ( o r mathematical modelling) coupled with ascent or random selection as steepest path searching. The which ation and direct optimization methods include dynamic programming, transport- is useful for optimizing programming, linear which a series of events o r things, is u s e f u l for for a l l o c a t i n g s o u r c e s to d e m a n d s (van der Veen,1967 the use and of a programming, Linear inequalities usually Dantzig, computer, 1963). programming requires b u t there a r e standard optimization programs available. D y n a m i c P r o g r a m m i n g f o r O p t i m i z i n g Compound P i p e s One o f can the simplest optimization be used without technique is a techniques, and indeed one which i s dynamic proway of selecting involve any normally the recourse to computers, gramming. an optimum i n fact o n l y a systematic program from The a s e r i e s of e v e n t s a n d does n o t may be used may flows. to select mathematics. diameters length trunk of technique t h e most economic along its a compound on pipe which vary in diameter depending main of pressures a and of For instance, a consider supplying the trunk The number main may is consumers from reservoir. The diameters along the be reduced as drawoff select takes place line. problem to t h e most economic d i a m e t e r f o r each section of p i p e . A simple example demonstrates the u s e of the technique. Consider the p i p e l i n e in Fig. and the head at the 3.2. Two c o n s u m e r s d r a w w a t e r f r o m t h e p i p e l i n e , i s n o t to d r o p b e l o w 5 m, below neither any each d r a w o f f p o i n t grade of line should point. hydraulic drop the p i p e p r o f i l e a t The e l e v a t i o n s each p o i n t a n d the l e n g t h s of each section of p e r mm d i a m e t e r per m of pipe are indicated. T h e c o s t o f p i p e i s EO.l 46 pipe. (In this head, case the cost it is is assumed simple to to be independent account of of such the a pressure although take variation). pipe The a n a l y s i s w i l l be s t a r t e d at the downstream end of the arrangement w i l l The head, H, (point A ) . The most economic be w i t h minimum at p o i n t B may be residual head i.e. 5 m, at point A. a n y t h i n g between 13 m a n d 31 m above the datum, analysis, we b u t to s i m p l i f y the heads with will only consider three possible 5 m increments between them a t p o i n t s B a n d C. Fig. 3.2 P r o f i l e of p i p e l i n e optimized b y dynamic programming The each o f diameter D of the pipe between A and B, corresponding to the three allowed heads may be determined from a head l s os 2.3 c h a r t such as F i g . and i s i n d i c a t e d i n Table 3.1 (1) along w i t h the corresponding cost. W e number 3 = 9, will also consider only three grade possible lines heads B at point C. C The x of but possible one of hydraulic these 3.1 grade the between and so is 3 is at an set adverse g r a d i e n t of figures is may be dis- regarded. possible and the In Table (I I) a line presented f o r each Thus to B if hydraulic 19 then between 6 and from 110 P / s x C. C H B = 13 and HC = hydraulic for a flow gradient of i s 0.006 diameter required is 310 rnm (from = Fig. 2.3). Now B, The cost of to this cost t h i s p i p e l i n e w o u l d be 0.1 must be added the cost of 310 x 1 000 f31000. the p i p e between A a n d i n t h i s case f60 000 (from Table 3.1 (I)). For each possible head 47 TABLE 3.1 D y n a m i c p r o g r a m m i n g o p t i m i z a t i o n of a compound p i p e I 1 1: 1 1 I .004 300 1 6 0 0 0 0 .0065 260 52000 23 .009 250 50000 111 19 L 1 -006 I 310 62000 - ._ 24 .0035 340 68000 29 .001 430 8 3000 __I. 5 1000:'f I --i 86000 79000 165000 48 HC there an i s one asterisk. be minimum total cost of p i p e between A a n d C, marked with which I t i s t h i s cost a n d t h e c o r r e s p o n d i n g d i a m e t e r s o n l y when proceeding to the next section is the of last pipe. and need recalled the In this example, next section between C and D t h e r e i s o n l y one p o s s i b l e h e a d a t D, namely the r e s e r v o i r and To level. In Table and this 3.1 (It I) the hydraulic gradients corresponding t h e c o s t s of pipe and diameters pipe for costs f o r section to Section are C - D are the indicated. of the added costs each optimum at C, arrangement the least up C. This i s done f o r Table p o s s i b l e head total total and cost cost selected from is 3.1 (I1 I). Thus the minimum diameters - possible S151 for 000 and the most economic - are 260, 310 It 340 be mm Sections to A - B, pipes B C and C standard D respecin tively. which section may the desirable keep to diameters for case as nearest s t a n d a r d diameter proceed the next or could b e selected each the c a l c u l a t i o n s one w i t h each length could be made up a n d one head of two sections; l a r g e r s t a n d a r d diameter with t h e n e x t smal l e r s t a n d a r d d i a m e t e r , result. b u t w i t h t h e same t o t a l loss a s the theoretical Of course many would be more s e c t i o n s o f increased by p i p e c o u l d b e c o n s i d e r e d and t h e more possible heads at accuracy considering each s e c t i o n . booster i t s cost pump The cost o f station the p i p e s c o u l d be v a r i e d w i t h presssures. be considered a t a n y should point. in A could i n w h i c h case the tables. a n d c a p i t a l i z e d p o w e r cost p r ove useful if many be added A c o m p u t e r may p o s s i b i l i t i e s a r e to b e c o n s i d e r e d , and there a r e s t a n d a r d dynamic programming programs a v a i lable. It the will b e seen t h a t t h e t e c h n i q u e of dynamic programming reduces n u m b e r of at p o s s i b i l i t i e s to be c o n s i d e r e d b y s e l e c t i n g each step. Kaliy t h e least-cost arrangement (1969) a n d B u r a s a n d Schweig (1969) describe a p p l i c a t i o n s of t h e t e c h n i q u e to s i m i l a r a n d o t h e r p r o b l e m s . T r a n s p o r t a t i o n programming f o r least-cost Transportation does not required programming the use of a is a l l o c a t i o n of resources technique The which is a normally of another computer. technique sources to use p r i m a r i l y for of consumers a l l o c a t i n g t h e y i e l d o f a n u m b e r of such the that a least-cost along system each is number cost of achieved. should The be delivering resource route linearly 49 proportional the to the is throughput of along no use that in route and for t h i s reason pipe technique probably selecting the optimum sizes. I t i s of use, however, i n selecting a least-cost an existing in pipe distribution with system, head, pumping p a t t e r n the friction a through head is provided or for small comparison static obtaining p l a n n i n g g u i d e before demands a r e accurately known. CONSUMER REQUIREMENT M 10 L l S N 15 L I S SOURCE YIELD 12 L I S Fi9. 3.3 Least-cost example a l l o c a t i o n p a t t e r n f o r t r a n s p o r t a t i o n programming An example serves to i l l u s t r a t e the technique. I n t h i s example, there A a r e two sources o f and €3 could d e l i v e r water, A and B, a n d two consumers, respectively M and N. 1 2 a n d 20 e / s a n d M and N r e q u i r e The cost 10 a n d 15 4 / s respectively. of thus t h e r e i s a s u r p l u s of water. pumping along routes A - M, A - N, I3 - M for and B - N a r e 5, 7, 6 a n d 9 p/1 000 l i t r e s respectively. The data are set out in a tabular source each block form solution column a in Tabel 3.2 The (I). unit Each cost of row of represents and each demand. the top step delivery along route in i s indicated i n right i s to corner the corresponding the table. The f i r s t 50 make that block an each of arbitrary yield the the initial assignment is of resources Starting in such a manner with the top is 10. in and demand the satisfied. left This the table, maximum M possible and allocation amount is satisfies bottom d e m a n d of column the written left c o r n e r o f b l o c k AM. i s completed, P r o c e e d i n g to t h e n e x t c o l u m n , the maximum possible a l l o c a t i o n r o w A. since the f i r s t first row column i s 2, in the which satisfies the y i e l d of So t h e n e x t b l o c k through the t o b e c o n s i d e r e d i s i n r o w 0 , n a m e l y c o l u m n N. table making resources allocation column. Proceed the maximum possible assignment a t each stage u n t i l a l l (even in a r e allocated is i f to the slack row, column). t,he Thus in the next the third the 13 the second then 7 TABLE 3.2 T r a n s p o r t a t i o n p r o g r a m m i n g o p t i m i z a t i o n o f an a l l o c a i o n CONSUMER : M REQUIREMENT 5 : ( 1 ) SOURCE Y I E L D A 12 B 20 m i N SURPLUS EVALUAT ON 10 15 7 NUMBER : 0 ---J 2 7 13 EVALUATION NUMBER: 5 7 -2 ( 1 1 ) 0 A 12 ~~ 2 B 20 10 7 4 Once an 7 the -2 figures are re-arranged initial until a allocation least-cost is made methodically would be the d i s t r i b u t i o n emerges. assign a To d e c i d e w h i c h relative evalua- most p r o f i t a b l e arrangement, t i o n n u m b e r t o e a c h r o w and c o l u m n a s f o l l o w s : Assign numbers the value that 0 to row 1 and work out the other evaluation such t h e sum o f is equal to the row evaluation the cost coefficient number a n d column for any evaluation number occupied 51 block. The v a l u e f o r so column M write the is 5, sum of for column N i s 7, f o r row B i s 2, and on. Now the row each of and column e v a l u a t i o n If this numbers sum if beneath bigger the cost coefficient the cost of unoccupied block it than coefficient the block, would p a y to introduce a resource a l l o c a t i o n immediately, sum from r a t e of but i n t o t h e block. T h i s i s not easy to see stems from the method of determining each e v a l u a t i o n T h e biggest possible the cost coefficients of occupied blocks. improvement sum and i s i n d i c a t e d b y the biggest difference between the the cost coefficient. The biggest introduce be put and i n fact in into is evaluation our case the o n l y , BM. The improvement amount would b e to which can an amount in block Block maximum drawing BM determined b y a closed loop u s i n g occupied blocks as corners i n Table 3.2 would ( I ) ) . Now f o r each u n i t which i s have to be subtracted from block from block to the block keep the (see the dotted c i r c u i t added BN, to block to BM, block one u n i t A N and added and subtracted In AM yields requirements BM consistent. since this this case maximum allocation to is 10, would evacuate AM. The maximum r e - d i s t r i b u t i o n i.e. 10 i s made, and the amount i n the block a t each corner of the closed loop adjusted by 10 to s a t i s f y y i e l d s a n d requirements. a time. After making number to the and most there that in Only one r e - d i s t r i b u t i o n of resources should be done at the best new allocation, as in re-calculate (11). the e v a l u a t i o n resource procedure by evaluation sums Table 3.2 Allocate p r o f i t a b l e block is no there further and repeat cost the r e - d i s t r i b u t i o n improvement, than at until the possible indicated the cost the fact i s no e v a l u a t i o n sum g r e a t e r we coef- ficient any in block. two In our but example more arrived optimum involving distribution steps, compl icated patterns more sources and consumers may need many more attempts. The example can o n l y serve to introduce the subject of t r a n s p o r t a tion with programming. in textbooks such as There on the der as are many of other conditions which are dealt technthis subject Veen mathematical optimization and Dantzig (1963) if niques Van (1967) and two example o n l y in the table serves an to a introduction. be evacuated small For instance, blocks of the say. happened simultaneously, one blocks could Computat ions at the end. be allocated then very quantity denoted by 'e' 'e' proceed as before and the q u a n t i t y disregarded 52 L i n e a r Programming f o r Design of Least-Cost Open Networks L i n e a r programming niques. systems, The use of the a i s one of computer simple the most powerful is normally given optimization for tech- essential here is complex hand. although example if in the done by The technique may o n l y is be used the r e l a t i o n s h i p between v a r i a b l e s application. design of Linear pipe programming with be in linear, be loops to so it is restricted optimizing resort mains to cannot closed used each loss, used for networks It without trunk successive tree-like the approximations. networks where can design is or the flow flow, branch diameter to known. and the cost Since are relationships the between head is a non-l inear, following technique used render of system linear: For each b r a n c h o r main p i p e , the length of number p i p e of pre-selected diameters a r e allowed and is each different diameter treated as the v a r i a b l e . The head losses The and costs a r e l i n e a r l y p r o p o r t i o n a l to the respective p i p e lengths. program thereby can be will indicate that some diameter pipes h a v e zero lengths, i n effect e l i m i n a t i n g them. treated at in the analysis. in Any other type of I t may linear constraint the (a a be r e q u i r e d to m a i n t a i n above a f i x e d minimum within pressure certain of points the network I inear certain inequality range. The the greater-than-or-equal-to-type) length o f p i p e of or total a c e r t a i n diameter may be r e s t r i c t e d because there i s i n s u f f i c i e n t p i p e a v a i l a b l e . DIAMETER m m UNKNOWN L E N t T H m OPTIMUM L E N G T H m HEAD LOSS m 250 X, 200 x2 I50 2 OD x3 150 XL L 00 1 - 6 6 TOTAL 5 . 0 50 012 3.2 0 0 Fig. 3.4 Least-cost t r u n k main b y a trunk l i n e a r programming two drawoff points (Fig. The example concerns main w i t h 53 3.4). and The p e r m i s s i b l e diameters of of the second leg, 200 the f i r s t 150 leg a r e 250 a n d 200 mm, There are thus four dif- and mm. v a r i a b I es , X,, ferent X2, X3 This and X4 simple of which are the example could alternatives used here lengths of pipe of diameters. of be optimized b y giving to the manual head tech- comparison loss, the costs all is correct the but linear programming demonstrate nique. The head losses per 100 m of p i p e a n d costs p e r m for the v a r i o u s pipes a r e i n d i c a t e d below:- D iameter mm Head loss @ 40 e / ’ s m/1OO m 0.25 0.71 @ 14 e/s m/1OO m 0.1 0.42 cost i~100/100 m 250 200 150 The form linear 5 4 3 expressed are in equation in constraints the on the of system the are below and coefficients equations tabulated Table 3.3 Lengths (I). Lengths a r e expressed i n h u n d r e d metres. + x1 0.25X1 X2 + 5 x3 x4 = 4 = 5 Head L o s s : Objective Function: The computations so + 0.71X2 + 0.1X3 + 0.42X4 5x1 + 4x2 + 4x3 + 3xq by setting all real variables variables = m i n i mum proceed to the to zero, into each it i s necessary to c introduce equality. 3.3 (I), artificial The slack and To slack equation a, at b satisfy in v a r i a b l e s a r e designated cost coefficients are set and Table their very h i g h values designated m. b a n d c a r e assigned i n i t i a t e the solution, the slack variables a, the values 5, 4 and 5 respective- l y (see the t h i r d column of Table 3.3 The numbers i n any indicate placed the by amount of particular the one (I)), the l i n e of main body of the t a b l e which would be Thus disone program unit variable the introducing of column variable. u n i t o f X, To would displace 1 u n i t of a and 0.25 whether it u n i t s of c. replacing any variable determine is worthwhile i n the program b y any other v a r i a b l e , a number known as the oppor- 54 T A B L E 3.3 L i n e a r P r o g r a m m i n g S o l u t i o n of P i p e P r o b l e m s P-qg. co>t V c r a b l e _ e_ Co ff. A _ _v o u n t a b C m 5 4 5 dALUE: !: l x2 4 x3 4 x4 3 a m b m c m Red. s , m m 0.25 0.71 0.10 0.42 1 5/.71 OPPORTUNI T Y i a x2 b C x1 2 4 1 5 1 x3 4 x4 3 a b 4 m m 5 4 1.45 1 1 1 1 I -0.46 lt0.46 0 0.1 0.42- -0.71 1 .71m-4 1 j l 4 3.45' 4 - 1 . l m 3-1.42m 0 0 I l l x1 2 4 1 5 x2 b x4 x3 4 x4 3 a m 1 b m c m 4 m 5 0.55 1 1.I 5 -2.38 2.38 3.38-8.2 0.76 1.69 1 0.5" 3 3.45 -1.1 11-1.lm 0.24 -1.69 1.1-0.69m 0 3.28-0.76m 0 IV x2 x1 4 4.5 0.5 4 0 1 -0.69 0.69 1 1 2.16 5 3 1.52 -2.16 I x4 0 0.31 0 m- rn m- ( N o f u r t h e r improvement posc iD l e 1 55 tunity number i s calculated the cost which for for each column. I f one u n i t of X 1 (0 x i.e. introduced, then x would increase b y (5 - (1 x m) - m the the of ) - (0.25 m)), value that i s designated each by the cost column the is the o p p o r t u n i t y calculated by cost value, opportunity entries the in multiplying coefficients the column in corresponding column of and program variable from second subtracting total thus formed the coefficient the column variable. The most p r o f i t a b l e v a r i a b l e t o the The is greatest cost is reduction now the per introduce would be X2, unit since i t shows value). column mini- ( o r negative o p p o r t u n i t y the key column. value X2 that column which designated lowest The key shows opportunity ( i n the cost mization case). To which Only one v a r i a b l e may be introduced a t a time. the maximum amount the of determine may be the key column ratios variable for each introduced, calculate replacement row as follows:Divide the amount number of the program variable The for each row by the corresponding ment be the the ratio is i n the key column. as that is the of lowest p o s i t i v e replacewhich The row could with selected maximum amount the constraints. introduced without lowest number positive at the v i o l a t i n g any ratio of replacement intersection is designated column the key and key row a n d row, the key the key number. After ( T a b l e 3.3 introducing a that new the variable, replacement the matrix is rearranged correct. The (11)) so ratios remain program v a r i a b l e and by the new variable i t s cost coefficient and its cost in the key row a r e replaced coefficient. The amount column as well as the body of t h e t a b l e a r e r e v i s e d as follows:Each number i n the key row i s d i v i d e d b y the key number. From each number in the number in a non-key row, the subtract the corresponding i n the key key column row m u l t i p l i e d b y divided (11). r a t i o of the o l d row number number. The by the key new tableau is g i v e n as T a b l e 3.3 The ratios procedure and of studying the table opportunity is repeated the so values until and is replacement no (IV) revising there 3.3 further shows hand negative all opportunity value. In example Table positive opportunity values the least-cost solution i s at 56 (indicated values). The ming reader Van the should der r e f e r to a s t a n d a r d textbook on l i n e a r programa full descan by the current program v a r i a b l e s and t h e i r corresponding (e.9. of Veen, (1967) a n d D a n t z i g There are many (1963)) f o r other cases cription technique. which be mentioned below:If the constraints equations, into are of the 5 (less-than-or-equal-to) variables of with zero cost type and not are just slack the coefficients them coef- introduced The 1.h.s. slack each constraint with to make cost equations. artificial variables high f i c i e n t s a r e then omitted. If the constraints artificial 1.h.s. cost of are of the 2 (greater-than-or-equal-to) with type, introduce into with the zero slack the variables high cost slack to coefficients variables make them constraint from and each subtract inequality coefficients equations. If the objective with is function highest be is to be minimized, is the opportunity but value the to negative value selected, if the the function maximized, the opportunity value with h i g h e s t p o s i t i v e v a l u e i s selected. The opportunity values i.e. represent they shadow the values value of the corres- ponding variables that indicate of introducing one u n i t of If the when very two v a r i a b l e i n t o the program. ratios a r e equal, in whichever the other row row it replacement of i s selected, will to be amount the program is variable zero a matrix rearranged. Merely assume have s m a l l v a l u e a n d proceed as before. example then the of two stage optimization, is namely first the layout and pipe diameters search given in are Stephenson also (1964). Non-linear instance programming and methods discussed. method. For Lam (1973) described a g r a d i e n t o p t i m i z a t i o n 57 REFERENCES Buras, N. and S c h w e i g , Z., 1969. A q u e d u c t r o u t e o p t i m i z a t i o n b y d y n a m i c p r o g r a m m i n g . Proc. Am. SOC. C i v i l E n g r s . 95 ( H Y 5 ) . Cross, H., 1936. A n a l y s i s o f f l o w i n n e t w o r k s of c o n d u i t s o r c o n d u c t o r s . U n i v e r s i t y of I I I i n o i s B u l l e t in 286. D a n t z i g , G.B., 1963. L i n e a r P r o g r a m m i n g and E x t e n s i o n s , P r i n c e t o n U n i v e r s i t y Press, Princeton. Isaacs, L.T. a n d M i l l s , K.G., 1980. L i n e a r t h e o r y m e t h o d s f o r p i p e n e t w o r k s a n a l y s i s . P r o c . Am. SOC. C i v i l E n g r s . 106 ( H Y 7 ) . Kal l y , E., 1969. P i p e l i n e p l a n n i n g b y d y n a m i c computer programm i n g . J . Am. W a t e r W o r k s Assn., (3). Lam, C.F., 1973. D i s c r e t e g r a d i e n t o p t i m i z a t i o n of w a t e r systems. P r o c . Am. SOC. C i v i l E n g r s . , 99 ( H Y 6 ) . S t e p h e n s o n , D., 1984. P i p e f l o w A n a l y s i s , E l s e v i e r , 204 pp. V a n d e r Veen, B., 1967. I n t r o d u c t i o n t o t h e T h e o r y of O p e r a t i o n a l R e s e a r c h . C l e a v e r Hurne, L o n d o n . Wood, D.J. and C h a r l e s , O.A., 1972. N e t w o r k a n a l y s i s u s i n g l i n e a r t h e o r y . ? r o c . A X E , 98 (HY7) p 1157 - 1170. L I S T O F SYMBOLS C D - cost diameter head loss head const a n t Iengt h flow - h H K e Q 58 CHAPTER 4 WATER HAMMER AND SURGE R I G I D WATER COLUMN SURGE THEORY Transient are often the pressures cause of caused bursts. by a change of flow r a t e in conduits associated The pressure fluctuations w i t h s u d d e n f l o w s t o p p a g e c a n b e s e v e r a l h u n d r e d metres head. Transients gories: surge, of in closed conduits are normally oscillation classed fluid is by into two cateto a Slow motion mass of the referred elastic whereas fluid rapid change is in flow accompanied to strain slow yield the and conduit in referred or as w a t e r the hammer. two For or small changes flow rate pressure theories t h e same r e s u l ts. It i s normally the easier is to a n a l y s e a applicable) system b y than by r i g i d column elastic theory. theory With (whenever theory r i g i d column pressible the tion umq theory A the w a t e r pressure an in the c o n d u i t difference i s t r e a t e d a s a n incomacross The the ends of mass. applied column produces the instantaneous acceleration. basic equacol- relating in a head bore d i f f e r e n c e between conduit to the t h e e n d s of rate of the water in uniform change velocity i s d e r i v e d from Newton's b a s i c l a w o f motion, a n d is (4.1 where conduit h is the difference v is the in head between g the is two ends, L i s the accelera- length, flow velocity, gravitational tion and t The with i s time. is useful of a for calculating column. the head rise associated calcupower in equation slow the deceleration water level up water I t may surge or be used f o r following load lating trip a or variations a pumping fed of in a line, a shaft power starting in changes The hydro-electric may be installation in steps by At pressure pipeline. in equa- tion solved b y computer, tabular form o r method graphical ly. The f o l l o w i n g e x a m p l e demonstrates the numerical of s o l u t i o n o f t h e e q u a t i o n : - 59 Example A 100 m l o n g penstock w i t h a c r o s s s e c t i o n a l a r e a , water hammer b y area, velocity load water a A,, o f 1 m2 is protected against bine, with a cross surge s h a f t a t the tur- sectional The initial complete rise in A2, of 2 m2 and an unrestricted orifice. and there is the a i n t h e c o n d u i t i s 1 m/s sudden rejection level in at the the t u r b i n e . surge shaft Calculate maximum neglecting friction. Take -0.098h. A t = 1 sec. Then from Equ. 4.1, Av = -ghAt/L = 0.5~. = -9.8h/ 100 = By c o n t i n u i t y , A h = A1vAt/A2 = l v / 2 t 0.1 1-2 2-3 3-4 4-5 5-6 6-7 Ah = 0 . 5 ~ h 0.5 0.976 1.404 1.763 2.035 2.207 2.271" m, A v = -0.098h -0.049 -0.096 -0.138 -0.173 -0.199 -0.216 -0.223 V 0.5 0.476 0.428 0.359 0.272 0.172 0.064 0.951 0.855 0.717 0.544 0.345 0.129 0.094 The maximum r i s e i s 2.27 tical w h i c h may b e compared w i t h t h e a n a l y 4.16, o f 2.26 taking m. The a c c u r a c y o f t h e time intervals A h s o l u t i o n o b t a i n e d from Equ. method numerical or and taking A v c o u l d be i m p r o v e d b y smaller t h e mean v a n d h o v e r t h e t i m e i n t e r v a l s to c a l c u l a t e The method c a n r e a d i i y b e e x t e n d e d to respectively. include h e a d losses, Another water a n d i s calculator-orientated. a p p l i c a t i o n of t h e r i g i d w a t e r column e q u a t i o n i s w i t h Following line, at the useful column end to separation. of a the the stopping pressure along of a pump at the upstream pumping frequently the line. will In drops such sufficiently cases slowly Equ. the the and cause vaporization beyond theory peaks water column vapour pocket decelerate analysis. r i g i d column be the is s u f f i c i e n t l y with accurate for time t 4.1 may integrated twice water column the r e s p e c t to to d e t e r m i n e If the distance stop will travel of before the 0 stopping. pocket 0 pumps the instantaneously volume vapour behind i s the water column o f length t w i l l be Q = A t v * / 2 9 h where v i n i t i a l flow velocity. 60 MECHAN I CS O F WATER HAMMER Water hammer occurs, as the name implies, The when a column of water i s r a p i d l y decelerated theory would indicate an (or accelerated). r i g i d water if a column in a is, the the gate infinitely l a r g e head r i s e valve p i p e l i n e c a r r y i n g l i q u i d were slammed s h u t however, instantaneously. There due to at a c e r t a i n amount o f r e l i e f u n d e r these c o n d i t i o n s , the p i p e is shut itself. the a Thus e l a s t i c i t y of the f l u i d a n d of d i s c h a r g e end of will will pack rise against a pipeline the gate, to if a valve of The fluid upstream rise. the causing the pressure in pressure with the sufficiently stop liquid accordance momentum l a w . the amount of The amount o f water required water to stopped p e r u n i t the volume time depends o n created replace by the compression of w a t e r a n d e x p a n s i o n o f t h e p i p e . I t can thus Ah, be shown that the relationship between the head r i s e the wave (4.2a) the r e d u c t i o n in v e l o c i t y i s A h = -CAV/g A V a n d the r a t e of p r o g r e s s of front where c i s t h e w a v e c e l e r i t y a n d g i s g r a v i t a t i o n a l equation is often referred to a s J o u k o w s k y ’ s law. acceleration. It can This be further p r o v e d from a mass b a l a n c e t h a t c = 1/ If 3 .iw kd EY the p i p e h a s a (4.3a) rigid lining ( e l a s t i c m o d u l u s E2 a n d t h e e q u a t i o n to use i s thickness y) , and r i g i d side f i l l ( m o d u l u s Es) (4.3b) where w i s the u n i t w e i g h t of liquid, K i s i t s b u l k modulus, y the p i p e w a l l fixity for of a the d is the p i p e diameter, k a factor E i s i t s e l a s t i c modulus, depends thickness a n d (normally tunnel plastic low which on the end pipe about 0.9). c may b e a s h i g h a s 1370 m/s for thin wall i s present r i g i d walled o r as low a s 850 m/s steel p i p e s . (see C h a p t e r I n t h e case o f pipe, a s ZOO or when free a i r 51, c may be a s m/s. The earlier, pressure thus in wave caused by the valve closure the referred head, the to as travels Fig. the so upstream, 4.1(1). superimposed on the wave static illustrated reservoir the When in the front reaches open into end, pressure that the pipe now forces water and backwards reservoir, velocity reverses pressure drops b a c k to s t a t i c ( r e s e r v o i r ) p r e s s u r e a g a i n . 61 PRE5WRE NAVE Fig. 4.1 Water hammer wave at d i f f e r e n t stages A That in The back negative wave wave will (2) in thus travels downstream from the r e s e r v o i r . the velocity velocity. travels it front t u r n reach the closed end. v 0 Now the entire pipeline wave pipe is -v 0 where was the original static, the negative up the of head the pipe, amplitude C ,g v/ Upon below reaching to reservoir. reservoir sucks to +v water into the the head so that to the velocity head. in the p i p e r e v e r t s waves and reverts static The sequence of w i l l repeat i t s e l f i n d e f i n i t e l y unless damped b y f r i c t i o n . ---+---1 Hz g ‘with no friction 0 2 L/c I 3 L/c 4L7c I t Fig. 4.2 Head f l u c t u a t i o n s at v a l v e end. 62 The 4.2. In variation the case in of head at the v a l v e lines, with the will be as indicated i n Fig. change The water in a i n flow downsudden dis- pumping most violent trip. conditions stream of i s normally the in pump associated is suddenly The a pump decelerated, wave velocity resulting reduction charge wave pressure. (Fig. 4.3), negative the travels towards and a the end where reverses at positive alter- returns towards the pumps. The pressure the pump nates from a pressure drop to a pressure r i s e . Wave front snit i d l y Vapour pressure Initial V = Vo F i g . 4.3 Water hammer head drop a f t e r pump t r i p The tion, wave i s complicated or the by line friction, flow variation. vaporize changes Thus air in if will cross there be secis a vaporization, pressure, air be as valves seen it gradual water negative in will and drawn most via and from solution. Fig. up 4.4 which The effect of illustrates a f r i c t i o n can wave shut at readily stages from different The to travels the p i p e l i n e from the wave are not a rapidly quite valve. due pressure the heads behind horizontal, ' p a c k i n g ' effect causing some flow across the wave f r o n t . The effect of equation. changes i n section The wave or b r a n c h pipes can be Ah' after included in one head change r e a c h i n g a junc- tion i s r e l a t e d to the o r i g i n a l head change Ah' 2Ah'A./c. I I by the equation Ah' = A1/c, A h I 2 /(1 + A 2 / A 1 + A3/A1 + where A . i s the cross sectional area of p i p e i and c + + + A 2'=2 A3/C3 ... 1 i4.4a) .. . . c2 (4.4b) c3- 63 ~ 1 Xz- F 'x c vo 9 3 "Distance from valve" 2 F i g . 4.4 Head a t p o i n t s a l o n g along p i p e l i n e w i t h f r i c t i o n , instantaneous stoppage for When a valve i n a g r a v i t y main i s closed g r a d u a l l y , minute waves emanating numerical ly for valve or the effect i s The analogous to a series of system form could of be analysed is of from the v a l v e . graphically. the The g r a p h i c a l principles and of analysis solution useful the demonstrating discharge simultaneous equation the water hammer equation. lar to the In fact the sines d r a w n on a g r a p h a r e v e r y similines adopted in numerical solu- so-called characteristic t ions. Fig. valve at to 4.5 illustrates a graphical analysis of a pipeline with a the discharge end. and the valve The v a l v e i s closed over for a p e r i o d equal four different 4 L/c discharge characteristics degrees of closure a r e p l o t t e d on the g r a p h . i s also indicated. at water the valve at The l i n e r e l a t i n g f r i c t i o n head loss to p i p e velocity To closure a n d S. compute one Thus the head the time L/c 4.2 after initiating applies hammer equation between p o i n t s R 64 A h -(c/g) Ahf Av - A h f (4.2b) Similarly where i s t h e d i f f e r e n c e i n f r c t i o n h e a d b e t w e e n R a n d S. t h e w a t e r hammer e q u a t i o n f r o m S t o R , applying A h + (c/g) Av thus + hf l i n e s of slope (4.2~) Computations the at waves point proceed a l o n g then t = + or - c/g. Ultimately peak a n d at die out d u e to f r i c t i o n . and is The m a x i m u m h e a d to t h e S occurs 4 L/c 182 m e t r e s a c c o r d i n g computations on F i g . 4.5. ELAST I C WATER HAMMER THEORY The velocity fundamental in differential may wave equations relating pressure to a conduit b e d e r i v e d from consideration of Newton's l a w o f m o t i o n a n d t h e c o n s e r v a t i o n of mass r e s p e c t i v e l y , and are: (4.5) ah - + -c 2 = v - ao at g ax The t o obey tion of last term in Equ. 4.5 with accounts for friction which i s assumed The assumpi s not flow Darcy's equation a steady-state Tests a constant f r i c t i o n factor. factor that for transient friction indicate conditions strictly correct. head losses d u r i n g t r a n s i e n t are higher normal flow t h a n those p r e d i c t e d u s i n g t h e f r i c t i o n f a c t o r a p p l i c a b l e to conditions. Energy is probably absorbed during flow reversals when t h e v e l o c i t y i s low and t h e f r i c t i o n f a c t o r c o n s e q u e n t l y relatively high. Methods of A n a l y s i s A common used for method of analysis of pipe systems for water hammer i s such pressures a chart for zero no to be g r a p h i c a l l y (Lupton, 1953). Fig. 4.6 the maximum a n d minimum heads a t the downstream v a l v e The v a l v e and the area i s assumed discharge to r e d u c e line friction. time T linearly is to over valve coefficient assumed constant. To u s e t h e c h a r t c a l c u l a t e t h e v a l v e c l o s u r e p a r a m e t e r cT/L 65 H ( m 1 20c 6' - 200 ::m R 5 55 S'cVALVE SHUT _/-- R 2 . /--_ / - - 52 53 t' RI _/-- 51 t d t = L/c R, -R x -t CHART S ' 0 F i g . 4.5 Graphical water hammer a n a l y s i s f o r slow valve closure with f r i c t i o n 66 and axis valve head loss parameter he/(cvo/g). /g) Read off on the vertical the maximum head parameter h ' / ( c v (dashed ( f u l l lines) a n d minimum by cvo/g a n d the head parameter -h/(cvo/g) answers are the lines). Multiply maximum a n d minimum heads respectively Note t h a t the c h a r t is for above a n d in a r e a below s t a t i c w i t h time, tics of head. linear reduction a c o n d i t i o n r a r e l y encountered in p r a c t i c e . and butterfly valves the are such that The c h a r a c t e r i s most of the flow sluice reduction occurs a t the water hammer the e n d of heads are valve stroke, than with the result t h a t the c h a r t . higher predicted by A more a c c u r a t e a n a l y s i s i s t h e r e f o r e n e c e s s a r y f o r T h e most economical tions for by particular the method of systems is solution of by digital important I ines. t h e w a t e r hammer e q u a computer. Solution is usually method o f characteristics (Streeter and Lai, 1963 a n d Streeter a n d Wylie, graphical expressed intervals. set equal method. in 1950) w h i c h d i f f e r s l i t t l e i n p r i n c i p l e f r o m t h e o l d The differential form water and hammer for equations successive are time is finite difference solved The c o n d u i t to i s d i v i d e d i n t o a number of i n t e r v a l s a n d At ax/c. Fig. The x 4.7. - t g r i d on which s o l u t i o n takes p l a c e i s from known conditions along the depicted in Starting pipeline at time t, one proceeds to c a l c u l a t e the h e a d a n d velocity a t each p o i n t a l o n g the l i n e at time t By adding, expressing equations 4.5 + At. 4.6 as total differentials and and one gets two simultaneous equations i n v o l v i n g dh a n d d v : (4.7b) Equs. time 4.7a and 4.7b may be solved t + At i n t e r m s of known and v ' at point p at P P h a n d v a t two other points q a n d r for h' at time t : (4.8a) (4.8b) 67 Valve closure factor C T/L F i g . 4.6 Maximum a n d minimum head a t downstream v a l v e f o r l i n e a r c Io s u r e At either speed. the terminal points, or a n additional condition i s usually is 4.7a a function or 4.7b is imposed; or pump with h is fixed, correct v of a gate opening The Equ. solved simultaneously the known condition computat ions t o e v a l u a t e t h e new at known h a n d v at time t + A t . The when commence conditions and are terminated the pressure f l u c t u a t i o n s a r e s u f f i c i e n t l y damped b y f r i c t i o n . Where t h e n Equs. a branch 4.8a pipe s occurs or there is a change i n diameter, a n d 4.8b snoulci b e r e p l a c e d b y E q u s . 4.9 a n o 4.10: 68 TIME A / Fig. 4.7 x - t G r i d for water method. hammer a n a l y s i s b y c h a r a c t e r i s t i c Effect of F r i c t i o n Fluid along the friction conduit. die away damps the is water no hammer waves influence as the they travel will to If there the exciting waves will gradually and pressure along the conduit tend s t a t i c pressure. The dicts wave. method the characteristic effect a method of solution by computer accurately is no discontinuity in prethe the At of of friction provided it there sharp wave front, i s necessary an analytical t o r e s o r t to some o t h e r solution is feasible at a analysis. front. Fortunately (1950) wave Ludwig wave demonstrated back is along that a by t h e a m p l i t u d e of line the with water hammer travelling stoppage friction fol lowing tion instantaneous 4.4): indicated hyperbolic func- (see F i g . xxv - tanh lines ( 4gd ' --./p)] 4 sudden pump the stopping pumping 0 cv (4.11) the maximum In pumping following pump than over-pressures friction cates head at is the greater will exceed head 4.8 if the indiwith approximately head 0.7cv / g . along Fig. minimum and maximum envelopes pipelines 69 various stream plot friction end. To heads use the following chart, instantaneous multiply the stoppage by at the upand ordinates cv / g the maximum a n d minimum hf/(cv / g ) , 0 head envelopes f o r the correct f r i c t i o n factor The when above o r below s t a t i c on a p i p e p r o f i l e d r a w i n g . only valid provided there is no column separation chart is the negative wave t r a v e l s up the p i p e l i n e i.e. should at no point fall below the minimum head below the pipeline envelope profile. mum 10 m It has, with however, been found from experience that a r e often s i m i l a r to the maxi- heads column separation those without separation. Fig. 4.8 may also be used to determine the maximum and minimum pipelines w i th fri cti o n end b y following sudden flow the c h a r t stoppage a t upside down versa. a closing valve. Turn heads along the downstream a n d r e a d o f f maximum envelope instead of minimum a n d vice- PROTECT I ON OF PUMP I NG L I NES (Stephenson, 1972) The pressure transients fol lowing power failure to electric motor d r i v e n pumps a r e u s u a l l y the most extreme t h a t a pumping system w i l l experience. should often also Nevertheless, be checked. the over-pressures Pumps with when steep caused b y s t a r t i n g pumps head/flow characteristics This induce h i g h over-pressures i s small head equal the pump t h e power i s switched on. when the pump i s because the flow so ( o r zero) i s switched on a wave partly with a to the closed v a l v e valves head i s generated. starting, the By closing delivery during over-pressures can be reduced. The over-pressures caused b y closing l i ne valves or scour valves should also be considered. If the the to pumps flow supplying will an unprotected p i p e l i n e a r e stopped sudIf line, the the to denly, close water a l s o stop. grade the pipeline sudden drop to profile is relatively deceleration a value the hydraulic may cause of the column pressure value less than atmospheric pressure. pressure. at peaks The lowest to which pressure could drop i s vapour thus occur Vaporization or even water column separation may along the pipeline. When the pressure wave is r e t u r n e d as a p o s i t i v e wave the water columns w i l l rejoin g i v i n g rise to water hammer over-pressures. 70 Fig. 4.8 M a x i m u m and m i n i m u m h e a d e n v e l o p e s f o l l o w i n g instantaneous pump stopping in pipelines w i t h friction 71 Unless pumping some pipeline method system of water will hammer protection to be is installed, for a a normally 0 have I n fact designed water hammer overhead equal to cv /g. high-pressure comparison lines the where water head. even t h i s i s often done w i t h may be small in hammer For if heads with pumping and short water lines this m a y be the is most economic solution, hammer protection i n s t a l l e d i t may be prudent to check that the u l t i m a t e s t r e n g t h of t h e p i p e l i n e i s s u f f i c i e n t should the p r o t e c t i v e device f a i l . The against reduce The philosophy water the behind is the design of most object methods of in most protection is to hammer similar. The cases downsurge i n the p i p e l i n e caused b y will then be correspondingly most into common pipe stopping or the pumps. even be upsurge reduced, of may entirely surge is eliminated. to feed The method limiting the down- water the as soon as the pressure tends to drop. Fig. 4.9 Pipeline p ro fi l e i I lustrat ing suitable devices f o r water hammer protection. locations Most of for various protective locat ions f o r various Suitable i n Fig. devices are i I lustrated 4.9. the systems i n v o l v e feeding water i n t o the pipe. Observe column that in all the cases tank the is sudden momentum c h a n g e of so the elastic the water beyond is prevented a slow of the water hammer Part into phenomenon of the converted kinetic to motion water surge column phenomenon. i s converted original energy energy potential ly the instead of under the e l a s t i c energy. effect to of the The w a t e r c o l u m n g r a d u a l in decelerates ends. If difference the and If, heads between would the it was in allowed the decelerate direction water impact column gather pump column to momentum cause is reverse against the water at hammer its over-pressures. of however, water which arrested with the point of maximum kinetic potential energy, no energy, there water coincides no sudden point minimum and may will be change The in momentum flow consequently be stopped to hammer a re- over-pressure. flux or v a l v e or vessel, reverse by installing throttling or in device a t the entrance the discharge t a n k air the pipeline. allow the A small o r i f i c e b y p a s s to the ree i t h e r s i d e to g r a d u a l - flux valve would then pressures on l y equalize. Fortunately and for charts are of not available the pump for the design so of air that water vessels investigation analysis is inertia effects, a water column and hammer theory normally for the necessary. of Rigid may be employed analysis surge tank action, i n some cases, of d i s c h a r g e tanks. system an incorporates water done are in-line hammer reflux valves is if a or If pump the pipeline valve, a bypass The of elastic may be analysis or, usually number program necessary. of analysis similar graphically a solutions systems envisaged, computer could b e developed. of a Normal ly the location, device and such as s i z e and d i s c h a r g e c h a r a c a discharge and to is be tank size of teristics be or protective by trial have to determined bypass In error. The location have in-line by most reflux these valves instances may a similarly determined the trial. computer as a program usually economical oped, and method of by solution, the general program could methodically, be develan opti- varying design parameters mum s o l u t i o n a r r i v e d a t . The following sections describe various methods o f reducing water hammer in p u m p i n g l i n e s , a n d offer design aids. 73 Pump Inertia If to the r o t a t i o n a l the pump i n e r t i a of for may a be a centrifugal after pump and motor continue failure, water hammer and rotate while power pressure transients will reduced. to The water rotating pump, motor e n t r a i n e d water on of the delivery continue feed i n t o the p o t e n t i a l vacuum the sudden deceleration short side, thereby a1 l e v i a t i n g the water column. The effect i s most noticeable on low-head, pipelines. After gradually the the power down supply until to it at the can motor no is cut off, the pump will slow longer deliver water against delivery than in the head e x i s t i n g the suction the time. it If the d e l i v e r y force water head i s t i l l s through in the the on higher pump head, will then reverse direction, with is the no pump reflux still or spinning control forward the and direction, side provided of the in there pump. valve delivery gather The pump will rapidly and of will the decelerate act pump as a momentum these the reverse The direction, turbine under conditions. reverse speed will increase u n t i l is a rapid i t reaches r u n a w a y speed. of the Under these conditions there a n d water hammer over- deceleration reverse flow pressures w i I I resu I t. I f there i s a r e f l u x v a l v e reverse still flow wi II be arrested, on the delivery water at side of the pump, the wil I but hammer overpressures occur. The pressure changes t h e pump f o l l o w i n g power f a i l 1963) o r b y computer. i s obtained b y equattransferred u r e may be c a l c u l a t e d g r a p h i c a l l y (Parmakian, The pump speed N ing the work done after a time increment A t i n decelerating the pump to the energy to the water: Solving f o r N 900wHQ A t A N = n MNFN ' where 1 - N2 = L N we get (4.12) the moment of in M is inertia of the pump impeller and motor, N of i the speed s the time above rprn, w FN i s the pump e f f i c i e n c y a t the b e g i n n i n g i s the u n i t weight of f l u i d , q interval, suction H i s the pumping As head head a n d i s the discharge. an approxima- 74 tion, FN = (N/No)Fo where s u b s c r i p t o r e f e r s to i n i t i a l conditions. head/discharge characteristics of the pump can be fairly The accurately represented b y the equation t i = aN2 + bNQ - cQ2 a, b and on c the are constants which can be evaluated of (4.13) provided the three are points known. head/discharge/speed characteristics pump Substituting pipe, and q = vA where A is the cross sectional area of two the un- u s i n g Equ. 4.8, two equations result involving knowns which may be solved f o r h and v at the pump. Fortunately summarized in the r e s u l t s of form. a l a r g e number of presented by analyses have been Parmakian indicate along chart Charts the maximum downsurge and the pipeline for upsurge at of the pumps and midway inertia and the various charts flow values also pump the pipeline speed re- parameter and the P. times The of indicate zero maximum speed and reverse reversal, pump maximum verse speed. Kinno which speed ing and Kennedy the effect (1965) of have prepared comprehensive charts include of l i n e f r i c t i o n and pump e f f i c i e n c y ; specific Of interest of be the the pump i s also discussed. if the the reverse upsurge pump was i s a chart pump is indicat- maximum upsurge that rotation could prevented. if Kinno reverse suggests flow reduced but considerably through permitted, with reverse r o t a - tion prevented. Fig. will ues 4.10 in summarizes various minimum values t the maximum systems taken and minimum pressures which Valthe occur for pumping head are following from power f a i l u r e . paper, and the Kinno's typical maximum head a r e adjusted will to cover that pump efficiencies around 85 p e r cent. occurs when ues be observed r e t u r n s to at the minimum head often ( t = 2L/c). flow reversal The v a l i s per- the f i r s t subsequen wave the pump if of the are upsurge in the pump mitted, the also presented of a the the c h a r t . These values if are lower than was the magnitude with upsurge which valve. If would occur flow head reversal reverse flow prevented prevented maximum reflux above was be headrise operating Ho would approximately equal to the lowest head-drop below H . 75 The the author has a simple have r u l e of an effect thumb in for a s c e r t a i n i n g whether the water hammer 0.01, pump inertia If the will reducing pressures. the pump Here M and AL ed from inertia parameter I = MNZ/wALHoZ at least exceeds i n e r t i a may reduce the downsurge b y i n e r t i a of the pump, 10 per cent. i n rpm i s the moment of N i s the speed i s the volume of water i n the pipe. Fig. The expression was d e r i v that 4.10, and it was assumed c/g is approximately e q u a l to 100. F i g . 4.10 M a x i m u m and rninimiJm h e a d s at p u m p a f t e r power f a i l u r e 76 Some i n s t a l l a t i o n s have a fly-wheel the be f i t t e d to the pump to increase the moment of inertia. heavy, In also most cases flywheel would have to impractically i t should be borne i n mind that start- i n g c u r r e n t s may thereby be increased. In subsequent sections the effect of pump inertia is neglected and the pumps a r e assumed to stop instantaneously. Pump Bypass Reflux V a l v e One against the of the simples hammer 4.11). arrangements is The a reflux reflux of protecting installed a in pumping parallel line with dis- water (Fig. in valve or pump non-return the pumps. be v a l v e would charge o n l y ing head the same d i r e c t i o n as the pumping head Under normal pumpthan the the reflux suction valve conditions and the would would higher pressure difference maintain i n a closed position. On stopping the pumps, the head i n the d e l i v e r y The head may water would be drop drawn drop The Pipe would tend to drop b y the amount to below the the suction bypass head, in The which cvo/g. case through to the valve. pressure friction would loss therefore o n l y in the bypass. suction pressure less any r e t u r n wave overpressure would be reduced a c c o r d i n g l y . REFLJX VALUE J S U C T I O N PIPE F i g . 4.11 Pump w i t h bypass r e f l u x valve. This cases, tion er method of water hammer protection cannot be used in all as the d e l i v e r y pressure w i l l often never drop below the suc- pressure. hammer The I n other cases there may s t i l l b e an a p p r e c i a b l e wati n v a l u e to use only the overpressure method (equal has initial the drop i n preshead is sure). really when pumping 77 considerably sure tion along less the than cv /g. pipeline should I n addition, length be the be initial drop i n presThe there sucmay entire level should tolerable. high or reservoir also relatively line. s t i l l be column separation Normally reservoir. fairly long the intake i n the d e l i v e r y pipes may draw be directly cases from the a constant intake head is However, and there where pipe water hammer could be a problem i n in a similar way it too. I n these cases a bypass r e f l u x v a l v e would, ed above, prevent the suction to that describpres- pressure exceeding the d e l i v e r y sure. It pump head, speeds, should during be the noted period that that water the may also be drawn i s below for through the delivery was head the suction specific the especially as is the if the machine designed pumps. high case with through-flow be omitted, In some cases bypass r e f l u x v a l v e could even a l t h o u g h there i s normal- l y a f a i r l y h i g h head loss through a s t a t i o n a r y pump. Surge Tanks The pressure, tank occur, in case of acts water while as a surface the in a surge the tank tank for is exposed to to atmospheric The may bottom of i s open flow in the p i p e l i n e . which or balancing in case tank of a the variations the pipe, discharging head tanks drop are filling at the can of a head rise. Surge used principally head be turbine in penstocks, pumping although It there is a r e cases where seldom that the they applied systems. line is hydraulic tank grade l i n e of a pumping low enough to enable an open a surge tank at the to be used. in and surge end of I t may be possible to construct and water protect hammer the by a peak pumps If the the the pipeline tank is profile against pipeline some between other as means. tank the relatively large, i t could length, be treated and in this the discharge could be intermediate pipeline section treated as an independent p i p e l i n e shorter length than the o r i g i n - a l pipeline. The f l u c t u a t i o n s of the water surface level ing ween power the failure pumps may and be surge studied tank i n a surge tank followThe transients water bet- analytically. are high-frequency hammer 78 phenomena ably. The which will not affect the water level in the tank of the noticewater analysis concerns the slow motion surges column between the surge tank and d e l i v e r y end of R i g i d water column water hammer waves theory will the line. since e l a s t i c The rate of may b e used in the s t u d y , not pass the open tank. deceleration of the water column i s d v / d t where = -gh/P (4.14) the level of the h is the and The height of the delivery head above surge very tank end. P i s the p i p e l i n e length between h gradually increases as the tank level in and delithe tank head the drops (see F i g . 4 . 9 ) . Another equation r e l a t i n g h a n d v c o n t i n u i t y of flow a t the tank o u t l e t : may be d e r i v e d b y considering A v = Atdh/t P where (4.15) are the cross sectional the flow from areas of the p i p e a n d tank i s assumed to be Ap and At respectively. zero. Solving Note that the pump side Equs. 4.14 and 4.15 a n d u s i n g the fact that at t = 0, h = 0 and v = v to e v a l u a t e the constants o f integration, one o b t a i n s an express ion f o r h : (4.16) From surge surge in is t h i s equation the (II it v - i s apparent , r that the the amplitude of the downtime tank is P m - and till to the f i r s t down- / 2 ) J AtP/A g: Time zero i s assumed be that i n s t a n t at which the water hammer wave reaches the surge t a n k . If pump the there i s a g r a d u a l deceleration of the water column between the then the above expressions w i l l and the rigid column for not hold, and for time a n d surge t a n k , correct continuity will have equation to be equation deceleration i n t e r v a I s. The orifice, extreme solved numerically successive fluctuations in tank level may be damped in with a throttling I n t h i s case the pressure v a r i a t i o n s than for the l i n e may be more the unrestricted orifice. Parmakian ( 1 9 6 3 ) presents c h a r t s i n d i c a t i n g the maximum upsurge f o r v a r i o u s t h r o t t l i n g losses. A have number of been sophisticated (Rich, variations in the design of surge tanks surge tank for proposed 1963). The differential 79 instance The tank includes may are a small-diameter varying riser in the m i d d l e of the tank. Such have a more cross section o r to hydro power m u l t i p l e shafts. plant than variations systems, applicable pumping as they a r e useful f o r damping t h e surges i n cases o f r a p i d load v a r i a t i o n on turbines. Discharge Tanks I n s i t u a t i o n s where the h y d r a u l i c g r a d e one which under tank would the p i p e l i n e p r o f i l e i s considerably lower than tank, from but l i n e i t may s t i l l be possible to use a operating surface conditions is isolated normal water the pipeline. The would be subjected to atmostpheric line, as opposed to pressure b u t be below the h y d r a u l i c g r a d e that of a surge tank. Fig. 4.12 Discharge tank A along rises. discharge tank would normally be situated on the first rise the p i p e l i n e a n d possibly on subsequent The tank the will b e more e f f i c i e n t a n d successively h i g h e r i n r e d u c i n g pressure v a r i a t i o n s the nearer be level in to the the tank is to via the h y d r a u l i c g r a d e a if reflux valve line. It should connected from pipeline i n s t a l l e d to discharge below valve the the tank surface held i n t o the p i p e l i n e elevation by the in the the p i p e l i n e head drops Normally the to the reflux line. valve it water be tank. in would shut pressure pumping a float A in small-bore the tank, bypass to should Fig. be the r e f l u x v a l v e , installed depicts a to connected the tank fill slowly tank after has discharged. 4.12 typical discharge arrangement. 80 The use of discharge tanks was reported in detail by Stephenson (1972). The f u n c t i o n of caused The by pump column a a discharge stoppage, between tank i s to f i l l any low pressure zone separation. end of the the be thus p r e v e n t i n g water column the tank) tank will and the discharge water pipeline action of (or subsequent head g r a d u a l l y decelerate the two ends. It under may the to difference between necessary prevent reverse motion of - the water column which could instal- cause water hammer overpressures t h i s could be achieved by l i n g a r e f l u x v a l v e i n the line. A the drop first tanks tank discharge lowest level tank to will which only the operate head Thus be in if the water surface would i s above otherwise the pipeline following tank pump stopping. a line the normal o p e r a t i n g head on the less than c v /g, 0 along should and subsequent should be successively higher. cv /g, I n cases where the head on the theory may i s considerably less than r i g i d water column be used to c a l c u l a t e the discharge from the t a n k : Integrating expression f o r Multiplying yields the Equ. 4.1 twice with respect column to time, one obtains an the distance the water distance by travels before stopping. the pipeline is this the cross sectional by the the tank; area of 0 the volume discharged sectional tank one, area of Q = APv 2/2gh, where A cross pipe, P is the distance between the or the next tank measured below if the discharge there is a n d the open end of and h is the the p i p e l i n e , the tank head on h y d r a u l i c g r a d e l i n e ( o r level of the next t a n k ) . Fig. a 4.13 of depicts the of the volume discharged from a the tank expressed as fraction discharge the g r a p h indicated by r i g i d column equation. a computer analysis The coordinates using elastic the head, were obtained from water hammer theory. at the tank is less I t i s i n t e r e s t i n g to note that when than by approximately h, is 0.5 cvo/g, and heads the discharge hammer column accurately predicted low. less r i g i d column successively and that theory, higher the water rigid overpressures theory are For becomes increase. exceeds applicable water hammer from overpressures a I t appears, that however, by the discharge column tank never indicated rigid water theory, p r o v i d e d the conditions discussed below a r e compl ied w i t h . 81 Fig. tank 4.13 i s only to a p p l i c a b l e f o r a s i n g l e tank along the line. The i s assumed be a t the pump end of the p i p e l i n e , o r else there immediately valve, upstream (on the pump would should be an side) of the in-line tank. reflux valve Without this reflux a p o s i t i v e wave r e t u r n from the tank towards the pumps. I n a d d i t i o n to water hammer the discharge from the overpressures which would r e s u l t a t the pumps, tank would exceed that f o r the assumed case where i t o n l y discharged The maximum overpressures indicated by the c h a r t occur downstream. along h' is the p i p e l i n e on measured of above the d i s c h a r g e side of the tank. the the discharge head, and is The overpessure expressed as a fraction cv / g . If upstream r e f l u x valve i s omitted F i g . 4.14 should be used. For peaks, line. very more The long than pipelines one with a number may the of be successively installed higher the discharge tank along tanks is should be likeliest. as i n s t a l l e d at lowest peaks where which water column occur line at any separation The head will p o i n t beyond a tank the downsurge t r a v e l s along the i s that of the water surface elevation of the preceding t a n k . Fig. along first valve second of it. Fig. between and for the a tank 4.15 indicates The at the chart the discharge from two tanks installed the pipeline. is is also o n l y appiicable line, of or provided else located be pump end of immediately a reflux the a reflux The should tank installed also upstream valve the tank. should have immediately upstream 4.15 the is really is of only applicable to the for cases where the distance tank tanks end length equal distance between however, the second open the ratios pipeline; and Fig. the c h a r t s be hardly vary different 4.15 could used a s a g u i d e f o r other cases. in and Fig. 4.15 tank, and h, is the difference the in elevation between the first the The second tank and the h2 i s difference i n elevation between second head at the discharge end of that between the the p i p e l i n e . two tanks corresponding is that pipe the length t 1 is tank and J? 2 between second a n d the discharge tank tank is is end of the pipelines lines. the line. and The The the discharge discharge h from the f i r s t from the are second indicated by indicated broken full by relevant and e substituted i n the v a l u e i n d i c a t e d on 82 tc 08 06 O L 9 h' c vo 0 2 0 10 08 Q ?gh __ A LV,' 06 OL 0.2 0 0 Fig. 4.13 D i s c h a r g e f r o m t a n k a n d m a x i m u m head r i s e w i t h i n - l i n e r e f l u x v a l v e u p s t r e a m of t a n k . 83 F i g . 4.14 Discharge from tank a n d maximum head r i s e (no in-line r e f l u x v a l v e ) . F i g . 4.15 Discharge from two t a n k s a n d maximum head r i s e ( e l = @ a n d r e f l u x v a l v e upstream of each tank). 2 85 v e r t i c a l scale to o b t a i n the respective discharge Q from each t a n k . The maximum overpressures i n d i c a t e d b y F i g . 4.15 i n the downstream side of the second tank. limit the lateral extent of I t is, i n v a r i a b l y occur however, possible to location of a end of the the overpressure b y j u d i c i o u s the last tank and the further the reflux valve In between delivery pipeline. hammer the tank t h i s case the r e f l u x v a l v e on could then possibly exceed should be dispensed the pump s i d e of with. the water from water tank may The discharge chart, on the and a theory that be indicated b y out hammer analysis carried based out1 ined e a r l i e r i n the chapter. The best p o s i t i o n f o r selected by trial and discharge error and tanks and i n - l i n e For ref l ux valves i s simple cases the experience. c h a r t s presented may suffice, or major pipelines with b u t f o r complex friction cases w i t h many peaks a complete analysis In parti- large heads, should cular, be c a r r i e d out, a final check either graphically o r b y computer. should be done f o r flows less than the maximum design c a p a c i t y o f the p i p e l i n e . Even though a number of tanks may be i n s t a l l e d along a p i p e l i n e , vaporization tanks. steeply water on is always there tanks, possible no along rising and sections the between the Provided between are local peaks, l i ne rises f a i r l y not lead to this I imited v a p o r i z a t i o n However, are air should hammer overpressures. rising sections. vessels should be i n s t a l led where vaporization and all Cases known vapour bubbles t r a v e l l i n g along g e n t l y r i s i n g mains have r e s u l t e d i n severe c a v i t a t i o n of a l i n e a l o n g the top of the pipe. A i r Vessels If tank force the or p r o f i l e of discharge into air in a tank pipeline to is not the high line, enough it to use a surge to protect may be possible water the in a p i p e b e h i n d the vessel The (a low-pressure air wave b y means of arrangement will is compressed illustrated typical vessel Fig. 4.16). pressure i n the vessel gradually decrease as water that in the i s released u n t i l line. At the pressure i n the vessel equals stage the decelerating the outlet be of water the a i r adjacent tend be to this column vessel will reverse. However, the whereas inlet should unrestricted, should throttled. A 86 suitable reflux arrangement valve, which is to have the water the discharge out through a shuts when water column reverses. A smaf I - o r i f i c e bypass would a l l o w the vessel to r e f i l I slowly. Fig. 4.16 A i r vessel Parrnakian be ( 1 9 6 3 ) suggests that the outlet head the a i r vessel inlet head loss should i s em- 2.5 times loss. However, t hi s relationship pirical effect vessel ratio a n d recent of the inlet research w i t h the a i d of computers has enabled the head loss to be by to i n v e s t i g a t e d thoroughly. parrnakian forward The a i r the to design of charts flow has reproduced head loss were compiled f o r head loss an equal reverse author flow 2.5. The compiled design charts covering extended r a n g e of to 4.19). p i p e l i n e s a n d v a r i o u s degrees of i n l e t t h r o t t l i n g ( F i g s . 4.17 The c h a r t s a r e s u i t a b l e f o r checking water column separation a n d f o r r e a d i n g off the r e q u i r e d a i r corresponding to any specified a l o n g the e n t i r e p i p e l i n e length, volume and degree of inlet throttling l i m i t to the overpressures. The c a l c u l a t i o n s for er; lies it was assumed that adiabatic Outflow t h r o t t l i n g i s neglected. p l o t t i n g the c h a r t s were performed b y computthe expansion law f o r and the a i r the i n the vessel between (HS 1.4 - constant) isothermal (HS = Fig. 4.17 Maximum a n d minimum pressure envelopes w i t h a i r vessel. 2 = 0.5. F i g . 4.18 M a x i m u m and m i n i m u m p r e s s u r e e n v e l o p e s w i t h a i r vessel. P = 1. 88 constant). further pumps, flow The relationship adopted was HS1'3 = constant. It was assumed t h a t t h e a i r vessel t h a t the pumps would stop was i m m e d i a t e l y d o w n s t r e a m of t h e instantaneously and that no reverse t h r o u g h the pumps was permitted. dimensionless parameters associated with the charts are The fol l o w s : as Pipeline parameter A i r vessel parameter Throttling parameter where S i s the initial air volume P = c v /gH 0 0 B = v 0'AL/gHoS C = Z/Ho in the vessel, and 2 i s the head 0- loss t h r o u g h t h e a i r vessel i n l e t c o r r e s p o n d i n g to a l i n e v e l o c i t y -v assumed to The outlet head loss was be negligible. Note t h a t Ho i s the absolute head ( i n c l u d i n g atmospheric head) i n t h i s case. 0.2 I Fig. 4.19 Maximum a n d minimum pressure envelopes P = 2. with a i r vessel. The c h a r t s a r e u s e d a s f o l l o w s to d e s i g n a n a i r v e s s e l : line parameter, P, The p i p e - i s c a l c u l a t e d from the maximum l i k e l y line velocity 89 and pumping to 4.19. head, and the corresponding chart selected from Figs. 4.17 T h e p i p e l i n e p r o f i l e i p l o t t e d on the a p p l i c a b l e set of s curves a n d a minimum-head fall The below value the The the of pipeline envelope selected at to minimum-head it does not such that to cause line is profile any the point selected vaporization. used the B corresponding to read off maximum-head overpressures envelope a l o n g the p i p e l i n e from actually depend on design the degree of i s to equal same c h a r t . throttling inlet represented b y C. The normal procedure minimize the overpressures, to a achieved b y s e t t i n g C approximately of m, 10 ( o r more). pumping head ( F o r a p i p e l i n e velocity of to the be order l/lOth of of approximately the 2 m/s a n d inlet I f the will be 200 the corresponding diameter works out main be pipe diameter). tolerated, it overpressures necessary to indicated select a thus still value cannot of smaller B (corresponding to a larger volume of a i r ) The volume than i n d i c a t e d b y the minimum pressure requirement. of air, S, i s c a l c u l a t e d once B i s known. The vessel c a p a c i t y should line, be s u f f i c i e n t to ensure no a i r escapes volume. This i n t o the pipei s the volume a n d should exceed the maximum a i r d u r i n g minimum pressure conditions a n d i s S ( H /Hmin) The outlet diameter is usually designed to 1/1.3 the be about one-half main p i p e diameter. suppress dissolve vortices in The outlet should be designed w i t h a bellmouth to air entrainment. The air in the vessel will and the water to some extent and w i l l h a v e to replenished b y means of a compressor. In-L ine R e f Iux V a Ives Normally not al a reflux valve i n s t a l l e d on i t s own in a pipeline w i l l the later- reduce water extent of of the hammer pressures, shock. In fact, in a if although in some i t may limit situations indiscriminate to water positioning reflux For the valves l i n e could be detrimental hammer pressures. led instance a pressure r e l i e f v a l v e was i n s t a l the may reflux also valve amplify would counteract from upstream of effect of the reflux valve It the other valve. reflections b r a n c h pipes o r collapse of vapour pockets. In-line surge down, side of reflux valves would tanks n o r m a l l y be used or air vessels. i n conjunction pump with tanks, the discharge or Following into the shut- tank vessel valve. would This discharge would water the p i p e e i t h e r violent pressure the reflux alleviate 90 drop valve a n d convert the phenomenon i n t o a slow motion effect. would then arrest the water column at the time of The reflux reversal, which coincides w i t h the p o i n t of m i n i m u m k i n e t i c energy and maximum potential energy of in the water column. There would therefore be little momentum change the water column when the r e f l u x v a l v e shut and consequently n e g l i g i b l e water hammer pressure r i s e . There a r e s i t u a t i o n s where water column separation and the format i o n of be in vapour pockets provided i n the p i p e l i n e f o l l o w i n g the vapour pockets d i d pump stoppage would not collapse resulting tolerable, water hammer pressures. Reversal of the water column beyond the reflux valve column vapour at the pocket could i n fact be prevented w i t h an i n - l i n e of the vapour pocket. downstream extremity be arrested at the water so would i t s p o i n t of minimum momentum, there would be l i t t l e head rise. Vaporization water If the hammer first the would occur at peaks in the pipeline where the pressure dropped to rise along the wouJd the vapour was pressure of higher to the than first the water. subsequent peak. The pipeline be peaks, extent theory. vaporization vapour confined be of the pocket could estimated using rigid column The decelerating the last peak head on and the water column between two peaks would be the d i f f e r Integrating an o r between ence the the discharge end in e l e v a t i o n p l u s the intermediate f r i c t i o n head loss. rigid water column equation with respect pocket, to t, one o b t a i n s expression f o r the volume of a vapour k?AvoZ/2gh, where h i s the decelerating head, cross sect iona I In lateral at a locating area. the C i s the water column l e n g t h a n d A i s the p i p e valve, allowance should be made f o r some reflux dispersion of the vapour pocket. i n the p i p e l i n e functioning The v a l v e should be i n s t a l l e d to trap the vapour pocket the water suitable dip to ensure i n order and proper of the v a l v e doors when column r e t u r n s . A small-diameter permit slow bypass to the r e f l u x v a l v e should be i n s t a l l e d to pocket, or r e f i l l i n g of the vapour else overpressures may should be air release occur on of the restarting of the pumps. of The diameter of the bypass the pipeline diameter. An order one-tenth 91 valve should be i n s t a l l e d in the p i p e l i n e a t the peak to release a i r which would come out of solution d u r i n g the p e r i o d of It low pressure. i s a common p r a c t i c e to i n s t a l l r e f l u x v a l v e s immediately downof the pumps. in and Such the reflux valves They would not prevent water stream hammer through pumps. In pressures the pump pipeline. merely prevent r e t u r n flow r e a c h i n g the prevent water hammer pressures some pump installations, automatically closing control valves, instead of r e f l u x valves, Kinno delivery to a r e i n s t a l l e d on the pump d e l i v e r y side. the a effect of c o n t r o l l e d closure return water flow through of a pump pump can (1968) valve. studied Assuming he limited how the be tolerable, describes hammer overpressures be s l i g h t l y reduced b y c o n t r o l l i n g the r a t e of closure of the v a l v e . Release Valves There are a number of sophisticated water hammer release v a l v e s (often r e f e r r e d to as surge r e l i e f a b l e commercial l y . matically The pipe in open are These valves gradually the v a l v e s o r surge suppressors) a v a i l - have h y d r a u l i c actuators which autoclose needle the valve after pump tripping. into a then valves leading normally type, or which discharge valves, to the suction r e s e r v o i r , reservoir. complete The range else sleeve mounted throttling valves the suction over the v a l v e s must of closure. have a gradual Needle a n d effect are with sleeve suitably the designed to minimize c a v i t a t i o n discharge velocities which a n d corrosion associated d u r i n g the t h r o t t l i n g high occur process. The v a l v e s a r e u s u a l l y reflux should valves not and i n s t a l l e d on directly suction to the d e l i v e r y side of the pump the suction as they reservoir. They discharge into the discharge pipe i n v a r i a b l y draw a i r through the throat, and t h i s could reach the pumps. by an e l e c t r i c a l fault or b y a pres- The v a l v e s may be actuated sure sensor The returns on (as Fig. 4.20). should pumps open as a valve to the fully before the negative wave. pressure wave p o s i t i v e pressure As the pressure the top of the piston pressure increases a g a i n within the v a l v e g r a d u a l l y closes, limits. The closing rate maintaining the desired may be a d j u s t e d b y a p i l o t v a l v e i n t h e h y d r a u l i c c i r c u i t . 92 Reflux Pump valve Acc u mu lot or Suction Fig. reservoir 4.20 Water hammer release h y d r a u l i c actuator valve arrangement with simp1 i f i e d The returns on valve to the should pumps open as a fully before the negative wave. pressure wave positive pressure As the pressure the top of t h e p i s t o n the pressure increases a g a i n within desired the v a l v e g r a d u a l l y closes, The closing rate maintaining I i m i ts. may be a d j u s t e d by a p i l o t v a l v e i n the h y d r a u l i c c i r c u i t . If no overpressure higher than the operating the f u l l is head at is a tolerable, head equal and if the v a l v e to the would be sized head. likely to discharge Where to be flow of operating hammer pumps, is reliability a problem importance, partial installed lower water of the during may be shutdown i n paradelivery t w o or more release valves set to llel. heads. In They could be operate at successively the event of normal pump shutdown a g a i n s t throttled delivery valves, at ion. the release v a l v e s could be disengaged to prevent t h e i r oper- The types of ing use This lines is control v a l v e s a v a i l a b l e as release valves f o r pumpin less than over is about f i v e seconds. Their kilometers most in n o r m a l l y cannot open limited water to therefore of pipelines two length. method hammer protection normally economical 93 for cases when the pumping head greatly exceeds cv /g, since the l a r g e r the pumping head, Since hammer there analysis is no the smaller the v a l v e needed. protection be against to underpressures, check that water a water column should performed separation i s not a problem. A above, less sophisticated has been valve used than on the control pump valves described is the which small installations, spring-loaded sure reaches release v a l v e . a prefixed The v a l v e i s set to open when the pres- maximum. Some overpressure i s necessary to open the v a l v e a n d to force water out. Choice of Protective Device The will best method on the of water hammer and protection physical for a pumping of line the depend The hydraulic table characteristics the ranges over system. accompanying summarizes which v a r i o u s devices a r e s u i t a b l e . ting When valve values tank the method of protection The most i n f l u e n t i a l parameter i n seleci s the p i p e l i n e parameter P = cvo/gHo. the pumping head Ho, a reflux smaller the head cvo/g bypassing of i s g r e a t e r than pumps may the suffice. to For successively a P it becomes necessary use a surge t a n k , discharge i n combination w i t h an i n - l i n e r e f l u x v a l v e , The protective order of a n a i r vessel, o r a release v a l v e . in approximate devices l i s t e d i n the t a b l e a r e a r r a n g e d cost, thus, until to increasing down select the most are suitable device, one checks the table the variables w i t h i n the r e q u i r e d range. It may line. be possible to use two o r more p r o t e c t i v e devices on not the same omical In This p o s s i b i l i t y should be ignored as the most econ- arrangement often the i n v o l v e s more than one method of protection. i n e r t i a of the of pump a often has a slight A particular in rotational the effect reducing required capacity tank or a i r vessel. comprehensive water hammer analysis would be necessary i f a series of protection devices i n combination i s envisaged. 94 TABLE 4.1 Summary of methods of water hammer protection Method of Protection ( i n approximate order of increasi n g cost) Required r a n g e of v a r i a b I es Remarks I n e r t i a of pump MN* wALHo2 > 0 * 0 1 Approxi mate on I y Pump bypass reflux valve Some water may a l s o be d r a w n through pump cv Normally used i n conj u n c t i o n w i t h some other method of protection. Water column separation possible P i p e l i n e should be n e a r h y d r a u l ic g r a d e l i n e so height of tank i s Dractical P i p e l i n e p r o f i l e should be convex downwards. Water column separation l i k e l y . In-line reflux va I ve __ gh 0 > 1 Surge tank h small Automatic release valve D i scharge tanks cv 0 > ' gh h = pressure head a t t a n k , p i p e l i n e prof i l e should be convex upwards P i p e i ine p r o f i l e p r e f e r a b l y convex downwards A i r vessel o __ < gHO cv l 95 REFERENCES Kinno, H. and Kennedy, J.F., 1965. Water hammer charts for c e n t r i f u g a l p u m p systems, P r o c . Am. SOC. C i v i l E n g s . , 91 (HY3) 247-270. Kinno, H. ,1968 W a t e r h a m m e r c o n t r o l i n c e n t r i f u g a l p u m p s y s t e m s , P r o c . Am. SOC. C i v i l E n g s . , 94 (HY3) pp 619-639. L u d w i g , M. and Johnson, S.P., 1950 Prediction of surge pressures i n l o n g o i l t r a n s m i s s i o n l i n e s , P r o c . Am. P e t r o l e u m I n s t . , N.Y. 30 . (5). L u p t o n , H.R., 1953 G r a p h i c a l a n a l y s i s o f p r e s s u r e surges in pumpi n g s y s t e m s , J . ~ n s t . W a t e r E n g s . , 7. P a r m a k i a n , J . , 1963. W a t e r Hammer A n a l y s i s , D o v e r P u b l i c . I n c . , N.Y. R i c h , G.R., 1963. H y d r a u l i c t r a n s i e n t s , D o v e r p u b l i c s . I n c . , N.Y. and L a i , C., 1963. W a t e r h a m m e r a n a l y s i s i n c l u d i n g Streeter, V.L. f l u i d f r i c t i o n . P r o c . Am. SOC. C i v i l E n g s . , 88 (HY3) pp 79-112. Streeter, V.L. and Wyl ie, E.B., 1967. H y d r a u l i c T r a n s i e n t s , McGrawHill. D., 1966. W a t e r h a m m e r c h a r t s i n c l u d i n g f l u i d f r i c t i o n , Stephenson, P r o c . Am. SOC. C i v i l e n g s . , 92 (HY5) pp 71-94. Stephenson, D., 1972. D i s c h a r g e t a n k s f o r s u p p r e s s i n g w a t e r h a m m e r i n p u m p i n g l i n e s . P r o c . I n t n l . Conf. o n p r e s s u r e surges,B.H.R.A., C r a n f ie l d. Stephenson, D., 1972. Water hammer p r o t e c t i o n o f p u m p i n g l i n e s , t r a n s . S.A. I n s t n . C i v i l E n g s . , 14 ( 1 2 ) . . L I S T O F SYMBOLS A B - p i p e cross sectional area a i r vessel p a r a m e t e r v 'AL/(gHoS) 0 c d E F - t h r o t t l i n g p a r a m e t e r Z/H p i p e l i n e diameter modulus of e l a s t i c i t y of p i p e w a l l m a t e r i a l pump rated efficiency Darcy friction factor g r a v i t a t i o n a l acceleration p r e s s u r e h e a d a t an i n t e r m e d i a t e s e c t i o n o f t h e p i p e l i n e water hammer h e a d r i s e measured above the d e l i v e r y h e a d f r i c t i o n h e a d loss h e a d loss t h r o u g h d o w n s t r e a m v a l v e f u l l y o p e n head (in in ( e x p r e s s e d as a f r a c t i o n ) f 9 - h - h' hf H - he - p i p e l i n e measured air above pump suction reservoir H as absolute, i.e. level plus c a s e of vessel design, take atmospheric head) Ho I J p u m p i n g head above suction r e s e r v o i r level p u m p i n e r t i a p a r a m e t e r MN'/WALH 0 0 ' p u m p p a r a m e t e r F M N Z c / l 80wALv gH 0 K - b u l k modulus of water length of an intermediate p a r t of p i p e l i n e pipeline length moment of inertia of rotating p a r t s of pump, motor and en- e L - M N P - t r a i n e d water ( = mass x r a d i u s of g y r a t i o n ' ) pump speed i n rpm p i p e l i n e parameter cv /gh 0 0 Q - volume of water discharged from discharge tank volume of a i r i n i t i a l l y time l i n e a r v a l v e closure time water v e l o c i t y i n p i p e l i n e i n i t i a l water velocity in pipeline i n a i r vessel s t - T v v w - weight of water per u n i t volume distance a l o n g p i p e l i n e from pump wal I thickness o f p i p e head loss through a i r vessel Darcy f r i c t i o n factor i n l e t f o r p i p e l i n e velocity = x Y - z - 97 CHAPTER 5 A I R IN PIPELINES INTRODUCTION It The flow or is recognised that air is present in or many water in pipelines. turbulent solution a i r may be absorbed at at the entrance to the free surfaces, line. The air An entrained thus be may air in i n free form large section. will i n bubbles or of pockets. to pocket implies a r e l a the pipe tively cross volume air, likely accumulate on top of along the The pockets may remain in travel l i n e to peaks. There they either equilibrium, be e n t r a i n e d by the f l o w i n g water or be released through a i r valves. Air It air i n solution when i s not likely to present many engineering problems to permit i s only to the pressure reduces s u f f i c i e n t l y that problems may arise. dissolved form bubbles The The water and rise then b u l k s a n d head to losses the to increase. to in bubbles coalesce the top of pipe those form large full pockets. drain Flow pipes, conditions except become s i m i l a r a pipeline it partly that in i s l i k e l y that the system, i n c l u d i n g the free a i r , w i l l be pressurized. Air on also the top valves are frequently of the to used to e l i m i n a t e the a i r of a slightly of which collects design filling are of pipe. release Air valves different during the used large air quantities air l i n e a n d to draw i n from the atmosphere d u r i n g vacuum con- d i t i o n s i n the line. PROBLEMS O F A I R ENTRAINMENT Air fects. drawn in through a pump air supply in can have can a number of ef- Minute a i r bubbles o r vacuous solution which promote c a v i t a t i o n rapidly col- - the formation of lapse and erode lers in particular cavities subsequently the pump o r pipe. due in to in the T h i s effect occurs i n pump impelperipheral cause speed which by lowers causing high pressures. Air drawn gulps can vibration flow to be unsteady. 98 Large quantities intermittent1 - -__ - a. Low level sump I- i Air e n t r a i n e d by a falling jet o I ' * 1 + To pump Air enters intake b. Free fall into sump __1- ____ ---+ c . Vortex formation FIG. -=-+ Well define surface dimple . 4 Surface dimple barely detectable Air drawn intermittent ly from bottom of vortex into intake Air core extends into intake (fully developed entraining vortex) 5.1 Inlet arrangements conducive to a i r entrainment. 99 Air emerge i n a r i s i n g main, from solution if whether ambient i n s o l u t i o n o r i n b u b b l e form, pressure the top of or temperature may i s reduced. Air in free form w i l l collect a t the p i p e l i n e and then r u n u p to h i g h e r points. vent air the pipes o r pocket Here i t w i l l e i t h e r escape through a i r v a l v e s o r by the velocity will result of the water past the be washed along The in the pipe. latter past i n a head loss due to Even if air is in acceleration of the water the a i r pocket. b u b b l e form, pipeline w i l l may dispersed increase. i n the water, the f r i c t i o n head loss a l o n g the Other problems caused b y a i r present i n pipes corrosion, reduced pump e f f i c i e n c y , malfunction- include surging, i n g o f v a l v e s or v i b r a t i o n s . Air water, size may in be present in the form or of in pockets solution. on the top of the bubbles, micro bubbles Bubbles range in from is 1 to so 5 mm. slow Micro bubbles may mm be smaller, and t hei r r i s e mm velocity mm/s) rising (e.g. in 1 bubble, for 90 rnm/s, a 0.1 bubble, 4 that to they stay suspension considerable time before the surface. I n fact turbulence that may create a n e q u i l i b r i u m sediment s t a y s i n suspen- concentration p r o f i l e i n the same way sion i n f l o w i n g water. w = dgZ/18 v The r i s e velocity of small a i r bubbles i s (5.1 1 where the kinematic viscosity v of water a t 20 C i s 1.1 x 10-6m2/s, d i s b u b b l e diameter a n d g i s g r a v i t a t i o n a l acceleration. For air bubbles to form readily a nucleus or uneven surface should be present. be released on by from the Then when conditions a r e correct, The capacity of At water air will rapidly to solution. dissolve air depends temperature and pressure. standard 20 C water may absorb pressure. This 2% a i r volume measured a t atmospheric f i g u r e v a r i e s from 3.2% at O°C down to 1.2% a t looo. AIR INTAKE A T PUMP SUMPS The major source of a i r i n pumping lines i s from the i n l e t sump o r forebay. Here the water exposed to the a i r on its temperature, will absorb a i r a t a r a t e of saturation of depending the water. pressure a n d degree 100 a. Air pocket w i t h s u b c r i t i c a l flow past. b. Air pocket w i t h super-critical flow past. c. A i r pocket Air in e q u i l i b r i u m position. pockets in pipelines. F i g . 5 .2 101 Air flowing in free form The may also be of dragged a vortex in or to the conduit by the the water. formation drawdown outside suction p i p e entrance w i l l entrance likely to velocity be and in. the entice a i r greater free i n t o the conduit. the turbulence, may later The h i g h e r the more air is or the drawn This air dissolve wholy partially carried when along pressures increase beyond the pump. the conduit. As I n any case i t i s it may be pressures again reduce, released from solution. The the configuration to of the pump sump has an important b e a r i n g on tendency draw in air. Extensive studies b y Denny a n d Young i n d i c a t e d how to design sumps (1957), Prosser to (1977) and others have intake. minimize a i r C i r c u l a t i o n i n the sump should be avoided b y and straight facing inflow. The inlet should be concentric be1 lmouthed approaches and preferably downwards upstream. Hoods ( s o l i d or p e r f o r a t e d ) above the i n t a k e minimize a i r intake. The degree of submergence hydraulic should jumps be are as to great be as possible. Fig. Air 5.1 entraining drops . o r avoided. indicates some i n l e t arrangements to be avoided. AIR ABSORPTION AT FREE SURFACES The rate of diffusion of gas across a liquid interface can be expressed i n the form -dM _ dt - AK (Cs- C) (5.2) transfer per u n i t time t, where M i s the mass r a t e of exposed, Cs A i s the area K is a l i q u i d f i l m constant, saturation. C i s the gas concentration a n d is the concentration a t K is a f u n c t i o n of temperature, v i s c o s i t y a n d turbulence. T h i s equation i s often w r i t t e n i n the form (5.3) where r i s the d e f i c i t r a t i o , Co i s the concentration a t time 0, i s the volume of water per surface area A ( V / A = depth of water). and V 102 HYDRAULIC REMOVAL OF A I R Air trapped the in a p i p e and allowed to pocket size. The water accumulate, cross will gradually area will increase air sectional therefore d i m i n i s h a n d the velocity of the water w i l l some stage, the water. some o r a l l of Alternatively air and a increase u n t i l at the a i r w i l l be dragged along the l i n e b y hydraulic i t away jump may form as in the pipe in entraining F i g . 5.2 The pipe carrying i n b u b b l e form, depicted relationship has between been a i r pocket volume, by a washout velocity workers, and and diameter investigated number of (1975). these r e s u l t s a r e summarized by Wisner et a l Kal inske a n d B l i s s (1943) produced the f o l l o w i n g equation f o r r a t e of water flow Q at which removal commences: 5 Q2 gD = 0.707 tan e (5.4) where D i s the p i p e diameter and g i s g r a v i a ional acceleration and e i s the p i p e slope angle. The term on the l e f t h a n d side of K a l i n s k e ' s the parameter and removed equation energy i similar s diagrams that to in the In specific fact it momentum a n d points drops to (Figs. the air 5.3 is 5.4). if the possibility critical. air. Wisner air the water depth below Then a h y d r a u l i c jump forms downstream which could e n t r a i n et al (1975) produced d a t a from which They the r i s e velocity of i s practically pockets may be deduced. slope and air i n d i c a t e r i s e velocity independent of is a function of Reynolds number vD/v and r e l a t i v e volume of (see F i g . pocket 4U/71D3 where U i s the a i r pocket volume 5.5) Hydraulic A Jumps hydraulic jump draws in air in the form of bubbles. These bubbles e x h i b i t a s u r p r i s i n g l y low tendency free form f o r the water, a long time. to coalesce a n d remain i n the bubbles by A i r may be absorbed from b u t t h i s takes a long time a n d many of the bubbles r i s e to the surface before they a r e absorbed. 103 104 1 > 1o2 = VD/v Fig. 5.5 E q u i l i b r i u m velocity of water f o r at l o 0 to 70° to the h o r i z o n t a l . air pockets in a pipe Kalinske rate of and air Robertson entrainment (1943) at a found from model experiments that hydraulic jump was given by the the equation Qd/Q = 0.0066(F1 - 1)le4 volumetric r a t e of upstream a jump air entrainment, number (5.5) where flow Qd rate is the Q i s the water I and F1 is the Froude vl//gyl. That r e l a t i o n s h i p was d e r i v e d f o r free surface downstream. greater air i n a r e c t a n g u l a r channel w i t h a by the author pipes indicate a Experiments entrainment considerably 5.6) rate i n closed (see Fig. Free F a l l s A jet falling free into a pool of water has a s i m i l a r air intake 105 effect was to a hydraulic by Avery they jump. Oxygen i n t a k e at the base of initial up free f a l l s studied a n d Novak (1978). a For an r a t e of oxygen defik g 0 /kWh ciency of for m 50%, head found a e r a t i o n at for to 1.6 losses, 2 low head losses, the decreasing higher was or head e.g. at 1 kW loss aeration the efficiency expended this only lost 1 in k g 02/kWh. the jump The term represents energy in air, or fall. for Assuming 21% oxygen would indicate aeration rates a i r u p to 8 kg/kWh. Water flowing into inlets with a free fall e.g. morning glory type s p i l l w a y s , able amount of o r even siphon s p i l l w a y s w i l l a l s o e n t r a i n a consider- air (Ervine, 1976). Gravity pipelines are therefore as much of a problem as pumping lines. 0 Fig. 2 4 6 F: ~ v J3A/B 5.6 A i r removal a t h y d r a u l i c jumps in c i r c u l a r conduits. A I R VALVES Air valves. fices air accumulating These up are to in a pocket of in a pipe may be released b y type air normally mm the 'small orifice' (typical orisufficient released are is 3 i n diameter). a chamber The v a l v e opens when to permit a ball to be accumulated in from a seat around the o r i f i c e . On the other hand a i r discharge d u r i n g f i l l i n g operations (before 106 This sectio parallel t o hydraulir gradient constitutes1 peak Section Of pipeline running parallel t o hydraulic gradient and constitutes peak Section of pipeline forming peak with respect t o horizontal and 0150 t o hydraulic gradient and peok with respect t o hydraulic gradient only No peok Horizontal Section Of Pipeline having d w n w a r d grade and point of increaseof downward grade Datum Section of pipeline having upward grade and point of decrease of upward grade Scour Horizontal Long descending section of pipeline Datum Long ascending section of pipeline FIG. 5.7 P o s i t ~ o no f a i r valves along pipelines 107 pressurization) may be through from is low. and air i n t a k e d u r i n g vacuum conditions a i r valves, the orifice the b a l l of when air in the p i p e i s rethe a 'large orifice' seat around which leased pipe the Fig. pressure valve inside 10.6 illustrates a double with both small and a l a r g e o r i f i c e . The sures size a n d spacing of outside the pipe and a i r valves w i l l permissible depend on ambient presinside, the size pressures of p i p e a n d water flow rates. The equations for the air discharge r a t e and are as through an orifice 1951). involve If the the c o m p r e s s i b i l i t y of follows than (Marks, pressure beyond the o r i f i c e p 2 i s g r e a t e r absolute i.e. gauge p l u s atmosphere a n d p, 0 . 5 3 ~ ~a l l ( pressures i s i n i t i a l p r e s s u r e ) , then (5.6) For p 2 ' 0 . 5 3 ~ ~ then pendent of p2. Then the flow becomes c r i t i c a l a n d flow r a t e i s inde- (5.7) where W a is i s the mass r a t e of flow of a i r , rn is the mass C i s a discharge coefficient, of air and the o r i f i c e area, density k is the a d i a b a t i c constant. Normally or out of whether it, p2 is the less air valve is for letting air into the pipe 1.405 than 0 . 5 3 ~ ~ Then . substituting k = for a i r a n d C = 0.5 Qa = 0.34 a i n t o the last equation, i t s i m p l i f i e s to / tne volumetric r a t e of flow of measured air at units are employed) h the initial (5.8) ( i n c u b i c metres p e r pressure, where second a Qa is SI if i s the area of the o r i f i c e , is the i s the i n i t i a l absolute head i n metres density to of air at initial pressure. of water a n d S a Since a i r density f u r t h e r to relative i s proportional the absolute head, t h i s simp i f i e s Qa = lOOa where Qa ( 5 9) is the air volume flow r a t e at initial pressure (+ O m absolute) in m 3 / s a n d a i s in m'. Thus t o r e l e a s e 1% a i r f r o m a p i p e f l o w i n g a t a v e l o c i t y of 1 m/s, low head (10 m absolute being the minimum f o r no vacuum) a n d under t h e n (5.8) 0.01 i.e. thus x r e d u c e s to ~ ~ . _ _ _ 1 m/s x A = 0 . 3 4 a J 9 . 8 x 10/1.15 x lo-’ (5.10) d = 0.006D the o r i f i c e diameter should be about 1% o f the p i p e diameter to r e l e a s e 1% a i r b y v o l u m e i n t h e p i p e . The (1950) cavity metres theory to of flow through for an the orifice flow was used air by Parmakian to f i l l a in derive equations through valves formed b y p a r t i n g water columns. If initial beyond head (absolute) the orifice, g o f water is hl, h2 is is a the head i s gravitational d is the acceleration, diameter, water for C discharge coefficient f o r the valve, orifice of the D i s the p i p e diameter, each a s i d e of the air V i s the r e l a t i v e velocity column valve, k is the then a d i a b a t i c constant f o r h2 > 0 . 5 3 hl, a i r and S i s t h e r e l a t i v e d e n s i t y of a i r , (5.11) a n d f o r H <C).53hl 2- (5.12) For air at 300 m above sea level and 3 air temperatures of 24OC p l u s 20% h u m i d i t y equivalent a b o u t 0.5. t o hl = t h e n Sa 9.97 i s 1.15 x 10- a n d atmospheric pressure i s For a i r valves C m of water. k i s 1.405. is HEAD LOSSES I N P I P E L I N E S Air suspended in b u b b l e form o r in p o c k e t s i n f l o w i n g water will increase t h e s p e c i f i c volume. T h e mean v e l o c i t y i s consequently h i g h e r 109 to convey a c e r t a i n volume of water per u n i t time. The head loss w i l l increase i n accordance w i t h an equation such equation as the Darcy- Weisbach (5.13) The velocity where v W v to use w i l l be v = ( 1 of + f)v W (5.14) i s the volumet- i s the velocity p u r e water f l o w i n g and f r i c concentration o f free a i r i n the pipe. The head loss around a s t a t i o n a r y a loss a i r pocket air i s due p r i m a r i l y to is such that a of velocity head. If the size of pocket h y d r a u l i c jump I f the velocity difference in forms, the head loss may be e v a l u a t e d from F i g . 5.4. i s subcritical velocity head throughout, is lost. It i t may be assumed t h a t the could be established more closely u s i n g momentum p r i n c i p l e s though. WATER HAMMER The water presence of hammer free air in Fox pipelines (1977) can reduce the s e v e r i t y of that the celerity considerably. indicates (speed) of an e l a s t i c wave w i t h free a i r i s c = / * p i s the mass density (5.15) (5.16) For l a r g e a i r contents t h i s reduces to c =where pipe of water, K i s i t s b u l k modulus, D i s the p i s the diameter, b i t s thickness, E i t s modulus of e l a s t i c i t y , absolute pressure and f c i s the free gas f r a c t i o n b y volume. Thus i s reduced r e m a r k a b l y f o r even r e l a t i v e l y low gas contents. air at a pressure head of 50 m of water 2% o f reduces the c e l e r i t y from about 1100 m/s f o r a t y p i c a l p i p e l i n e to 160 m/s. The Joukowsky water hammer head i s A h = SAv 9 (5.17) is the Ah. change in velocity of flow. There i s thus a large where A v reduction in I f the a i r collects a t the top of the p i p e there i s no 110 reason on to see why the same equation cannot a p p l y . Stephenson (1967) the other h a n d d e r i v e d a n equation f o r the c e l e r i t y of a bore i n a The c e l e r i t y d e r i v e d from momentum p r i n c i p l e s i s for partly full pipe. smal I a i r proportions c = J gAh/f (5.18) This indicates a celerity where Ah i s the head r i s e b e h i n d the bore. a n d Ah = 50m. thought a is of 158 m/s f o r f = 0.02 There valves in i s a school of pipelines The as which f a v o u r s the i n s t a l l a t i o n of a i r of reducing to water the hammer impact of overap- means pressures. intention primarily wi II , cushion p r o a c h i n g columns. cessively reduction large in Calculations of air idea in however, indicate that an ex- volume The i s r e q u i r e d to produce any stems from the use of air significant vessels air to in head. a l l e v i a t e water air hammer pipelines. I t will be r e a l i s e d that vessels i s under h i g h pressure i n i t i a l l y a n d therefore occupies a smal I volume. Upon pressure reduction following a pump relatively trip, the a i r from an a i r vessel expands according to the equation (5.19) air. low The size of air v a l v e s to draw i n the be found on puk = constant where U i s the volume of volume of necessary air at (vacuum) pressures w i l l a n a l y s i s to be excessive f o r An unusual l a r g e diameter pipelines. to a i r coming out of solution in problem due possibly a r i s i n g main was reported b y Glass (1980). Here a t h i n stream of a i r along after the a top of trip. the line a supposedly number of collapsed on years the a pressure rise pump After p i p e b u r s t along a l i n e a l o n g the s o f f i t . REFERENCES Avery, S.T. and Novak, P, 1978. Oxygen t r a n s f e r at h y d r a u l i c structures. Proc. ASCE, HY11, 14190, pp 1521-1540. 1957. The prevention o f vortices i n Denny, D.F. a n d Young, G.A.J., intakes. Proc., 7th Con. I n t . Ass. Hydr. Res., Lisbon E r v i n e , D.A., 1976. The entrainment of a i r i n water. Water Power and Dam Construction. pp 27-30. 1977. H y d r a u l i c A n a l y s i s o f Unsteady Flow i n Pipe NetFox, J . A . , works. Macmillan, London. Glass, W.L., 1980. C a v i t a t i o n of a pump p i p e l i n e . Proc. I n t . Conf. Pressure surges. BHRA, Canterbury. 111 K a l i n s k e , A.A. and B l i s s , P.H., 1943. Removal o f a i r f r o m p i p e l i n e s b y f l o w i n g w a t e r , C i v i l E n g i n e e r i n g , ASCE, 13, 10. p 480. K a l i n s k e , A.A. and R o b e r t s o n , J.M., 1943. C l o s e d c o n d u i t f l o w , T r a n s . ASCE. 108, 2205, pp 1453-1516. M a r k s , L.S., 1951. M e c h a n i c a l E n g i n e e r s H a n d b o o k , 5 t h Ed. McGraw H i l l , N.Y. 2235 pp. P a r m a k i a n , J., 1950. A i r i n l e t v a l v e s f o r s t e e l p i p e l i n e s . T r a n s . , ASCE, 1 1 5 , 2404., pp 438-444. P r o s s e r , M.J., 1977. T h e H y d r a u l i c D e s i g n of Pump Sumps and Int a k e s , BHRA, and C I R I A , L o n d o n . 48 pp. Stephenson, 1967. P r e v e n t i o n o f v a p o u r p o c k e t s c o l l a p s e i n a p u m p i n g l i n e . T r a n s . , S o u t h A f r i c a n I n s t . C i v i l E n g s . 9 , ( l o ) , pp 255-261. W i s n e r , P . , Mohsen, F.M. and Kouwen, N., 1975. Removal o f a i r f r o m w a t e r l i n e s b y h y d r a u l i c means. Proc., ASCE. 101, HY2, 11142, pp 243-257. LIST a - OF SYMBOLS orifice area area wal I thickness wave celerity A - b c - c c - d i s c h a r g e coef f i c i e n t gas concent r a t ion i n i t i a l concentration c o n c e n t r a t i o n at s a t u r a t i o n b u b b l e diameter p i p e internal diameter modulus of e l a s t i c i t y volumetric concentration of a i r Froude number g r a v i t a t i o n a l acceleration head a d i a b a t i c constant co cs d D E f - F 9 - h k k - I i q u i d f i Im c o n s t a n t bulk m o d u l u s K m - mass d e n s i t y o f a i r m a s s r a t e o f t r a n s f e r o r s p e c i f i c momentum pressure water discharge r a t e volumetric r a t e of air entrainment gas d e f i c i t M P Q ‘ d r - - ratio 112 s t - r e l a t i v e density o r s p e c i f i c g r a v i t y time a i r pocket volume water v e l o c i t y volume of water p e r surface area r i s e velocity u v - v w - o f bubbles w Y - mass r a t e of flow of a i r depth of flow Darcy f r i c t i o n factor p i p e slope a n g l e k i n e m a t i c viscosity mass density of water x e v P - 113 CHAPTER 6 EXTERNAL LOADS Low large as tion pressure pipes, especially mains sewers, gravity mains or even loads diameter as pumping should be designed f o r e x t e r n a l soil load a c t i n g cause well internal vacuum loads. The v e r t i c a l inside the in combina- with pressure p i p e could the pipe to collapse unless the p i p e i s adequately supported o r stiffened. S O I L LOADS The load transmitted to a pipe from the external surroundings depends on a number of factors: Rigidity sidefill of pipe: The more r i g i d take. a pipe is relative to the trench thus the more load i t w i l l l a r g e p a r t of The s i d e f i l l tends to settle, causing a the b a c k f i l l to rest on the pipe. T h i s occurs w i t h f l e x i b l e p i p e too to some extent, as a p i p e i s supported l a t e r a l l y b y the f i l l a n d w i l l not y i e l d as much as a free s t a n d i n g pipe. Type lation of trench o r f i l l : for Fig. 6.1 i l l u s t r a t e s v a r i o u s possible i n s t a l load transmitted to the p i p e v a r i e s conditions pipes. The w i t h the w i d t h a n d depth of trench since f r i c t i o n on the sides of the load. Embankment f i l l s may on the relative also t r a n s m i t settlement of trench affects the r e s u l t a n t different loads to a pipe, depending s i d e f i l l and topfi I I . Young sive and Trott and and (1984), a n d C l a r k e charts for (1968) have developed soil loads on extenin equations trench evaluating conditions. pipes of various embankment Although many their assumptions a r e subject yet no other to question, the f a c t remains t h a t there i s as theory w i t h which to c a l c u l a t e s o i l loads on pipes so the (ref. Spangler, 1956). engineer must use t h i s theory w i t h d i s c r e t i o n Trench Conditions The s o i l load transmitted to a r i g i d pipe in a trench depends on t h e w i d t h a n d depth of trench a n d the s o i l b a c k f i l l properties. trench (Fig. 6.la), fill at the sides of For a normal vertical-sided 114 the p i p e w i l l be neglected. the sides of trench fill settle more than On the other the pipe, a n d the s i d e f i l l support can the b a c k f i l l a g a i n s t The cohesion between The of h a n d the f r i c t i o n of the load. is the the trench and the takes some of of the sides trench to neglected. coefficient friction friction the developed is therefore proportional between the f i l l active a n d the sides of pressure to the trench, vertical on any a n d the r a t i o K of pressure horizontal in the in horizontal the the soil. the Equating trench to vertical u p w a r d forces slice the downward forces, Marston e v a l u a t e d the total load on a p i p e at depth H ( 1 9 1 3 ) : Upward load per unit length of Pipe a t depth h + ah below ground s u r f ace : W + d W = W + yBdh - 2K t a d Wdh/B Solution g i v e s W = CdyBZ -2K(tane )H/B where t h e load coefficient C d = 2Ktan6 load. K = - r a t i o of l a t e r a l s o i l pressure to v e r t i c a l 1 - s i n 9 f o r a c t i v e s o i l conditions 1 + sin 0 a n g l e of a n d cohesionless soil @ = = i n t e r n a l f r i c t i o n of b a c k f i l l e H B a n g l e of f r i c t i o n between b a c k f i l l a n d sides of trench h e i g h t of f i l l above p i p e trench w i d t h u n i t w e i g h t of b a c k f i l l m a t e r i a l n o r m a l l y ranges from 0.11 Cd = = = Y Ktane for soft c l a y s to 0.16 for sands and coarse crushed stone. Ktan8. Note that i s given i n Fig. (H/B 6.2 for v a r i o u s values for than approximately f o r deep trenches, greater l o ) , Cd approaches a l i m i t i n g v a l u e of 1/(2 K t a n e ) . T h i s implies that takes more of or so the the s i d e f r i c t i o n trench. For i n the trench shallow load the deeper t h e (H/B < l ) , Cd is very wide trenches approximately equal to H/B, W = yHB (6.2) i.e. most of the b a c k f i l l load i s taken b y the pipe. The trench equa- 115 ALTERNATIVE /-FORM SIDE o S R R O W TRENCH b : WIDE TRENCH SHALLOW EMBANKMENT c W I D E TRENCH D E E P EMBANKMENT _- dSHALLOW EMBANKMELT PLSlTlVE PROJECTION c : DEEP POSITIVE -__ EMBANKMENT PROJECTION f : EMBANKMENT NEUTRAL PROJECTION TA2r - - - - - -- - - - --- -g SHALLOW E M B A N K M E N T h: NORMAL DENSITY FILL ---/ __-_.__ ---- N E GAT1VE PROJECT1 ON DEEP EMBANKMENT N E GAT IVE P R O JE CT ION i EMBANKMENT I N D U C E D _R- N C H T E 1 TUNNEL OR H E A D I N G OR THRUST BORE Fig. 6.1 A l t e r n a t i v e backf i I I s 116 tion the indicates trench that the load on a r i g i d p i p e increases i n d e f i n i t e l y as This i s not the case and a t some trench (see width increases. no width the equation then load longer a p p l i e s a n d embankment conditions (see F i g . both the 6.lb next section) evaluate and the the apply trying and 6 . 1 ~ ) . I t i s necessary to criterion (using Fig. to trench Fig. 6.2) that embankment criterion (using 6 . 3 ) , and select load which i s least. In the case of a 'V' trench, the trench width to use i s that at the crown of the pipe. I n t h i s case @ instead of 0 plane is is i n the formula f o r the sides pipe the is Cd of i s used since the shear i n the f i l l not against well compacted pipe and the on the trench. If the then side-fill the load relatively flexible on the depends pipe diameter a n d not to the same extent on the trench w i d t h : W = C YBD (flexible pipe) d C d = H/B and i n t h i s case (6.3) Note that f o r small H, W = YHD Embankment Conditions A p i p e bedded on a f i r m surface w i t h a wide embankment f i l l over it is said to be under embankment original 6.le). is conditions. ground It is If the it to crown is as a a of the pipe projects above the level referred positive complete above If projection positive natural (Figs. projection 6.ld) if and the and pipe the rigid and is lies completely ground level, embankment relatively shallow. the p i p e crown projection or i s below the n a t u r a l ground (Figs. 6.lg level one has a negative For very deep trench condition and 6 . l h ) . trenches u n d e r embankments t h e conditions may be the same as f o r the trench If the condition crown is ( r e f e r r e d to level with here as the complete trench c o n d i t i o n ) . ground level it i s a neutral the n a t u r a l projection For tends to the to (Fig. 6.lf). complete positive projection case the f i l l beside the p i p e tends s e t t l e more than downwards on the directly fill above the pipe. above The s i d e f i l l drag directly the p i p e and increase the load on the pipe. W = The r e s u l t i n g load per u n i t l e n g t h of p i p e i s CcyD2 117 where the load coefficient e cc = 2K tan@. / D H 2Ktan@ -1 LOAD COEFICIENT C , F i g . 6.2 Load coefficient C d f o r trench conditions. The l i n e v a l u e of condition C l a b e l l e d complete p r o j e c t i o n condition for Ktan@ = 0.19, in F i g . 6.3 g i v e s the which i s the minimum adverse f r i c t i o n only a c e r t a i n h e i g h t of f i l l . For deep embankments, above the p i p e w i l l s e t t l e at a d i f f e r e n t r a t e to the s i d e f i l l . depends on the product He, settlement r a t i o s where This height, ratio u of the pipe projection and the u = projection of p i p e crown above o r i g i n a l ground level diameter of p i p e 118 s = settlement of adjacent f i l l o r i g i n a l l y at crown levelsettlement of p i p e crown reduction i n thickness of adjacent f i l l below crown level of adjacent fill includes the settlement of the o r i g i n a l The settlement ground level a n d the compaction of includes settlement of the s i d e f i l l . The settlement of the the p i p e crown the bottom of p i p e and v e r t i c a l deflection of the pipe. The v a l u e of tion value well soil to 1.0 s n o r m a l l y v a r i e s from 0.3 for rock or unyielding for soft y i e l d i n g foundafoundation. soil A common i s 0.7 b u t 0.5 The i s recommended i f the foundation a n d s i d e f i l l a r e product for su is used i n F i g . 6.3 to e v a l u a t e the I t i s not compacted. resulting load coefficient v a r i o u s embankment conditions. necessary to e v a l u a t e H The equation for C . for deep embankments a n d incomplete p o s i t i v e projection conditions ment (i.e. condition, minimum but i s more compl icated than f o r the shal low embankit was e v a l u a t e d by Spangler f o r friction) condition, and Ktan4 = 0.19 adverse these values are g i v e n i n F i g . 6.3. Fig. the pipe 6.3 also gives more values the of C for the case when the top of 5). settles than for adjacent = backfill (i.e. are (i.e. negative Spangler friction) label led evaluated for this C case, and Ktanb the 0.13 minimum in favourable Fig. the and values trench indicated 6.3, mech- complete incomplete conditions since anics a r e s i m i l a r to those f o r trench conditions. For Fig. the negative projection (or incomplete trench) condition (see 6.19 = and 6 . l h ) w i t h the p i p e i n a trench under an embankment, (6.6) i n Fig. 6.3 f o r negative su b u t with D w CnYB2 Cn where i s the same as C replaced b y 6 i n a l l expressions. u = I n t h i s case the projection r a t i o i s depth of p i p e crown below n a t u r a l ground level w i d t h of trench ratio i s a n d the settlement s = settlement of n a t u r a l ground level-settlement of level of top f i l l i n trench reduction in thickness of s o i l in trench above crown 119 1 F i g . 6.3 Load coefficient C (Spangler, 1956). f o r embankment conditions The settlement of the level of the top of the f i l l i n c l u d e the settlement of the bottom of the pipe, a n d compaction of i n the trench may deflection o f the p i p e the f i l l i n the trench above the crown of the pipe. to - 1.0 f o r u = 2.0. s may r a n g e from - 0.1 f o r u = 0.5, It i s possible to reduce the load on pipes under a n embankment b y a certain it by amount lightly condition of compacted fill d i r e c t l y above the p i p e i.e. inducing a s removing and replacing compacted (Fig. fill directly, For this negative projection 6.li). condition may r a n g e from -0.5 The load f o r u = 0.5 per unit to -2.0 f o r u = 2.0. a completely f l e x i b l e p i p e under is l e n g t h on an embankment whether W = i n p o s i t i v e o r negative projection condition YHD load on a r i g i d pipe i n a trench up to i t s crown level (6.7) (neutral The p r o j e c t i o n c o n d i t i o n ) i s a l s o yHD. 120 C l a r k e suggests that pipe the l o a d on trench, a tunnel a or thrust bore i s simifactor allowing lar for this to that on a in a w th reduction t h e cohesion of t h e m a t e r i a l above. conclusion are not convincing The a s s u m p t i o n s i n a r r i v i n g a t and further theory would be we1 come. Clarke also suggests that uniform surcharges depth some of large extent This be t r e a t e d a s embankments a n d preferable take place to using the equivalen t theory, different determined. load is pure elastic soil fills at as transfer soil must between densities and masses which settle differently. The pipe is soil the density which (but less would not result in the maximum The load on a saturated normally submerged) than a for density. the submerged case, as less conditions the water are severe produce saturated pressure would uniform load. radial pressure l i k e l y to c r a c k a p i p e t h a n a p u r e v e r t i c a l Example - N e g a t i v e p r o j e c t i o n case The top of a pipe and in a 2 m wide is a trench high is 1 m below natural the ground trench. level there 7 m embankment above E v a l u a t e the load on the p i p e . - = Projection r a t i o u = 1 2 0.5 Settlement r a t i o s = -0.4 s a y . H/B = 8 / 2 = 4 . From F i g . 6.3, load coefficient C = 3.1 L o a d p e r m o f p i p e = CnyB2 = 3.1 x 18000 x 2*/1000 = 220KN/m SUPER IMPOSED LOADS It is customary by to use loads elastic to a theory to evaluate the pressures transmitted infinite, The f a c t in surface buried pipe and elastic material to assume a semithe p i p e . homogeneous, that isotropic, surrounds t h e s i d e f i l l may s e t t l e d i f f e r e n t l y to t h e p i p e i s i g n o r e d and suitable factors if the p i p e s h o u l d be a p p l i e d to decrease the the theory transmitted load is flexible. U n f o r t u n a t e l y no such f a c t o r s a r e a v a i l a b l e yet. If the t h e l o a d a p p l i e d o n t h e s u r f a c e i s of l i m i t e d l a t e r a l e x t e n t then induced pressure on any horizontal plane below the surface 121 decreases w i t h depth. consequently the The deeper the p i p e , the w i d e r the spread and On the other h a n d the lower the maximum pressure. total v e r t i c a l force must remain equal to the superimposed load. Formulde point the The load, for or evdluating the transmitted loads due to a surface in a pressure of limited or i n f i n i t e extent, are given sections below. A suitable vary impact f a c t o r should a l s o be a p p l i e d . the type of 1.3 impact factor the surface, will and with load a n d depth of p i p e slow moving vehicles to below varies from for 2.0 f o r fast moving vehicles cover but depth i f the p i p e i s shallow. than The impact factor and isolated reduces f o r point safe loads, to greater the p i p e diameter the amount of full value reduction of the i s debatable and factor until i t may be conclusive adopt the impact f i g u r e s a r e a v a i l a b l e (see also Compstan et a1 1978). T r a f f i c Loads The following loads are 1969). loads each 30 kN spaced 0.9 m a p a r t . two wheel loads each 73 kN spaced 0.9m useful for design purposes (see a l s o Concrete Pipe Assn. (1) I n fields Under apart. (3) Under eight main wheel roads : two wheel (2) light roads : and heavy traffic (BS 153 type HB load) : loads each 112 kN comprising two rows 1.8 m a p a r t l a t e r a l l y , measured from i n n e r of four wheels each 0.9 m a p a r t a x l e to inner axle. (4) Airport 0.66 m. runways: four 210 k N wheel loads spaced at 1.67m x Pipelines would n o r m a l l y be designed f o r f i e l d I f construction l o a d i n g a n d strength- ened under h e a v i e r t r a f f i c . design loads e x t r a t o p f i l l loads a r e l i k e l y to exceed should b e placed to spread the load d u r i n g construct ion (Kennedy, 1971 ) . g i v e s the v e r t i c a l stress a t depth H Stress Caused by Point Loads Boussinesque's below p o i n t as e l a s t i c theory load a n d a distance X h o r i z o n t a l l y from the p o i n t load P 122 3P H 3 27r(HZ + X ' ) The stress at the stresses any due 5/2 point to the due to two o r individual load o r w = (6.8) more loads w i l l be the sum of The maximum stress could and the loads. occur d i r e c t l y under e i t h e r somewhere between them, worst case should be selected b y p l o t t i n g the stress between them. For the large pipe diameter, and some the stress w i I I v a r y value a p p r e c i a b l y across be taken. of The pipe and pipe diameter Pipe average should Concrete for Association loads (1969) l i s t s the total load i n kg/m surface wheel (l), ( 2 ) a n d (3) i n the p r e v i o u s section, v a r i o u s p i p e diameters and depths. Line Loads The v e r t i c a l stress at any depth H below a l i n e load of i n t e n s i t y q per u n i t l e n g t h is, b y e l a s t i c theory, w = 2q~3 n ( X Z + H 2) 2 Uniformly Loaded Areas The surface stress could intensity at any depth beneath the a loaded area on the be e v a l u a t e d b y assuming point loads, distributed load to com- p r i s e a number of load. ma1 a n d summating the stress due to each i n f i n i tesiof a F o r t u n a t e l y Newmark has performed the i n t e g r a t i o n of point loads loaded to give the vertical area. stress under the corner uniformly are given under each a with rectangular Newmark's influence stress at coefficients any i n Table 6.1. To e v a l u a t e the v e r t i c a l surface one loaded area, directly d i v i d e the above point loaded area into rectangles Calculate corner the p o i n t i n question. the r a t i o s L / H the rectangle a n d Y/H and read the load where L the a n d Y a r e the l e n g t h and b r e a d t h of influence factor of from load for the by the such corresponding due by table. Evaluate the stress intensity and to the each rectangle multiplying particular rectangle. loaded influence stress coefficient due to rectangle, If the p o i n t assume summate the each i n question f a l l s outside the boundaries of the loaded area extends to above the p o i n t and area the s u b t r a c t the stress due to the i m a g i n a r y extensions. 123 TADLE 6.1 Influence factors f o r v e r t i c a l pressure under the corner of a uniformly loaded r e c t a n g u l a r area (Capper a n d Cassie, 1969). o 0222 00435 Similar loaded into also influence and or coefficients strips, small but point a r e available for the stresses under can be resolved are circles normally loads any shape rectangles influence without much e r r o r . There charts available for evaluation 1969). of stresses under any shape loaded area (Capper a n d Cassie, The stress a t any depth under a uniform load of v e r y is the intensity of the surface load since there is l a r g e extent no lateral dispersion. T h i s could also be deduced from Table 6.1 for large L and Y. Effect of R i g i d Pavements A load rigid pavement and The is = - above a p i p e has the effect of therefore reducing a depth the H distributing due the to a of laterally load. stress below a intensity rigid surface stress at pavement thickness h, W C_P/R2 = r a d i u s of (6.10) stiffness or where R E h = modulus of e l a s t i c i t y f o r concrete) (28 000 N/mrnz 4 000 000 p s i = pavement thickness 124 U = = Poisson's r a t i o (0.15 f o r concrete) modulus of subgrade for reaction, which varies from k 0.028N/mm3 poor support to 0.14 N/mm'. A typical v a i u e f o r good support i s 0.084 N/mm3 thickness. R is normally of H/R about and three times the slab Cr is for a a function X/R and i s tabulated i n Table 6.2 s i n g l e point load P on the surface. normally has the effect of about five times its A concrete slab thickness of s o i l f i l l i n a t t e n u a t i n g a p o i n t load. TABLE 6.2 Pressure coefficients for a point load on a pavement (Amer. Con. Pipe Assn., 1970) W Pressure on p i p e = CrP/R2 Depth of Top of Pipe Below Pavement Point Load Radius o f Stiffness Horizontal Distance from Point Load H P R X __ H R (1 00 ___ l!3 101 - 08 1 2 ObX -~~ 20 24 28 n 03 (Ifil 08 12 16 ?0 089 076 062 051 061 054 047 l!d2 032 03 1 03? 032 010 020 U? i 0: 2 017 022 026 llib o:? 021 019 OIR 24 28 32 36 40 41 043 037 036 03 I 073 O? I 019 018 012 027 025 013 0XJ 018 Olh 014 02% 020 016 015 015 013 012 cil? on9 014 012 01 I 48 52 56 018 015 014 01: 010 or19 60 63 012 011 010 Ol! ni; 009 00s 008 68 12 75 gn nux 007 uni 037 [I!)& 009 OOR ons 'I-; 00OOh 007 ~. 007 0' 0 - 125 REFERENCES American Concrete Pipe Assn., 1970. Design Manual-Concrete Pipe, Arlington. Capper, P.L. a n d Cassie, W.E., 1969. The Mechanics of Engineering Soils, 5th Ed., Spon., London. 1968. B u r i e d p i p e l i n e s , MacLaren, London. Clarke, N.W.B., Concrete Pipe Assn., 1969. Loads on B u r i e d Concrete Pipes, Tech. B u l l . No. 2, Tonbridge. Cray, P., Schofield, A.N. a n d Shann, C.D., lc7C. Compston, D . G . , Design a n d Construction of B u r i e d T h i n Wall Pipes. CIRIA. Kennedy, H., 1971. E x t e r n a l loads and foundations f o r pipes, J . Arc!. Water Works Assn. March. Marston, A . and Anderson, A . O . , 1913. Theory of loads on pipes i n ditches and tests o f cement a n d c l a y d r a i n t i l e s a n d sewer p i p e . Iowa State Univ., Engg. Res. I n s t . B u l l . Spangler, M.G., 1956. Stresses i n pressure p i p e l i n e s a n d p r o t e c t i v e c a s i n g pipes, Proc. Am. SOC. C i v i l Engrs., 82 ( S T 5 ) , pp 1054-1115. Young, D.C. and Trott, J.J., 1984. B u r i e d R i g i d Pipes. Elsevier Applied Science, London. p p 230. L I S T O F SYMBOLS trench w i d t h load coefficient, case load coefficient, load coefficient, case load coefficient, d i ameter effective modulus of e l a s t i c i t y of s o i l modulus of e l a s t i c i t y pavement thickness or v a r i a b l e depth depth of cover r i g i d pavemerot trench condition embankment condition, negative projection embankment condj tion, positive projection depth of f i l l below p l a n e of equal settlement momen t of inert ia modulus of subgrade reaction modulus of subgrade reaction r a t i o of l e n g t h of l a t e r a l to v e r t i c a l s o i l pressure loaded area bending moment bending and y or deflection to coefficient bottom and (subscripts side t, b, s, x refer top, moments a n d hori- zon t al and v e r t i ca I d i stort ions respective I y ) 126 pressure p o i n t load l i n e load per u n i t length radius r a d i u s of stiffness settlement r a t i o wal I thickness project ion r a t i o v e r t i c a l pressure W W W l a t e r a l soil pressure permissible r i n g load permi ssi b l e v e r t i c a I load vertical load per u n i t length w horizon t a I distance w i d t h of load area a n g l e of bottom support def I ect ion u n i t weight of soil a n g l e of trench friction between backfill and sides of a n g l e of f r i c t i o n of b a c k f i l l m a t e r i a l Poisson's r a t i o 127 CHAPTER 7 CONCRETE PIPES THE EFFECT OF BEDDING sewer not per or drain pipes are designed to withstand specify and the Non-pressure external the loads, load internal unit run pressures. of pipe The for Various standards classes due to design are different stresses at the pipes reinforced accordingly. loads are at the the main vertical and the The soil external bending main loads, compressive stress crown, by live of the bottom haunches the and stresses are and haunches. horizontal stresses self caused and loads, water vertical weight weight ( i n t e r n a l water pipes). pressure a n d transient pressures a r e neglected f o r non-pressure Concrete pipes a n d the other ly a designed flat rigid loaded to withstand The a r i g i d non-pressure pipes a r e normalline load while supported on the the of vertical per the unit bed. thus load called length r e q u i r e d to f r a c t u r e strength. Although a number pipe is laboratory laboratory practical strength factors of is could be calculated the theoretically, load (The of and influence the load theoretical reliable. the experimental strength constraint determination of of is more and tensile lateral concrete very uncertain effect the supports may be a p p r e c i a b l e ) . Alternative standard The will testing arrangements f o r is defined in pipes a r e i I lustrat- ed that in Fig. 7.1. strength B r i t i s h Standard 556 as inch load which concrete produce a c r a c k or 1/100 (0.25 load wide mm) f o r unre- inforced pipes, or pipes the 60% of inch the ultimate mm) for crack reinforced load for 90% of 1/10000 (0.025 prestressed c y l inder type concrete pipes. The strength u s i n g the 3-edge in excess bearing bearing test test. is usually 5 the to 10% of that was for the 2-edge and Recently 3-edge b e a r i n g test t o r y strength. Pipes wide higher standardized t h i s i s now defined as the labora- laid of in trenches arc by are usually supported The over is a relatively length than the bedding. strength strength bending consequently moments are the laboratory as the 128 less. F i g . 8.2 summarizes the theoretical b e n d i n g moment c o e f f i c i e n t s for pipes supported over various angles (defined i n Fig. 8 . 4 ) (CPA, 1962). 0 mm 15&brmm rubber 2 -EDGE 3-EDGE 3-EDGE FOR ANY OIA UP TO l8OOrnrn Fig. 7.1 S t a n d a r d c r u s h i n g test b e a r i n g s f o r r i g i d p i p e s The the ratio of field strength to laboratory of bedding strength and is defined as bedding factor. Various types the corresponding b e d d i n g f a c t o r s a r e l i s t e d b e l o w (CPA, 1967; ACPA, 1970):- TABLE 7.1 Bedding factors Class A Class A Class B Class C Class D 120" R.C. c o n c r e t e c r a d l e o r a r c h 120° p l a i n c o n c r e t e c r a d l e o r a r c h Granu Ia r bedding H a n d s h a p e d t r e n c h bottom H a n d trimmed f l a t bottom t r e n c h 3.4 2.6 1.9 1.5 1.1 For rigid concrete pipes the lateral support of the sidefill in the t r e n c h does n o t a d d n o t i c e a b l y to t h e s t r e n g t h . A factor of safety K of 1.25 to 1.5 i s normally used w i t h u n r e i n - forced concrete pipe. so t h a t : - When p i p e i s p r e s s u r i z e d , i t s h o u l d be designed external load f i e l d strength Unreinforced + or internal pressure bursting pressure reinforced (not < 1 K (7.1 concrete pipes are prestressed) 129 normally drains. subjected certain only The to used concrete internal for may non-pressure be stressed and pipes in even such as if sewers the pipe and was a if tension though pressures, concrete has tensile strength, c r a c k s may develop a n d leaks a r e likely the tensile stress i s maintained (Kennison, 1950). Concrete Special pipes normally may be do not require for lining or wrapping. for in- precautions necessary certain liquids, stance sewers a r e often made w i t h r a t e of corrosion of thus limestone aggregate to m a i n t a i n the the same r a t e as the cement, the aggregate a t m a i n t a i n i n g an even surface. The f r i c t i o n coefficients of concrete cast, can compare favourably pipes, especially when c e n t r i f u g a l l y w i t h those of l i n e d steel pipes. PRESTRESSED CONCRETE PIPES Prestressed pressure for long pipes. concrete is becoming a popular competes medium for large-bore with It has steel the Prestressed concrete over economically diameter. pipelines that for approximately 800 mm advantage ses steel than the prestressing steel can be stressed to h i g h e r strespipes. The thick wall to plain-walled must be if thickness o f prevent p l a i n walled collapse pipes reasonably buckling, and d i s t o r t i o n even pressures. when the thickness the use of i s not r e q u i r e d to r e s i s t i n t e r n a l high-tensi le pipes, steels is restricted Consequently manufacturing plain-walled steel b u t t h i s i s not the case w i t h prestressed concrete pipes which a r e more r i g i d than steel pipes. Prestressed wires core onto a concrete core. The pipes helical each are formed is by winding pretensioned coated. winding subsequently The forming the b a r r e l of p i p e may be concrete cast vertically is i n a mould o r c e n t r i f u g a l l y then steam cured to ensure i n a h o r i z o n t a l position. rapid strength increase The concrete before winding. lined with the Alternatively mortar. The the core may steel load cylinder under be formed w i t h improves wire, a steel c y l i n d e r watertightness, and acts as distributes concentrated forcing. stressed the longitudinal bars or reinpre- Plain concrete cores are often reinforced with The longitudinally as well as c i r c u m f e r e n t i a l l y . longitudinal reinforcing resists l o n g i t u d i n a l bending i n the trench as well as local 130 bending stress i n the core w a l l s d u r i n g c i r c u m f e r e n t i a l are pretensioned and released once winding. the core The has longitudinal set. wires Fig. 7.2 Prestressed concrete p i p e The prestressing close to y i e l d p o i n t . wire It i s wound loses a h e l i c a l l y onto the core a t a stress of i t s stress due to creep proportion i s put and s h r i n k a g e before the p i p e into service. A concrete c o a t i n g i s a p p l i e d as soon as possible a f t e r w i n d i n g to get as much stress as possible t r a n s f e r r e d to the c o a t i n g d u r i n g the s h r i n k a g e of the core. The tensile strength of the core is neglected in accounting for f i e l d pressures b u t of manufacture do i f t r a n s i e n t stresses i n the f i e l d o r i n the process cause cracking, the cracks A soon seal due is to the inherent done some stage. on h e a l i n g p r o p e r t i e s of the pipe of immediately water concrete. after the h y d r o s t a t i c test but be usually and this winding core before c o a t i n g permitted at seepage Further through may load tests may be done immediately before dispatch of t h e pipes from the works, and i n the field. joined with spigots a n d sockets sealed w i t h steel o r concrete b u t care i s sockets to ensure (bends no and The pipes a r e u s u a l l y rubber needed stressing tees) may insertions. in or the The socket may design of be of of the integral socket concrete will occur. spalling Specials be f a b r i c a t e d from steel o r cast iron, and are f i t t ed with matching spigots a and of sockets. joints Small which angle may bends take up are to n o r m a l l y made up over number 2" deflection, depending on the type of j o i n t . C i rcurnferent i a l The wire This is tensile wound Prestressing stress onto in the prestressing wires immediately a f t e r the the core i s less than the a p p l i e d tensile force. side stress. At the of the in The i s because the core deforms under the p r e s t r e s s i n g of prestressing any section, the pipe side to one instant section the i s under at of the the stress whereas point steel of the other is i s free. its final The s t r a i n strain. core winding half relaxation stress a f t e r winding wi II therefore correspond to h a l f the t o t a l s t r a i n of the concrete core and Afs = i f n co 1 the modulus o f fco elasticity of steel to that of where n, i s the r a t i o of the time, hence the concrete a t i s t h e core stress a f t e r w i n d i n g and f i s the steel stress, fso = where f f SI . - i f n co 1 initial steel stress and f 51 . i s the so i s the steel stress a f t e r winding. f Since f o r e q u i l i b r i u m of forces f t co c so s = (7.2) and where S fSo = fcotc'S (7.3) i s the steel cross sectional area per u n i t length o f p i p e , a n d tc i s the core thickness. Circumferential After static may Prestress a f t e r the core, Losses is usually which by this subjected to a hydrothe prestressing and a steel winding to the p i p e Any test detect has cracks. creep place undergo usually taken time, certain amount of concrete creep has occurred. The concrete stress j u s t before the test becomes f . CI = fco (7.4) 132 where u is the combined steel a n d concrete creep coefficient between winding and testing. The corresponding steel stress i s : fsi The = fCitC/S for any particular test loading may be calculated (7.5) using stress Equs. 7.9 - 7.15 b u t r e p l a c i n g subscripts 2 b y 1 a n d s e t t i n g the core tb equal to zero. The c o a t i n g should be a p p l i e d and cured testing. This ensures t h a t the s h r i n k a g e as much compression to the as possible a f t e r of the thickness as q u i c k l y and creep concrete core transfer c o a t i n g as possible. The c o a t i n g adds to the cross sectional area a n d reduces stresses thereby a l s o l i m i t i n g the creep of the core. After up to the pipe has been cured and i s r e a d y for service (usually is three months a f t e r m a n u f a c t u r i n g ) the c i r c u m f e r e n t i a l tension taken by the core and the coating: fS,SCf Equating t + f t c2 c b2 b the movement due to e l a s t i c compression, creep (7.6) and s h r i n k - age of the core a n d coatings to that of the steel: Deformation of the core: fc2-f - + - c1 Ec2 w c f .+f CI c2 Ec2 2 + v c2 = sl -fs2 ES (7.7) ( E l a s t i c ) (Creep ) (Shrinkage) ( E l ast ic-steel ) Deformat ion of coating : Sl b2 b2 b2 52 - f ES ( E l a s t i c ) (Creep) ( S h r i n k a g e ) ( E l a s t i c deformation of steel) Now if the properties of the concrete core and coating are s i m i l a r , c2 - the e l a s t i c modulus E Eb2 v c2 = vb2 = v and the s h r i n k a g e coefficient Solving Equs. 7 . 5 - 7 . 8 f o r f say. sl - f52’ 133 2+ w v E c 2 ( t c + t 6 K b ) + tcfcl w c fsl - fS2 = S ( l + w c ) + (tc+tb2+wc)/n __ 2 2 2+Wb (7.9) Hence from 7.8 (7.10) (7.11) Circumferential There are a Stress Under F i e l d Pressure number of field loading conditions which should be examined i n c l u d i n g :(1) In open trench with internal test or operating pressure p l u s self weight a n d weight of water. (2) I n b a c k f i l l e d trench with i n t e r n a l pressure p l u s l i v e load p l u s self weight a n d weight of water. (3) I n backfilled empty. trench with live load p l u s self weight and pipe (4) In backfilled trench with internal pressure, self weight, weight o f water a n d t r a n s i e n t pressures. The most highly plus stressed bending sections under are usually at the plus crown (due to pres- prestressing sures), cal sing at external loads internal the haunches ( d u e to prestressing p l u s bending p l u s v e r t i a n d a t the support plus horizontal ( d u e to prestresplus internal load p l u s plus i n t e r n a l pressure) plus vertical bending loads pressure). Compressive area per unit and tensile forces a r e taken of wall comprising the d i r e c t l y on p i p e core the effective pl us coating length p l u s transformed steel section: A = t + tb + ( n 2 - 1 ) S moments pipe plus I (7.12) to Bending weight moment of due soil of loads, are of external resisted wall. The live by loads and weight per water length the effective of the of inertia unit distance c e n t r o i d of t h e effective section from the i n s i d e of the core i s : 134 (7.13) where d i s the diameter of the prestressing wire. The corresponding distance to the outside of the c o a t i n g i s : e 0 = t c + t b - e i n e r t i a of the effective section i s : (7.14) The moment of e3 I=____ + 3 e 0 + ( t c + ds/2 - e I 2 ( n 2 - 1 ) S. (7.15) Long itud in a I Prestressing Some prestressed pipes are prestressed longitudinally is added as to we1 I as circumferential l y . tensile c r a c k s the The longitudinal prestressing prevent i n the concrete d u r i n g w i n d i n g of bending moment i n service. The the core a n d due to l o n g i t u d i n a l b a r s or longitudinal wires a r e p l a c e d i n the. mould f o r before causes in the casting local the core. When the the concrete core a n d pretensioned wire is wound onto the core, it bending stress and shear bars assists in i n the core walls. the The tension principle longitudinal reducing resulting stresses b y i m p a r t i n g a compressive stress to the concrete core. As for the c i r c u m f e r e n t i a l wires, the longitudinal bars lose some stress due to creep of the steel a n d concrete. SlL’ core cross sectional area ly stressed to I f the b a r s a r e i n i t i a l area i s AS, the p i p e is f . their total is A cross sectional and the creep r e l a x a t i o n coefficient uL, then immediately a f t e r release of the l o n g i t u d i n a l b a r s , the stress i n the core becomes: u f c o ~L f . A SlL s + nlAS (7.16) a n d the l o n g i t u d i n a l steel stress becomes fsoL = fcoLAc’As The core is the normal l y prestressed circumferential l y The h e l i c a l wire (7.17) immediately after release of longitudinal bars. i s wound from one at the p o i n t of theory for end to the other. application of The r a d i a l shear stress i n the core, the winding, is derived from elastic pressurized c y l i n d e r s (Timoshenko and Woinowsky-Krieger, 1959) and i s 135 approxima tel y q = 0.54 S f S O / v f stress a f t e r winding, (7.18) and D is i s t h e circumferential steel so the e x t e r n a l diameter of the core. where The maximum local longitudinal tensile and compressive stresses due to bending i n the core w a l l d u r i n g w i n d i n g h a v e been determined experimental l y to be approximately fcmL = 0.3fco where fco i s the core c i r c u m f e r e n t i a l stress a f t e r winding. The effect of the l o n g i t u d i n a l steel on the cross sectional a r e a has been neglected in Equs. 7.18 and 7.19 as the steel is (7.19) near the neutral mum a x i s a n d the expressions a r e approximate stress in the core wall anyway. The rnaxithe assis- tensile may be d e r i v e d w i t h tance of a Mohr d i a g r a m ( F i g . 7 . 3 ) : I f fcmL > fcoL, c t L =/qz which i s u s u a l l y the case, + then fcml - f ( 2 and i f f c o L > fcmL then f c t L = h2 + ( f C 0 L - FcmL 2 2 I SHEAR STRESS Fig. 7.3 Mohr c i r c l e f o r stress i n core d u r i n g w i n d i n g . + ""4 2 - 2 COL ( 7.20a ) - fcoL 2 cmL (7.20b) 136 It will be seen from Equs. 7.20 a and b to that f COL the larger the is longitudinal prestress, which i s proportional ctL' the smaller the p r i n c i p l e t e n s i l e stress in the core f Longitudinal S t r e s s e s A f t e r L o s s e s The pipe longitudinal bars act to resist longitudinal bending of the in the f i e l d . in The p i p e a c t s a s a beam s p a n n i n g between uneven At this stage in points and the will bedding. a c e r t a i n amount of and some shrinkage creep have occurred will is the concrete longitudinal As the be compressive longitudinal neglected. stress stress h a v e been not high, t r a n s f e r r e d to the concrete the c o a t i n g . can creep usually S h r i n k a g e of t h e c o r e does r e d u c e t h e t e n s i l e s t r e s s i n t h e b a r s and t h e c o m p r e s s i v e s t r e s s i n t h e c o r e becomes: u f A L siL s fc2L = + - v ESAS (7.21 ) Ac the the n2AS is in due service, to longitudinal The bending extreme stresses fibre are Once added to pipe stress prestressing. bending stresses a r e - - fc3L - MD 21 and (7.22) t h e e f f e c t i v e moment o f inertia of where M i s t h e b e n d i n g moment the section i s I = 64 l l (D 4 - d 4 (d + 2t + d 5 ) * 8 + (n2 - 1 ) AS (7.23) P r o p e r t i e s of Steel and C o n c r e t e The steel used for w i n d i n g prestressed concrete p i p e should h a v e a s h i g h a y i e l d s t r e s s a s p o s s i b l e and a y i e l d s t r e s s o f 1650 N/rnmz (240 000 p s i ) shrinkage concrete it i s n o t uncommon. taken place, This will e n s u r e t h a t a f t e r c r e e p and in have the r e m a i n i n g compressive stress the and is fairly to high. confine The steel stress w i l l d r o p a f t e r w i n d i n g , working stresses to is normal less than 50% o f yield stress. Steels work with high yield stresses are often b r i t t l e and difficult to w i t h and in f a c t the u l t i m a t e s t r e n g t h may not be much h i g h e r 137 than the yield stress. Care is therefore necessary of steel in selecting the prestressing w i r e . 200 000 N/mm2 The to (30 x 10 T h e modulus of e l a s t i c i t y 6 psi). i s approximately steel may creep s l i g h t l y between concrete they are is a f t e r prestressing a n d steel creep but it is difficult distinguish test, in so between w i n d i n g and This loss works stress usually considered around together. occurs in the steel typically 5% a n d w i t h i n a few hours a f t e r w i n d i n g . Concrete day cores are cast under of vibration or centrifugally and 28 cube c r u s h i n g strengths 60 N/mm2 ( 8 700 p s i ) a r e f r e q u e n t l y 7 200 p s i ) i s desir- achieved. able for of the High e a r l y strength (e.9. 50 N/mm2 o r w i n d i n g as e a r l y as possible. strength at the time Compressive stresses u p to 50% (any cube will a r e permitted d u r i n g w i n d i n g cracks most p r o b a b l y h e a l ) . Working compressive stresses should be confined to less than 1/3 of the 28 day cube strength. The less bending about tensile 10% stress of the in the core d u r i n g w i n d i n g strength in the at that due age, to should be and the than cube calculated bending strength in bending the tensile stress be core to longitudinal the cube field should limited about 5% of i n order to a l l o w f o r unknowns a n d to prevent any p o s s i b i l - i t y of cracks developing. No c i r c u m f e r e n t i a l tensile stress i s permitted i n the core i n the f i e l d f o r normal o p e r a t i n g conditions b u t tension i s sometimes the p e r m i t t e d under should be transient than conditions. about The the tensile stress cube in coating i s for less 10% of strength. a n d the (This b u r i e d pipe. Exposed pipes may develop cracks tensile stress should be less t h a n t h i s . ) BS 4625 does not permit tensile stress but in the a core tensile for normal of operating 0 . 7 4 7 m if 0.623 plus water backfill pressures, permits stress hammer pressure i s included, works hydrostatic test. a n d a tensile stress of is the crushing / F during (Where F strength of 150 mm cubes a t 28 d a y s , a l I i n N/mm2 . ) The modulus of elasticity of concrete increases to w i t h the s t r e n g t h and v a r i e s from 20 000 N/mm2 ( 6 000 000 p s i ) (BSCP 2007, ( 3 000 000 p s i ) 40 000 N/mm2 1970; Ferguson, 1958). The creep coefficient, creep s t r a i n = w, of concrete i s defined b y the equation AL/L = w fc/Ec 138 where fc is the average compressive stress during the time that creep occurs a n d E i s the f i n a l modulus of e l a s t i c i t y . w varies with time a n d the method of c u r i n g . the r a t e of after three creep reduces w i t h (at the time of Creep i s high f o r time. w ' g r e e n ' concrete and two days is 1.3 1.3 i s approximately 0.3 testing the core) casting factory and months a f t e r casting. Hence f o r the coating, the coefficient i s used to c a l c u l a t e creep, the time between f a c t o r y I t may b u t f o r the core, the creep coefficient f o r a n d f i e l d conditions i s 1.3 - 0.3 = 1.0. test be 30% h i g h e r f o r pipes not p r o p e r l y cured o r exposed to the elements i n the f i e l d . Shrinkage ing, typical of concrete also depends l a r g e l y on the method of c u r v, v a r y i n g from values of s h r i n k a g e per u n i t length, to Example Calculate winding, circumferential curing and concrete under and field steel stresses during for the after conditions prestressed concrete p i p e described below: Effective p i p e tc = 75 mrn, length L = 4 m, tb = bore d i = 2 000 rnm, steel winding core thickness coating 25 mm, 5 mm diameter at x 15 mrn c/c. 8 mm S = 0.00131 m2/m of pipe. L o n g i t u d i n a l wires 24 N o . internal live pressure diameter, Vertical soil A S = 0.00121 loading due x m2. to Maximum 0.8 N/mmz. soil = and load 0.04 N/mrn2, lateral pressure 0.5 of vertical 0.02 N/mmz. Bottom support e f f e c t i v e l y over 30" inside. arc. Neglect selfweight a n d weight of water Steel: L o n g i t u d i n a l prestress = 400 N/mm2 .Winding prestress = 1000 N/mmz. ES = 200 000 N/mm2. Creep coefficient u = 0.95. Concrete: = 30 000 N / m m 2 , CI from f a c t o r y test to f i e l d test. n E Ec2 = 38 000 N/mmz, Wb = 1.3, Creep w 4 : v = 10 shrinkage = 1.0 . 1 = = 200 000/30 000 200 ooo/38 000 = 6.7 = 5.3 n 2 Stresses due to w i n d i n g - fco - 1 000 x 0.0131 0.075 i 0.00131 x 6 . 7 / 2 = 16.5 N/mm2 (7.2) 139 = so 16.5 0.075 0.00131 = 880 N/mmz (7.3) Works t e s t o f c o r e : fcl fSl = = 0.95 x 16.5 0.95 x 8 0 8 = = 15.7 N/mm2 840 N/mm2 (7.4) a f t e r curing : f -f = s2 = 2+1 .o 1 O-4x38x1 0 (0.075+0.025m) 075x15.7xl.O ' +O. 0.00131 ( d ) ( . 7 + . 2 ) 5 3 2+1 0 l$+00500*/. 76 N/mmz 840-76 = 764 N/mmz 76 (200 000 38 Oo0 = 6.4 N/mmz 2+1 .3 = (7.9) s2 fb2 = = - (7.10) (7.11) c2 764~0.00131-6.4x0.025 0.075 loading: 11.2 N/mm2 Under f i e l d Transformed section A = 0.075 + 0.025 + (5.3-1)0.00131 = 0.105 m'/m (7.12) C e n t r o i d to inner surface e = )(0.075+0.005/2)(0.00131) 0.12/2+(5.3-1 0.1+0.00131(5.3-1) = 0.0515 01 . (7.13) 0.0515 3 Cent r o id t o outer surface e Moment o f inertia = - = 0.0485 (7.14) I = 0*05' +0*04853 + (0.075+0.005/2-0.0515)2 53 x(5.3-1)(0.00131) Stresses a t b a s e B : ( t e n s i o n - = 85.9~10-~m~/m (7.15) v e f o r concrete stresses) T e n s i o n d u e to n e t i n t e r n a l p r e s s u r e : ft = 0 8 x 2 - 0.02 x 2.2 . - -7,4 N/mmz 8.2: NS 2 x 0.105 B e n d i n g moment c o e f f i c i e n t s f r o m F i g . For vertical load, Nb = 0.235, and f o r h o r i z o n t a l l o a d , = 0.125 Net b e n d i n g moment = = 0.235 x 0.04 x 2.2/2 - 0.125 x 0.02 x 2.2/2 0.00755 140 Stress on o u t e r face f - b3 fb2 - f t + -MeO I 0.00755 85.9 x 0.0515= -IN/mm2 Stress on i n n e r face f Steel s t r e s s : e = c3 = 11.2-7.4- x (on outer side of centroid) 0.075 + 0.005/2-0.0515 = 0.026 = 764 + 5.3 (7.4 0.00755 x 0.026) = 791 N/mm2 85.9 x Although stresses similarly, the stresses a t at t h e b a s e a r e u s u a l l y t h e most s e v e r e , on the circumference should the other points be checked and c h e c k s s h o u l d b e d o n e b o t h w i t h and w i t h o u t t r a n s - ient winding, t e s t i n g and i n t h e f i e l d . REFERENCES Am. C o n c r e t e P i p e A s s n . , 1970. D e s i g n M a n u a l - C o n c r e t e P i p e , A r l i n g ton. BSCP 2007 P a r t 2, 1970. R e i n f o r c e d and P r e s t r e s s e d C o n c r e t e S t r u c t u r e s , BSI, L o n d o n . C o n c r e t e P i p e Assn., 1962. L o a d s o n B u r i e d C o n c r e t e P i p e s , Tech. B u l l e t i n No.2, T o n b r i d g e . C o n c r e t e P i p e Assn., 1967. B e d d i n g and J o i n t i n g o f F l e x i b l y J o i n t e d C o n c r e t e P i p e s , Tech. B u l l e t i n No. 1 , T o n b r i d g e . F e r g u s o n , P.M., 1958. R e i n f o r c e d C o n c r e t e f u n d a m e n t a l s , Wiley,N.Y. 1950. D e s i g n of p r e s t r e s s e d c o n c r e t e c y l i n d e r p i p e , J. K e n n i s o n , H.F., Am. W a t e r W o r k s Assn., 42. T i m o s h e n k o , S.P. and W o i n o w s k y - K r i e g e r , S., 1959. T h e o r y o f P l a t e s and S h e l l s , 2 n d Edn., McGraw H i l l , N.Y. L I S T O F SYMBOLS A d D - cross sectional area inside diameter outside diameter distance from centre of g r a v i t y modulus of e l a s t i c i t y stress (compressive o r tensile) e E f F c r u s h i n g s t r e n g t h o f 150 mrn c u b e s a t 28 d a y s 141 I K L - moment of inertia factor o f safety length bending moment e l a s t i c modular r a t i o E shear stress steel area per u n i t length of p i p e thickness creep coefficient f o r steel and concrete before f a c t o r y test s h r i n k a g e coefficient creep coefficient s M n - /E c q - s t - u - v w - Subscripts b c s - coating core steel bending shear tensile longitudinal initial after winding at time of f a c t o r y test a t time of laying m - 9 t - L I 0 - 1 2 - 3 - under f i e l d pressure 142 CHAPTER 8 STEEL AND FLEXIBLE P I P E 1 NTERNAL PRESSURES The due pipe weight to highest internal there pressure fluid are The a pipe has to resist is are normally those the self pressure. no The pressure uniform for around and and bending stresses except for the water effects. general equations resulting stresses in a hollow cylinder are: Circumferential wal I stress Fw = p.d.' I I - podo' d i 2 doZ( P , P doL - ) (8.1 ) do2 - diL d.' p.d.' I 1 - podo' Radial stress where p is Fr = do2 - d.' i s diameter at d + d i z do2 ( PP , - 1 (8.2) d. doZ - d i z i s pressure, diameter i.e. d w h i c h the stress i s sought, diameter. internal and i s external The e q u a t i o n s a r e f o r p l a i n stress, For a cylinder free to expand longitudinally. the p a r t i c u l a r case of n o e x t e r n a l p r e s s u r e the c i r c u m f e r e n t i a l s t r e s s i s a m a x i m u m on t h e i n n e r s u r f a c e a n d i s di2 F max W = di + do2 P + do 2t the wall thickness is normally small in In with practice comparison the diameter, a n d the w a l l thickness of a steel p i p e designed to resist i n t e r n a l pressure i s obtained from the formula where t is t h e w a l l t h i c k n e s s p i s the i n t e r n a l pressure d i s the e x t e r n a l diameter f i s t h e y i e l d s t r e s s o f t h e steel G i s the design factor J i s the j o i n t factor. E q u . 8.4 overpredicts the true stress by some 1% for every 1% of t/d. On t h e o t h e r h a n d , just u s i n g d instead of 1% t / d . (d-t) would under- 3 r e d i c t s t r e s s b y 1% f o r e v e r y 143 The will design factor G allows a safety which margin. What factor to use depend on been the accuracy the with loads a n d t r a n s i e n t pressure economics and the conse- have assessed, a burst. working pressure, quences of I f the p i p e l i n e i s protected a g a i n s t water hammer of 0.6 o r even 0.7 a factor i s reasonable, of the order b u t i f there to 0.5 over-pressure, are many a factor unknown loads, use of of 0.3 would be wiser. The j o i n t varies pipes. Smal I-bore, pressures wal Is, the the only, more in factor J allows furnace for imperfections i n welded seams, to and from 0.85 for butt-welded joints 1.0 for seamless high but pressure the pipes the are designed to resist the internal the of larger diameter and loads. in in thinner important pipe should become the e x t e r n a l also be possible, Vaporization which case fluid the may be this with internal pressure considered acting conjunction e x t e r n a l loads. If the p i p e VF i s restrained longitudinally, v is a longitudinal ratio and tension of magnitude is induced where Poisson's F is the circumferential wal I tension. TENS I ON R I NGS TO RESIST I NTERNAL PRESSURES Pipes which have to resist very high internal It pressures may be strengthened to form b y b i n d i n g w i t h hoops a n d s p i r a l s . in the thick On i s often d i f f i c u l t pipes p l a t e s which would be r e q u i r e d to r e s i s t other hand it some h i g h pressures. the may be possible to form the p i p e of t h i n n e r p l a t e than would be r e q u i r e d f o r an unstrengthened pipe, a n d w i n d i t w i t h s t r a p s o r rods. internal rings pressures do not perform the required to resist col lapse The r i n g s r e q u i r e d to r e s i s t same function as the stiffening against in external and loads. does load, The w i n d i n g not need to to r e s i s t be internal as pressures acts the rings to tension as prominent resist the external which should increase the moment of i n e r t i a of l o n g i t u d i n a l section I n fact the through the p i p e a n d therefore be as h i g h as should be possible. tension r i n g s , as they w i l l be c a l l e d , 144 as f l a t a n d b r o a d as possible to keep the distance between them to a There will be in high the longitudinal pipe wall bending rings stresses if and minimum. circumferential are f a r apart. are usually be stresses between the r i n g s I n comparison, a number s t i f f e n i n g r i n g s to r e s i s t e x t e r n a l loads of diameters a p a r t . pipes which are Tension r i n g s may to be subjected to spaced to also used strengthen old h i g h e r pressures than o r i g i n a l l y designed for. Using of the stress-strain r e l a t i o n s h i p and the d i f f e r e n t i a l equations equil i b r i u m f o r c y l i n d e r she1 I s under the action of r a d i a l pressure, (1959) d e r i v e d a n equation f o r subjected to Timoshenko a cylinder the radial displacement of a radial pressure a n d w i t h tension r i n g s at equi-spaci n g Put and b4 a . = = 12(1-v2) dZt' bs (8.5) (8.6) for s t e e l ) , d i s the p i p e diameter, r i n g spacing. where v t i s the P o i s s o n ' s r a t i o (0.3 i s the w a l l - thickness a n d s the centre-to-centre cosh a sinh a sinh a sinh a cosh a sinh a Let + - x1 + + cos a sin a sin a sin a cos a sin a (8.7) - x2 - (8.8) - x3 + Then the r i n g stress, Fr, i s g i v e n by (8.11) where A = cross sectional area of The circumferential pipe wall the r i n g . stress, Fw, mid-way between rings is given by = FW @[l 2 ( F - - 1 ) X 4 ] + 2t 2t r Pd bending stress in the p i p e under the (8.12) rings, a n d the longitudinal Fb i s given by 145 g! r i i D C a, 3 m L a, c m [r C .- U a, C I I I I < 0 I 1 I m P 2 . 0 ” m In L a, I m a C .LL D m > N a a C .L m C .- L C d 0 .- r D .- E m m QJ c m a, C .- 5 U m .U m m 5 m m a, m 3 - 5 .- - C c i a, vi m L a, a, - m 5 i .- a .LL V m 146 (8.13) The shown A) stresses that are indicated by Fig. 8.1, for v = 0.3. It may be a s s i s d e c r e a s e d t h e r i n g s t r e s s Fr tends to f pds/ (ts + w h i c h c o u l d h a v e been anticipated. the circumferential wall N o t e t h a t f o r s m a l l A, a p l a i n pipe, W Fr tends Also, to equal stress of pd/2t. f o r s m a l l s, the circumferential p i p e wall stress F tends to 4 pds/(ts Fb + A ) , w h i c h w o u l d b e e x p e c t e d , and t h e l o n g i t u d i n a l tends to zero. For l a r g e r i n g spacing ( > approx. F tends to 2-1, beding stress 1 1 pd 2t (8.14) + 0.9lA/t& 1.65 tJtd/A Fb tends to pd 2t (8.15) + 0.91 and F t e n d s to @ i.e. t h a t f o r a p i p e w i t h o u t r i n g s . 2t I t may be observed b y comparing F F r and Fb f r o m F i g s . W W’ 8.la, 8.lb in and 8 . l c t h a t t h e m a x i m u m s t r e s s f o r most p r a c t i c a l r i n g s i z e s i s the circumferential pipe wall stress. Also, fact Fw, if Fw is only the reduced s / J y z i s l e s s t h a n a p p r o x i m a t e l y 2.0. l e s s than same 2 J l d of and I n other words, r i n g spacing should be area A should be of the r i n g cross sectional as the p i p e w a l l ts, the order magnitude rings, longitudinal cross sectional area between to enable the r i n g s t o b e o f use. DEFORMATION O F CIRCULAR P I P E S UNDER EXTERNAL L O A D For sures, under large diameter and flexible pipes under low internal pres- the external external load is frequently by buckling, t h e c r i t i c a l one. due Pipes may f a i l to arching or load overstressing bending, For excessive deflect ion. elastic rings under plane stress subjected to vertical loads only, Spangler (1956) e v a l u a t e d t h e b e n d i n g moments and d e f l e c t i o n a t the circumference. The worst b e n d i n g moments critical occur at points around the crown, the i n v e r t or t h e s i d e s . T h e b e n d i n g moments p e r 147 Angle of bottom suwor? p degrees Angle of tmttom support p degrees Fig. 8.3 D e f l e c t i o n c o e f f i c i e n t s for loaded pipe. 148 u n i t length a r e g i v e n b y a n equation of the form M = N R W (8.16) the a pipe radius, where and N R is is W Nb i s the v e r t i c a l and NS f o r load per top, unit length sides are coefficient. The (Nt, bottom and in respectively). vertical and horizontal changes diameter p r a c t i c a l l y equal a n d opposite a n d a r e of the form A = NnWR3/EI (8.17) where N A i s a coefficient. is (8.18) and the 8.3 g i v e values of bottom of the and The moment of i n e r t i a I per u n i t length of p l a i n p i p e w a l l I = t3/12 8.2 at Figs. moments vertical line unit Nt, Nb a n d Ns f o r the and bending for the top, sides respectively, The N A deflections a pipe diameter. coefficients are for a load or length), load d i s t r i b u t i o n and for different across the w i d t h of angles of bottom the p i p e support 6 ( W per , as indicated i n Fig. Collapse of has to 8.4. a steel p i p e w i l l p r o b a b l y not occur u n t i l the diameter some 10 o r 20 percent. diameter limited to are sometimes I n p r a c t i c e deflections tolerated. up been distorted the be 5 percent of normally The deflection should linings, about 2 percent to prevent damage to a n d for pipes w i t h mechanical j o i n t s . i.e. the cross sectional area a n d wetted The h y d r a u l i c properties, perimeter a r e not affected noticeably f o r normal d i s t o r t i o n s . LOAD W /UNIT LENGTH OF PIPE UPTHRUST F i g . 8.4 Pipe l o a d i n g and deflections 149 Effect of L a t e r a l Support The of lateral support of sidefill in a and trench increases the s t r e n g t h deformations. Without flexible pipes considerably reduces lateral support to a p i p e the r i n g bending stresses a t the s o f f i t a n d haunches o r deflections would l i m i t the v e r t i c a l e x t e r n a l load the p i p e could carry. But it is a pipe in a compacted fill will deflect outwards l a t e r a l l y as the may sidefill loaded v e r t i c a l l y thereby the with sides the of the pipe. load i n c r e a s i n g the pressure of An equilibrium condition to the against be established vertical being transferred The haunches b y a r c h action as well as b y r i n g action. stress due to the a r c h action carry In the i s compressive so that the load which the p i p e can i s considerably h i g h e r than i f the p i p e were a c t i n g in bending. extreme case, the lateral stress will equal the v e r t i c a l load stress a n d the p i p e wal I w i l l equal where If could to wd/2t w = be i n p u r e compression, w i t h the stress W/d no noticeable determined by lateral the (8.19) the p i p e underwent would be distortion bending the load it support arch strength plus whatever strength i s given i.e. to the p i p e b y the s o i l pressure on load per u n i t area the sides of the pipe, on the p i p e i s the permissible v e r t i c a l w where w = w b + w a bending load (limited either (8.20) by ring i s the permissible b bending stress or more l i k e l y to lateral soil by deflection). w equal pressure on i s the a r c h i n g load, a the sides of the p i p e , which, conbut i s usually For sand, servatively, greater than may be taken as the a c t i v e soil pressure, this as indicated in subsequent one equations. the a c t i v e lateral pressure i s approximately dead load o n l y t h i r d of the v e r t i c a l i t i s approximately pressure due to soil and for clay h a l f the v e r t i c a l pressure. I f the v e r t i c a l active and away lateral soil load i s g r e a t e r than the sum of the r i n g load p l u s pressure, the pipe wall will deflect out laterally increase the from the lateral pipe pressure. The h o r i z o n t a l stress w i I I decrease and Barnard (19571, using elastic theory, 150 suggests assuming a pressure equal wall triangular vertical stress d i s t r i b u t i o n w i t h the horizontal pressure minus r i n g load a t the p i p e The to total decreasing l i n e a r l y to zero at 2.5d away from the p i p e w a l l . l a t e r a l deflection of each side of the p i p e i s (w-w,) corresponding AX/2 = 1.25 d/ES e l a s t i c i t y of the s o i l . (8.21 ) The factor where E 1.25 i s the effective modulus of should be pressure increased as the l a t e r a l deflection increases, since the increases for of as the r a d i u s of c u r v a t u r e decreases. the diameter The and radial factor 1.7 time, for becomes 1.4 a a deflection of 5 percent. 2 percent of deflection The deflection also increases w i t h and an a d d i t i o n a l 25 to 50 percent of the i n i t i a l deflection can be expected e v e n t u a l l y . If the creep On deflection other of hand the soil is large, lateral support can decrease. e.g. load. The the pipe materials which exhibit creep, plastics, can compensate f o r this, a n d could even shed v e r t i c a l relationship from between stress and s t r a i n f o r triaxial varies consol i d a t i o n widely the s o i l should tests. be determined modulus degree of of of laboratory of The effective on soil type, elasticity soil depending compaction o r n a t u r a l density, c o n f i n i n g pressure, it duration low l o a d i n g and moisture content. for is loose c l a y or as high F o r example may be as as 2 The N/mmz as 20 N/mm2 f o r loosely dense sands. modulus for fill approximately 3 N/mmzfor compacted f i l l , 5 N/mrn2 to 95% compacted to 90% Proctor density a n d 7 N/mmz f o r f i l l Proctor density. compacted sands. The r i n g as indicated to Values h i g h e r than 100 have been recorded for moist load on by Equ. the p i p e 8.17. i s p r o p o r t i o n a l to t h e e l a s t i c deflection equal the t o 0.108, Taking N , 30' and which corresthe entire ponds bottom support over load over pipe width and p u t t i n g AY A = AX = A , then s o l v i n g f o r A/d from 8.17 and 8.21, (8.22) d - 0. 108wd3 8E I +0.043ESd3 pipe For p l a i n I = t3/12, so one has an equation f o r deflection as a function of diameter, loading, soil modulus and the ratio wall th i ckness/di ameter. A - d - 0.108~ 0.67E(t/d)' + 0.043Es (8.23) 151 The r e l a t i o n s h i p between deflection a n d wal I thickness f o r p l a i n p i p e i s p l o t t e d i n F i g . 8.5. I t w i l l be observed that a steel p i p e wall thickness as low to as 4% of the the diameter soil will be is sufficient greater to restrain distortion 2% p r o v i d e d modulus than 5MPa a n d soil Pipes trench to are load i s less than 50 kPa. sometimes the strutted vertical internally diameter during and backfilling the of the increase The reduce horizontal diameter. lateral support increases when the s t r u t s a r e removed The v e r t i c a l deflec- a n d the p i p e tends to r e t u r n to the r o u n d shape. tion a n d tendency to b u c k l e a r e consequently reduced considerably. G STRESS DUE TO C I RCUMFERENT I A L BEND I N It i s possible to compute w a l l stresses due to bending a n d a r c h i n g 1979). If i t can be assumed that the load i s spread over ( a = (Stephenson, the f u l l 60' w i d t h of the p i p e 180') and the bottom support i s over ( 6 = 60") f o r f l e x i b l e p i p e , then from (8.17) a n d F i g . 8.3, = AY 0.103wbd 4 /8E1 (8.17b) (8.21b) the r i n g load i n terms of w Now from (8.21), A X = 2.5(w-wb)d/ES Equating the total AY a n d A X , load, w I /d3 I/d3 a n d s o l v i n g for w b w The b = + 0.006ES/E in the wall, (8.24) bending moment M, is due to ring load a n d is a maximum a t the base a n d from (8.16) M where the = 0 . 1 9 ~ d 2 / 2 hence b e n d i n g stress f = Mr/l b b is the distance from the centre of pipe). g r a v i t y of (8.25) the section the to r extreme f i b r e (t/2 for p l a i n wall The balance of load i s taken W - in a r c h action of the p i p e according to (8.20) so 0. 006wES/E a I /d' + 0. 006ES/E (8.26) The bottom w a l l hoop stress i s fa where = wad/2a is the cross sectional area of (8.27) wall per unit length ( t a for plain wall pipe). 152 The = total lateral compressive stress permissible i n the w a l l at the base i s f i n terms of fb + fa, therefore is l o a d i n g p e r u n i t area permissible stress f (l/d3 w = 0.1 + 0.006ES/E)f (8.28) r/d + 0.003 dE /Ea load w i s a f u n c t i o n of the permis Thus the permissible v e r t i c a l s i b l e stress, the r e l a t i v e thickness t / d a n d the r a t i o o i n Fig. 8.5 moduli of soi f o r p l a i n wal ES to steel pipe, E. The r e l a t i o n s h i p i s plotted w i t h E = 210 000 N/rnmz, a n d f = 210 N/mrn2. pipes, can the permissible load increases w i t h wal I thickness be taken so For t h i c k as more load i n r i n g bending. that the soil the For t h i n n e r pipes, the deflection the pipe becomes is large side-thrust limit increases to until wall i n p u r e compression, Actually side w a l l and i s due the hoop stress. hoop stress exceeds that a t the base, so (8.27) p l u s (8.25) i s not the l i m i t i n g stress f o r h i g h a r c h i n g . On the same c h a r t i s p l o t t e d b u c k l i n g load W = /32ESEl/d3 proposed b y ClRlA (1978) allows for (8.29a) lateral investiis The b u c k l i n g equation, This the support. gated by may be compared w i t h an a l t e r n a t i v e equation Transport and Road Research Laboratory (which found to o v e r p r e d i c t w ) : W = (16Es2El/d3) / 3 1 g i v i n g a deflection of from (8.23). (8.29b) 2% i n the diameter i s also p l o t t e d The load w d on the c h a r t for is any The c h a r t thus y i e l d s the l i m i t i n g c r i t e r i o n The lowest permissible load w by comparing and E rings deflection, p a r t i c u l a r w a l l thickness r a t i o . in each case from the selected chart overstressing and b u c k l i n g lines f o r the r e l e v a n t t / d Similar charts should be p l o t t e d where . a r e used or stiffening a n d where a l t e r n a t i v e m a t e r i a l moduli and permissible stresses a p p l y . By careful design it is possible to reach the limit in two more c r i t e r i a a t the same load. T h i s i s c a l l e d balanced design. More General Deflection Equations Spangler the (1956) in a allowed more for lateral way support than to the pipe The due to backfill theoretical Barnard. equation he d e r i v e d f o r v e r t i c a l deflection i s : 153 UZWd3 8 E l + 0.06Esd” i f UZ A = (8.30) i s substituted for N and a v a l u e of T h i s corresponds to ( 8 . 2 2 ) A 0.15 i s assumed f o r N A i n the denominator ( i n s t e a d of 0.108 i n 8.22) Here U = Z = s o i l consolidation time l a g factor bedding constant (varies from ( v a r i e s from 1.0 to 1.5). support to 0.11 for point 0.083 f o r b e d d i n g the f u l l w i d t h of p i p e ) , n o r m a l l y taken as 0.1. 1 = moment of i n e r t i a of p i p e w a l l per u n i t length. passive resistance modulus of s i d e f i l l . pressure the fact inside a that the pipe may also E = The Due to contribute to its stiffness. vertical diameter i s compressed to s l i g h t l y less t h a n the h o r i z o n t a l diameter, al pressure becomes g r e a t e r tends to return the than the v e r t i c a l u p t h r u s t due t o i n t e r n the s i d e t h r u s t b y an amount of 2@ which p i p e t o a c i r c u l a r shape. A more general expression f o r v e r t i c a l deflection thus becomes A = UZWd3 8 E I + 0.05ESd’ + 2 UZpd3 (8.31) Q W 0.002 0.005 0.01 0.02 0.03 Relative thickness t / d F i g . 8.5 Permissible load on p l a i n p i p e 154 ST FFENING RINGS TO Morley RESIST BUCKLING W I T H NO SIDE theory for the The SUPPORT (1919) developed a uniform external buckling theory of stiffened indicates in p r a c - pipes under pressure. than the often stiffening tice. The ring spacings wider also neglects i s considered necessary possibility of failure theory under com- bined internal a n d e x t e r n a l pressures and bending. The equations do, however, y i e l d an i n d i c a t i o n of s t i f f e n i n g r i n g spacing. Using which an analogy the can with a strut, Morley external developed pressure, an w, equation which a indicates she1 I maximum v e r t i c a l take and without assumes cylindrical no axial b u c k l ing. the wall The equation a l lows f o r thickness is small in expansion, comparison w i t h the diameter. w = 24 1 - v 2 v i s Poisson's r a t i o , (8.32) El d7 I = t3/12, so t For p l a i n p i p e , w = 2E 1 - v2 (3) (8.33) Experiments i n d i c a t e d a p e r m i s s i b l e stress 25% less than the theoretic a l , so f o r steel, w = 1.65 E t (8.34) tubes, material the to col lapse i t s elastic pressure limit wi II For thick-wal led be that which stresses the w a l l ( w = 2ft/d) whereas f o r intermediate wal I thickness, and elastic yield. An f a i l u r e w i I I be a combination of b u c k l i n g formula indicating the maximum empirical permissible pressure on a p i p e of intermediate thickness i s (8.35) where f i s the y i e l d stress. load may be increased i f s t i f f e n i n g r i n g s a r e used to It was found by experiment t h a t the collapse load, The e x t e r n a l resist w, s, buckling. i s i n v e r s e l y p r o p o r t i o n a l to if s the distance between s t i f f e n i n g r i n g s , i s less than a c e r t a i n c r i t i c a l length, L. 155 From experiment L = 1 . 7 3 E (8.36) so i f w w = = 2E ( t / d ) 3 for s t i f f e n i n g pipe, then f o r s t i f f e n e d p i p e , L2E ( t / d j 3 = 3.46 permissible stress is less than the theoretical (8.37) due to The actual imperfections i n the m a t e r i a l a n d shape of p i p e , so the p r a c t i c a l r i n g spacing i s g i v e n by (8.38) If the full elastic r e n g t h of pressures i.e. he p i p e i s to be developed w = o resist spacing vertical shou I d be external 'Jt, then the ring (8.39) Rings w i l l o n l y t be of use i f w >1.65E ( - ) 3 . I t should also be ascerd 2f t tained that w z - , which i s the e l a s t i c y i e l d p o i n t . d = Pft/d, then r i n g s w i l l o n l y be of use i f If w t/d<f/E = 1/30 (8.40) F u r t h e r studies of b u c k l i n g of s t i f f e n e d p i p e a r e g i v e n f o r m i l d steel. b y Stephenson (1973) a n d Jacobsen (1974). W Y Fig. 8.6 Pipe w i t h s t i f f e n i n g r i n g s 156 Example 1 : Tension Rings A The 500 mm bore p i p e i s to take an maximum and permissible the maximum working wall internal in pressure of wall can be is 5 N/mm2. to be is 100 10 stress the N/rnm*, thickness which rolled mm. and Assume a calculate 10 rnm diameter w i r e the required spacing is av ai l abl e for of the binding. b i n d i n g the p i p e An unstiffened p i p e c o u l d take an i n t e r n a l pressure of “ow pd 2t = 2 x 500 100 = 125, s o we r e q u i r e F/@ 2t = 120 0 1 5 = 0.8 Tension r i n g area parameter By inspection of Figs. t 1 82A -r‘td 1 . 8 2 ~ ~ ~= 1o 02 ~ . 10 ~ ‘ 1 0 x 5 0 0 the r i n g spacing r e q u i r e d to 8.la and 8.1b, reduce both the c i r c u m f e r e n t i a l p i p e w a l l stress a n d the r i n g stress to the desired v a l u e i s g i v e n b y s / m = 0.45, : . s = 0.45 J10 of x 500 = 32 mm. i s s l i g h t l y more than if Notice t h a t the amount steel required the p i p e were merely thickened to take the e x t r a pressure. becomes more noticeable the wider the r i n g spacing. it T h i s effect For wider spacing is the limiting tensile is usually in the the circumferential so wall stress which stress system, there i s l i t t l e point i n using high- r i n g s i f the p i p e w a l l i s of m i l d steel. Example 2: St i f f e ning R i n g s Design a 3 m diameter a uniformly distributed steel pipe with stiffening 60 kN/m2 with a r i n g s to support modulus of 3 load of soil N/mm2. Maximum steel stress = 103 N/mm2, delection 2%. Select t = 10 mm Then s / d = (210 000/503) ( . 0 0 3 3 ) 3 / 2 (8.39) 157 = 0.39 : . s = 1177 mm; Select 1200 mm. no b u c k l i n g i.e. ring Use 100 mm h i g h r i n g s w i t h h/b = 10 m a x f o r t h i c k n e s s b = 10 mm Centroid from c e n t r e w a l l c Moment o f i n e r t i a = = (h+t)bh 2( bh+ts) = 4.25 mm (8.41) (8.42) I = h3b -+ S(tc)' + 12s hb t3 12 + tC2 3104 mm3/mm = Extreme f i b r e d i s t a n c e r = h + (8.43) 100.8 mm A/d = Deflection: 0.1~0.060~3~ (8.22b) 8x210 0 0 x 3 1 0 4 ~ 10-9+0.05x3x33 = 0.017 = 1.7% Maximum w a l l s t r e s s f = = (0.1x0.10/3.0+0.003x3x3/(210000x0.011 3 1 0 4 ~ 1 0 - ~ /+0.006x3/210000 3~ 1.7 N/mm2. The section an ) ) 0.06 could or thus be modified. design By v a r y i n g the r i n g p r o p o r be possible i.e. both tions, optimum balanced may deflection l i m i t a n d stress l i m i t a r e attaine d simultaneously. REFERENCES B a r n a r d , R.E., 1957. D e s i g n a n d d e f l e c t i o n c o n t r o l o f b u r i e d steel p i p e s u p p o r t i n g e a r t h l o a d s a n d l i v e l o a d s , Proc. A m . SOC. f o r T e s t i n g M a t e r i a l s , 57. C l R i A ( C o n s t r u c t i o n I n d u s t r y Research a n d I n f o r m a t i o n A s s o c i a t i o n ) , 1978. D e s i g n a n d C o n s t r u c t i o n o f B u r i e d T h i n - d a l l P i p e s , Report 78, L o n d o n , 93 p p . Jacobsen, S., 1974. B u c k l i n g o f c i r c u l a r r i n g s and c y l i n d r i c a l t u b e s u n d e r e x t e r n a l p r e s s u r e , Water Power, 26 ( 1 2 ) . Morley, A . , 1919. S t r e n g t h o f M a t e r i a l s , L o n g m a n s Green E. Co., pp 326-333. S p a n g l e r , M.G., 1956. Stresses i n p r e s s u r e p i p e l i n e s and p r o t e c t i v e c a s i n g p i p e s . Proc. Am. SOC. C i v i l E n g s . , 82(ST5) 1054. 1973. S t i f f e n i n g r i n g s f o r p i p e s , P i p e s and P i p e l i n e s Stephenson, D., I n t l . , 18 ( 4 ) . Stephenson, D. ,1979. F l e x i b l e p i p e t h e o r y a p p l i e d to t h i n - w a l I nPVC p i p i n g , P i p e s a n d P i p e l i n e I n t l . , 24 ( 6 ) , 9-17. 158 Timoshenko, S.P. and Woinowsky-Krieger, S., 1959. a n d Shells, 2nd Ed., McGraw H i l l , N.Y., Ch. 15. Theory of Plates LIST OF SYMBOLS a - bs, o r area per u n i t length cross sectional a r e a of r i n g A b C distance from centre of w a l l to c e n t r o i d of w a l l section p i p e diameter i n t e r n a l p i p e diameter e x t e r n a l p i p e diameter modulus of e l a s t i c i t y passive resistance modulus of s i d e f i I I permissible w a l l stress d d. F - wal I stress bending stress circumferential stress bending stress under r i n g r i n g stress, o r r a d i a l stress i n p i p e w a l l wal I stress circumferential design factor r i n g height depth of b a c k f i l l above pipe I J - moment of inertia - j o i n t factor r a t i o of a c t i v e l a t e r a l pressure of f i l l to v e r t i c a l pressure c r i t i c a l r i n g spacing bending moment moment or deflection coefficient i n t e r n a l pressure pipe radius distance from c e n t r o i d to extreme f i b r e of beam r i n g spacing wal I thickness K 159 U V - deflection time l a g factor Poisson's r a t i o vertical pressure, subscript a refers to arching, b to W bending a n d d to deflection W Y - vertical load p e r u n i t length ( W = wd) r i n g thickness bedding constant def I ect ion z A 160 CHAPTER 9 SECONDARY STRESSES STRESSES AT BRANCHES If in the a hole i s cut wall will in the w a l l of a pipe, side of the circumferential the of a hole. small The stress increase on axis each at tangential hole stress on the horizontal the side elliptical i n a p l a t e i s (Tirnoshenko a n d Goodier, 1951), (9.1 S' = S(l S + 2 a/b) uniform vertical and b stress is applied to the axis where the a is the plate, length. a is For horizontal hole axis a = length b In and the the vertical circular applied the also the stress S ' case i s consequently three times hole o r of the branch on a the pipe may stress. of on a circular side circumferential increase to stress each that hole o r The branch three hole times in a in the p l a i n pipe. is it given will in be Fig. stress If the rein- distribution pipe force able wall beside a stress is plate 9.1. to at a all significant necessary the w a l l to where b r a n c h p i p e occurs. Reinforcing i s also desirespecially with low minimize pipework entrance pipe is distortion. i s to A common practice pressure mize the the main use s k i r t s at loss. than In such the b r a n c h connection to m i n i cases the size of hole cut in head larger the bore o f the b r a n c h p i p e and r e i n b r a n c h pipes at r i g h t the p i p e conthe branch forcing angles nection pipe cular force of is the the may to is be especially barrel to weld necessary. For small a a s u i t a b l e method of a collar onto the strengthening pipe main around (Fig. 9.2). The w i d t h of c o l l a r may be c a l c u l a t e d f o r any p a r t i by assuming otherwise out of the w' the have main the of col t a r been pipe, takes taken i.e. thickness which piece collar and the circumferential the diameter where t' would cut across 2t'w' = tD, thickness, t the the width, the D the of branch the main p i p e outside pipe. This pipe diameter is thickness wall in assuming are that permissible and that stress the the c o l l a r width is and main small walls the same, collar compared w i t h the b r a n c h p i p e diameter. 161 s t t f t t t t t t Fig. 9.1 Stress d i s t r i b u t i o n beside a hole i n a p l a t e under a uniform stress S. Fig. 9.2 Collar reinforcing at a branch pipe 7- lp-Sornetimes used LI Fig. 9.3 L a t e r a l w i t h e x t e r n a l crotch plates 162 For l a r g e r diameter b r a n c h pipes and branches at v a r i o u s angles to the m a i n pipe, crotch p l a t e s a r e p r e f e r a b l e to c o l l a r s ( B l a i r , 1946). Crotch P l a t e s Various types of s t i f f e n i n g p l a t e s have been proposed f o r r e i n f o r c (1941) pioneered the design a nomograph was ing laterals. of crotch The Swiss f i r m Sulzer Bros. and a design a i d plates, i n the form of l a t e r p u b l i s h e d b y Swanson et a l plates pipes. cases. and which The Trial would be welded (1955). The design was f o r e x t e r n a l the j u n c t i o n of the i n t o the c r o t c h a t nomograph was p r e p a r e d b y a n a l y s i n g a sections were selected were compatible. l a r g e number of and r e v i s e d u n t i l forces balanced r e c t a n g u l a r sections f o r crotch deflections Only p l a t e s were considered although Figs. on use 9.3 T sections may have g r e a t e r r i g i d i t y . p l a t e s based parameters f o r to 9.7 a r e design c h a r t s f o r e x t e r n a l crotch but expressed in dimensionless Swanson's in any results, of system units. small The design c h a r t s a r e f o r s i n g l e c o l l a r diameter laterals) and for double crotch plates (normally for p l a t e s ( f o r l a t e r a l diameter n e a r l y equal to the m a i n p i p e diameter). The method of design u s i n g the c h a r t s i s as follows: C a l c u l a t e Pd / f t knowing t h e maximum i n t e r n a l pressure P, the 1 main p i p e diameter dl, the permissible p l a t e stress f a n d an assumed p l a t e thickness t. Read off from Fig. 9.5 the crotch plate bl width expressed in terms of plate the main p i p e diameter dl. for a 90" lateral with and cl a r e the crotch as the widths the same diameter main pipe. If are the branch is read at an a n g l e to the b a r r e l , and or the diameters correct the unequal, Kb K from Fig. 9.6 and crotch p l a t e w i d t h b y m u l t i p l y i n g bl The Read c/dl plate the and widths are now b y K b a n d c1 b y Kc. p l a t e top the angle depth of b=d (bl/d,) K a n d c=dl(c,/dl)K 1 b r a t i o a/dl corresponding to b/dl lateral from Fig. 9.7 and . or the hence c a l c u l a t e a, Check plate the top depth of each plate. either plate width If so, whether i s g r e a t e r than 30 times the is liable again. to The buckle, shape so and thickness. the plate the plate and increase thickness try weight of p l a t e s could be optimized b y t r i a l . 163 Fig. 9.4 E x t e r n a l crotch p l a t e s The shape the of the line p l a t e should of intersection then of be the drawn for fabrication pipes. Single plates by may developing often be bent at i n t o shape whereas double p l a t e s w i l l intersection point, and if be f i l l e t welded together the t h i n enough, may a l s o be bent to follow the intersection of the b r a n c h a n d the b a r r e l . b /d, c, dtJ, 8 1.0 0.5 0 0.5 20 -1 pd 15 . f t Fig. 9.5 Crotch p l a t e side w i d t h 164 Fig. 9.6 Effect of l a t e r a l diameter and angle on c r o t c h p l a t e s i z e . 165 For right large installations to a t h i r d p l a t e may the main pipe be r e q u i r e d , 9.3). placed at Although angles the a x i s of (see F i g . design c h a r t s f o r merely a d d i n g a 3-plate designs a r e not a v a i l a b l e , design. Swanson suggests t h i r d p l a t e t o a 2-plate Discretion should be used i n r e d u c i n g the thicknesses o r widths of the two c r o t c h p l a t e s i n such circumstances. The deflections are reduced considerably by a d d i n g a t h i r d p l a t e though. Whether judgement. crotch The p l a t e s should advises be used at all i s also a matter of if the internal author using crotch plates design pressure P of safety, of i s g r e a t e r than the wall t, is y t a"/135Gd2 where G i s the factor 1 thickness of the main p i p e , d2 i s the a i s the a n g l e between the a x i s of diameter the b r a n c h p i p e a n d the b r a n c h p i p e a n d b a r r e l . y i s y i e l d stress. Internal Bracing (Stephenson, in 1971) external crotch plates prompted Escher Certain Wyss L t d . pipe disadvantages (Suss a n d Hassan, External crotch and 1957) to i n v e s t i g a t e i n t e r n a l b r a c i n g for plates act in bending, steel than consequently internal use 'Y's. material inefficiently require more crotch p l a t e s which could be i n p u r e tension. An internal web may also act as a guide vane. T h i s effect, com- b i n e d w i t h a g r a d u a l taper of the pipes a t the j u n c t i o n , losses through is reduces head water flowing webs The for some flow configurations. For the case of loss w i t h two pipes to a confluence, less than with the head a internal junction. considerably standard 'T' arrangement of the b r a n c h p i p e j o i n i n g the main p i p e a t a skew angle with both pipes gradually flared at the confluence, together with i n t e r n a l b r a c i n g f o r the acute a n g l e (see F i g . pcmping into two station branch delivery pipes, pipes. such as For 9.8) i s recommended f o r water f l o w i n g from a main p i p e station suction pipes and pumping penstocks f o r performed to hydro-electric stat ions, h y d r a u l i c model tests should be and determine the best angles of divergence a n d taper, the arrangement of the i n t e r n a l b r a c i n g . The o v e r a l l external weight of steel for internal bracing is less than f o r transport c r o t c h plates. The compact arrangement f a c i l i t a t e s a n d reduces excavation costs. Unless confluence, ing the pipes are designed with cone-shaped flares paths, with at the internal bracing will and p r o t r u d e i n t o the flow head losses than caus- increased velocities higher external crotch p l a t e s o n l y . there w i l l diffusers On the other loss. with h a n d i f the expansion i s too a b r u p t be a h i g h head increases rapidly The head loss coefficient f o r conical the a n g l e of flare once the angle between the w a i l a n d a x i s exceeds s u i t a b l e compromise f o r appears to about 7; degrees (Rouse, 1961). A the angles of f l a r e f o r a 45-degree confluence to be 74 degrees internal pipes to the axis for the main pipe and 15 degrees to the a x i s f o r t h e b r a n c h p i p e . The branch use and of main bracing a confines the angle between the practical range. For confluence angles approaching 90 degrees ( I T ' j u n c t i o n s ) the b r a c i n g web would obstruct the flow in in the the main main pipe. For very small angles of confluence the hole cut p i p e becomes l a r g e r a n d the b r a c i n g would be impractically a 45-degree pipe heavy. T h e design c h a r t s presented here a r e confined to and to confluence, would have for any other angle with a of approach the branch be constructed the use of bend immediately before the f l a r e . Note that i n t e r n a l b r a c i n g i s confined to the acute angle, as internal bracing at be the obtuse angle with would obstruct flow. The obtuse a n g l e must strengthened external crotch plates. To minimize head losses, the diameters of the main incoming p i p e , p i p e should be such t h a t the velo- the b r a n c h p i p e a n d the confluent c i t i e s i n a l l pipes a r e approximately equal. If all branches of the confluence are tangential to a sphere whose centre l i e s a t the surfaces w i l l flat. the There may main pipe the the intersection of t h e i r axes, the intersection of be i n planes. T h i s means t h a t the b r a c i n g webs a r e be a k i n k i n the obtuse a n g l e intersection l i n e where flare meets the confluent of it pipe (see plate Fig. 9.8). may To be eliminate continued would be resulting the problems where torsion, should 'B' beyond strong point bend. The pipe walls enough to t r a n s f e r the loads to t h i s p l a t e , and the r e s u l t i n g arrangement simp1 i f i e s f a b r i c a t i o n . To determine the p r o f i l e s of were set distance the lines of intersection of the cone point surfaces, and the equations horizontal up r e l a t i n g the cone r a d i i a t any along the i n t e r s e c t i n g p l a n e to the disUsing the tance from the intersection of the axes along the main a x i s . fact that the elevations of the surface of both cones a r e equal on the intersection I ine, The a n g l e of the the coordinates of the intersection I ine were derived. intersection p l a n e to the main a x i s , 8 , i s given by the equation t a n confluence a x i s and The ceeding angle, B @ = (cos Q - cos a cos is the angle of e ) / s i n a cos branch e , where a i s the its the cone surface to e i s the a n g l e of the main cone surface to i t s a x i s . profiles the w e r e obtained b y computer a n a l y s i s pro- intersection in steps along i n t e r s e c t i n g plane. T h i s was done simul- taneously w i t h the stress a n a l y s i s . Although simple must pipe it i s possible to analytically, study the stresses case in the bracing for 'Y's the general i s v e r y complex a n d be solved by computer, line. In fact proceeding i n small increments a l o n g the previous studies have relied on model intersection studies to o b t a i n the stresses a t the intersecting plane. The analysis was based on membrane theory i.e. the pipe walls can take no b e n d i n g stress. is The c i r c u m f e r e n t i a l w a l l stress in a cone PR/(cos 0 ) per u n i t w i d t h a n d the l o n g i t u d i n a l w a l l stress PR/(2 cos e ) per unit width where P i s the l i q u i d pressure a n d R i s the r a d i u s of the cone p e r p e n d i c u l a r to the a x i s . The forces due to the cone wall stresses on an element of the intersection I i n e were resolved i n t o three components, p e r p e n d i c u l a r to the intersection plane, The results v e r t i c a l l y a n d h o r i z o n t a l l y in the plane. that the perpendicular forces on the interthe indicated section p l a n e were i n a l l cases zero. resultant force line, of in the was plane, to The p o s i t i o n and d i r e c t i o n of four was points along the s i d e of It the the intersection l i n e of plotted g r a p h i c a l l y . observed that action the r e s u l t a n t was constantly i n s i d e the intersection p l a n e a n d a c t i n g i n tension on the i n t e r n a l b r a c i n g p l a t e . The tension. centre bracing crown, Hence most economical internal b r a c i n g p l a t e would be one i n pure T h i s s t a t e could be assured i f the r e s u l t a n t force f e l l on the line of the plate. in Thus Figs. from plate the the 9.8 the may width to crown be of the at the widest the internal or plates is twice indicated the 9.10 to centre, distance of the r e s u l t a n t force. in terms of the the thickness plate derived anywhere permissible stress, and width else calculated the r e s u l - knowing the p l a t e thickness tant be force on found the and position and magnitude of l i n e of the cones. bracing thicker intersecting the in most I n some cases i t w i l l plate thickness is that economical case a impractically and the thin, which shape p l a t e may be selected, The n a r - corresponding are interpolated bending from the c h a r t s . and rower contain plate plates i n combined than to the the and tension consequently the was more steel perpendicular from the p l a t e in p u r e tension. resultant for force at The w i d t h of points = various f obtained /tw2 equation extreme f i b r e stress, 6F (u-w/Z) + F/tw, on A where f i s permissible p l a t e tensile stress, F i s magniin tude of question resultant the force which acts a t a distance u from the p o i n t intersection analysis line, was w is plate width and t is plate crotch thickness. similar performed for the e x t e r n a l p l a t e s b r a c i n g the obtuse angle. The design flare charts, of to Figs. 9.8 to a 9.10, were compiled and f a c i l i t a t e the and The various angles of crotch the plates for pipe and 45 degree ' Y ' branch pipe. main most suitable flare angles should be selected from h y d r a u l i c considerations. determine head losses could be conducted i f warranted. Model tests to 169 -.--- 6; / / ..L I j Lc=!23 tcn2 2 G.03303 e \ 0 " \ WITH R E C O M M E N D E D A N G L E S b TOP H A L F OF EXTERNALCROTCH PLATE B TE c TOP HALF OF INTERNAL C R O T C H ~ P L , 4 F i g . 9.8 Crotch p l a t e s f o r 7io/15O confluence. 170 b TOP H A L F OF EXTERNAL CROTCH PLATE 6 c TOP HALF OF INTERNAL CROTCH PLATE A Fig. 9.9 Crotch plates f o r p l a i n p i p e confluence 171 I OL 0.2 0 02 0.L X / D 0.6 b TOP HALF O F EXTERNAL CROTCH PLATE B c TOP HALF OF INTERNAL CROTCH PLATE A Fig. 9.10 Crotch p l a t e s f o r confluence pipe. plain pipe with 15" taper 172 The design procedure f o r a trial plate width, t, say the crotch p l a t e s would then be to select maximum indicated, and compute the the p l a t e thickness, crotch plate for from the corresponding formula. the obtuse angle is rigid To ensure that the to enough withstand buck1 i n g under bending compression, less less than than the p l a t e thickness should not be should also p r e f e r a b l y not be w/30. the The wall After plate thicknesses of thickness selecting the main p i p e , to ensure d u r a b i l i t y a g a i n s t wear. the p l a t e thicknesses, the corresponding p l a t e shapes a r e interpolated from the a p p l i c a b l e c h a r t . STRESSES AT BENDS The than wall stresses in a fabricated or cast iron bend are higher those i n a p l a i n p i p e w i t h the same w a l l thickness. induced are as the bend by tends to straighten thrusting the Longitudinal out, local the stresses bending outside are stresses wall, caused anchor blocks on against and circumferential the stresses inside of the bend a r e m a g n i f i e d because on the outside of l e n g t h of The the w a l l on the i n s i d e i s less than the bend. increase in c i r c u m f e r e n t i a l stress stress a n d stress on is it the normally is safe of more severe than to design the bend. only The increase i n l o n g i t u d i n a l worst circumferential on the for the inside wall thickness outside of the bend could a c t u a l l y stress, but it be reduced i f account i s taken o n l y of circumferential i s safe to keep the same thickness as on the i n s i d e of the b l o c k . Circumferential Using membrane theory i n g stress, of stresses a r e c a l c u l a t e d below. i.e. assuming the p i p e w a l l takes no bend- the c i r c u m f e r e n t i a l force on a length of w a l l on the inside to the bend i s equated the t h r u s t due to the i n t e r n a l pressure on 9.11, the i n s i d e segment of p i p e shown shaded i n F i g . ft f (R-D/2) = -PD 0 = P(R-D/4) 0D/2 (9.2) (R-D/4) 2t i.e. ratio (R-DJ2) the normal (R-D/4) w a l l thickness at the bend should be increased i n the (R-D/2) where R i s the r a d i u s of the bend a n d D is / the p i p e diameter. 173 Fig. 9.11 Stress concentration a t a bend In etc., work addition discussed caused in for to the so-called secondary stress at bends, junctions in pipe- above, there a r e sometimes movements, t e r t i a r y stresses strains or by relative elastic temperature variations designed pipeline installed. axial and piping in systems. These stresses a r e r e a l and plant a n d should be or at large exposed chemical pipework thrust interconnections if no movement joints or anchors a r e system w i t h could be A pipe lateral system can be treated and design as a s t r u c t u r a l The such thrusts movements. techniques system as analysed bution, using structural or moment-distriwhich a r e (See also slope-deflection in f i n i t e element standard methods, many o f available the form of computer programs. Crocker a n d K i n g , 1967). THE P I P E AS A BEAM Longit udi na I Bend ing Pipes should longitudinal settlement between of normally even be if designed they are to to r e s i s t some bending be buried. i n the direction the Unevenness o r o r span with the bedding Three could possible cause sections to c a n t i l e v e r patterns together supports, bending 174 corresponding critical The maximum b e n d i n g moments a r e i n d i c a t e d i n F i g . which a simply supported pipe 9.12 . span could accom- modate i s c a l c u l a t e d below. The m a x i m u m f i b r e s t r e s s i s (9.3) Fb = M/Z M is t h e b e n d i n g moment and Z t, is small where is t h e s e c t i o n m o d u l u s . For a p i p e whose w a l l d i a m e t e r D, thickness, in comparison w i t h the i n t e r n a l Z = nD2 t / 4 = (9.4) (9.5) (9.6) So if M WL2/8 Fb = W L Z / ( 2 n D 2t ) = o r L2 and 2nD2 t Fb/W pipe of specific weight y if a yw is conveying water at a specific weight L = J8DtFb/(ywD D = 1 m, + t 4ySt) = (9.7) F b = 100 N/mm2, yw Thus f o r ys 0.012 m, the - 10 000 N/m simply 3 , = 80 000 N/m then maximum permissible supported s p a n L = 26 m or 86 f t . For low internal water pressures, b u c k l i n g of the w a l l s may also b e a p r o b l e m and t h e p o s s i b i l i t y s h o u l d b e i n v e s t i g a t e d ( e s p e c i a l l y a t t h e s u p p o r t s w h e r e t h e s h e a r s t r e s s is h i g h ) . See also P e a r s o n , P i p e S t r e s s at Saddles The m a x i m u m local stress in a continuous o r s i m p l y supported p i p e 1954): (9.8) 1977. supported in a s a d d l e i s (Roark, F = (0.02 - 0.00012 ( B - 90°))(Q/t' )Loge (f) where span, due to Q Q i s the total saddle reaction. Note t h a t f o r a s i m p l y s u p p o r t e d i.e. a i s the r e a c t i o n d u e to two ends r e s t i n g o n the support, the weight of pipe of length equal to the span, as for continuous pipe. If Q i s i n Newtons a n d t i n mm t h e n F i s i n N / m m 2 . 175 WlUNlT LENGTH WlUNlT LENGTH WlUNlT LENGTH REACTION MAXIMUM BENDING MOMENT. WL12 wL2/a Wll2 WLI2 WLl2 0 WL DEFLECTION 5 x 2 3 z El a. Simply Supported b. Fixed Ends c. Cantilevered F i g . 9.12 Beam moments and deflections The a n g l e of crete width or of strap the bottom support, 6 saddles. , i s n o r m a l l y 90" is practically is small or 120' for conthe pipe The stress provided it independent of with the support compared diameter. To t h i s local stress a t the saddle must be added the rnaxi- mum l o n g i t u d i n a l bending stress a t the support f o r the p i p e a c t i n g as unless a j o i n t occurs a t the support. a continuous beam, R i n g Girders Steel ground may pipes etc. may be laid above ground over ravines, marshy B u c k l i n g of t h e p i p e a n d stresses i n these circumstances as there i s no s i d e f i l l Rigid r i n g be more severe than and under the ground, support the p i p e saddles cause stress concentrations. a r e useful in cross i n these circumstances. section, The or g i r d e r s at each support may the the be back plain fixed of The rings with in rectangular all the T o r H shaped, r o u n d the pipe. ring may The be local p i p e bending stress using the ring vicinity in evaluated theory developed Chapter 8. longitudinal bending stress i n the p i p e w a l l under a r i n g is 1.65 0.91 Pd + h J%T/A 2h (9.9) 176 where be A i s the cross sectional any longitudinal area of in the r i n g . the pipe To due t h i s stress must to beam action added stress between supports. T h e r i n g stress i n the r i n g g i r d e r i s 1 In + 1 0.91A/(hj hd) addition there Pd 2 7 will be local stresses due to t h e method of (9.10) fixing the r i n g girder to the supports. Legs a r e securely fixed to the r i n g The weight g i r d e r a n d rest on a s l i d i n g or of the p i p e a n d contents r o l l e r b e a r i n g on a p i e r . i s t r a n s f e r r e d to the bottom h a l f of the r i n g g i r d e r a n d thence through the legs to the p i e r . A more comprehensive a n a l y s i s in Crocker and King of the stresses See also i n r i n g girders Cates is presented Scharer (1967). (1950) and ( 1933). TEMPERATURE STRESSES Pipes outside with high differences to r a d i a l The in temperature between inside and will be subject differences. maximum on the a n d c i r c u m f e r e n t i a l stresses due to l o n g i t u d i n a l stresses surfaces, being if temperature have their circumferential and on the inner value a n d outer compressive the and i n n e r surface and tensile on the inner wall is above the outer surface temperature on the heat flow t h a t on the outer wall, i s steady. I f the w a l l is thin i n comparison w i t h the p i p e diameter, equations: the stresses may be approximated b y the f o l l o w i n g on the i n n e r surface F = Fe c = F = -20 P = aET -2(1-u) a ET (9.11) a n d on the outer surface F where (9.12) a i s the thermal coefficient o f expansion, E i s the modulus of elasticity, T i s the temperature difference, v i s Poisson’s r a t i o , Fc i s c i r c u m f e r e n t i a l stress and Fe i s l o n g i t u d i n a l stress. i s compressive a n d is always less than the The r a d i a l stress maximum c i r c u m f e r e n t i a l and l o n g i t u d i n a l stresses, For b e i n g zero on both boundaries. the stresses are rela- normal c I imatic temperature differences 177 tively ‘C, A low. v = Thus f o r T = 10°C, E = 200 000 N/mmz, a = = 12 x per 0.3 f o r s t e e l p i p e , t h e n F m a x stress a may of also be as result 17 N/mmz. in a longitudinal induced pipe restrained longitudinally temperature change after instal lation. The m a g n i t u d e o f after installation) supports). t h i s stress (see Ch. i s aET (tensile if the temperature drops an 10 f o r analysis including effects of REFERENCES B l a i r , J.S., 1946. R e i n f o r e c e m e n t o f b r a n c h p i p e s . E n g i n e e r i n g , 162. Cates, W.H., 1950. D e s i g n s t a n d a r d s f o r l a r g e d i a m e t e r s t e e l w a t e r p i p e , J. Am. W a t e r W o r k s Assn., 42. C r o c k e r , 5. and K i n g , R.C., 1967. P i p i n g H a n d b o o k , 5 t h E d . , M c G r a w H i l l , N.Y. P e a r s o n , F.H., 1977. Beam b e h a v i o u r o f b u r i e d r i g i d p i p e l i n e s . P r o c . Am. SOC. C i v i l E n g r s . , 108 ( E E 5 ) 767. 1954. F o r m u l a s f o r s t r e s s and s t r a i n , McGraw H i l l , N.Y. R o a r k , R.J., p . 418. Rouse, H., 1961. E n g i n e e r i n g H y d r a u l i c s , W i l e y , N.Y., S c h a r e r , H., 1933. D e s i g n of l a r g e p i p e l i n e s . T r a n s . Am. SOC. C i v i l Engs., 98 ( 1 0 ) . Stephenson, D., 1971. I n t e r n a l b r a c i n g f o r p i p e c o n f l u e n c e s . T r a n s . , S.A. I n s t n . C i v i l E n g r s . , 13 (11). Sulzer, 1941. P a t e n t e d s t i f f e n i n g c o l l a r s o n t h e b r a n c h e s o f highpressure p i p e l ines f o r hydroelectric power works. Sulzer Technical R e v i e w , 2 ,lo. Suss, A. and H a s s a n , D.R., 1957. R e d u c t i o n o f t h e w e i g h t and loss o f in d i s t r i b u t i o n p i p e s f o r h y d r a u l i c p o w e r l a n t s . Escher energy Wyss News, 30 (3) 25. Swanson, H . S . , C h a p t o n , H.J., W i l k i n s o n , W.J., King, C.L. and N e l 1955. D e s i g n o f w y e b r a n c h e s f o r s t e e l p i p e s . J. A m . son, E.D., W a t e r W o r k s A s s n . , 47 ( 6 ) 581. Timoshenko, S. and G o o d i e r , J.N., 1951. T h e o r y o f E l a s t i c i t y , McGraw H i l l , N.Y. L I S T OF SYMBOLS A a,b a,b,c - a r e a of r i n g g i r d e r h o r i z o n t a l and v e r t i c a l a x e s o f an e l l i p s e - c r o t c h p l a t e t o p and s i d e w i d t h s p i p e diameter modulus of e l a s t i c i t y permissible crotch p l a t e stress r e s u l t a n t force on c r o t c h p l a t e a t a n y point, factor o f safety wal I thickness o r stress D or dE f F G - h 178 span o r length bending moment water pressure (same u n i t s as f ) saddle reaction radius stress a p p l i e d to a p l a t e crotch p l a t e thickness temperature difference distance from p i p e w a l l to F w i d t h of crotch p l a t e at any p o i n t load p e r u n i t l e n g t h horizontal crotch p l a t e distance from crown along centre-I ine of Y - vertical plate distance above mid-plane or crown of crotch section modulus a n g l e of confluence of b r a n c h p i p e w i t h main p i p e coefficient of temperature expansion a n g l e between crotch p l a t e and main p i p e a x i s , o r a n g l e of support specific weight angle of flare, or taper, of main pipe (measured from a x i s to cone) a n g l e of f l a r e , Poisson's r a t i o o r taper, of b r a n c h p i p e CHAPTER 10 PIPES, FITTINGS AND APPURTENANCES PIPE MATERIALS Steel Pipe Steel i s one of the most high versatile materials for tensile strength. pipe walls, relatively as it to i s d u c t i l e yet work, has a It is easy a n d the welded j o i n t f r e q u e n t l y used w i t h steel i s the strongest type of j o i n t . Steel grades used f o r p i p e s i n the U.K., and their corresponding minimum y i e l d stresses a r e as follows: BS 4360 Grade 40 Grade 50 Grade 55 : 230 N/mm2 355 N/mm2 : 450 N/mm2 290 N/mm2 US 572 Grade 4 2 Grade 50 Grade 60 Grade 65 : : for 345 N/mm2 414 N/mm2 448 N/mm2 high-pressure pipelines but The for they higher grades are preferred low pressure p i p e l i n e s the lower grade steels a r e more economical, a r e easier to weld, a n d on account loads. steel of the e x t r a wall thickness they a r e more r e s i s t a n t to e x t e r n a l Small-bore seams, welded to (less than 450 mm) pipes are rolled without and up but larye-bore pipes are made from steel plate, in bent lengths either horizontally or spirally. site. Pipes a r e made Steel pipe for 10 m and more a n d j o i n t e d on asbestos cement and it is more expensive small bores to 2nd than concrete, low pressures, and plastic coating pipe and requires sheathing prevent corrosion. Cast Iron Pipe Cast iron is more corrosion-resistant I n fact actual than steel, but more expensive and more r i g i d . used f o r p l a i n p i p e , tapers and flanges. sand c a s t i n g 'specials' i s now r a r e l y such a s bends, grey a l t h o u g h i t i s used f o r Plain p i p e s a r e n o r m a l l y formed of iron 180 or and ductile iron by of centrifugal ductile iron spinning. pipes are Standard specified pressure in classes and dimensions BS 4772 of grey i r o n p i p e s i n 854622. Asbestos Cernent Pipe Asbestos cement is able to is resist p i p e i s made of relatively cheap, high cement and asbestos f i b r e , stresses. Although which tensile and asbestos it is cement relatively strong corrosion-resistant, 'specials'. susceptible to shock damage and cannot be used f o r Joints a r e made w i t h a sleeve f i t t e d w i t h r u b b e r sealing r i n g s . Concrete Pipe Reinforced ical loads and in for large or prestressed concrete pipes a r e s u i t a b l e and economThey on are able of diameters. than steel to resist external wall buckling thickness, to be easier are account Their their extra corrosion and resistant. later main weaknesses There i s as appear jointing making connections. yet not much long-term experience w i t h prestressed concrete pipes. Plastic Pipe Technological this has been o f advances special in plastics in in the 1960's were r a p i d and Unplasti- interest pipeline engineering. cized p o l y v i n y l c h l o r i d e gases, Kingdom for small for drains, and pipes a r e now used extensively irrigation is is and also sewer used pipes to more a f o r chemicals, i n the United limited expensive has extent than waterpipes, Europe. pipes Polyethylene although High it bore large usually UPVC diameters. density polyethylene recently been used w i t h some success f o r Glass lines. it l a r g e diameter p i p e l i n e s . used to a l i m i t e d extent with as an it for fibre is and resin is also pipefiller It comparatively for some expensive but used inert is suitable specialised applications i s corrosion- resistant, r i g i d , Although and is still l i g h t and strong. has not yet stood the r i g o r o u s test of time pla sti c pipe not acceptable under many by-laws, i t s many advantages a r e causing The i t to g a i n r a p i d acceptance amongst engineers. working stress of plastic i s less 14 N/mrnz so p l a s t i c cannot be used f o r limited l a r g e diameter high-pressure mains. I t i s also subject to can cause strength and deterioration w i t h time a n d to its flexibility buckting collapse. in difficult loss as It i s resistant many corrosive f l u i d s a n d a n d gas i t can is less can be used pipes. be The locations such as undersea o u t f a l l s i s lower than f o r a l i n i n g to other friction most m a t e r i a l s a n d types of pipes. It used beneficially subject to encrustation than other types of p i p e , accommodates g r e a t e r ground movements a n d i s easier a n d l i g h t e r to l a y . On the other h a n d it has a high coefficient of thermal expansion, so joints may be loosened and may i f the p i p e contracts on cooling. distort or even collapse under I t i s susceptible to damage load. Ribbed and stiffened pipes a r e b e i n g developed to overcome these l i m i tations. P l a s t i c p i p i n g i s n o r m a l l y made of thermoplastic which i s r e l a t i v e ly easy to As extrude when heated. Polyethylene and it PVC are thermoused Polyearlier plastics. in an PVC i s f l e x i b l e a n d e x h i b i t s creep, (UPVC) f o r than i s generally pipes. u n p l a s t i c i z e d form is easier were to the manufacture of and for this ethylene work UPVC reason developments with polyethylene. With improvement i n production techniques UPVC i s now cheaper than polyethylene a n d i t holds c e r t a i n other advantages. expansion It is stronger and has a smaller coefficient of thermal than polyethylene, (HDPE) has although improved recent ly-developed Polyethy- high-density lene for polyethylene properties. i s more d u c t i l e than UPVC a n d f o r t h i s reason i s often p r e f e r r e d gas p i p i n g . for Rubber toughened p l a s t i c s such as ABS have a l s o been pipework. of Properties low of plastics are tabulated of plastics, water developed flexible in the appendix. Because the elasticity hammer pressures a r e less severe than f o r other m a t e r i a l s . Plastic though factory pipes may be j o i n t e d are or by solvents for large of fusion welding, al- these fitted methods flanges difficult spigots diameters. with rubber Screwed o r rings are and sockets also used. The manufacture of moulded bends, tees a n d branches is difficult i n UPVC a n d even more so i n HDPE so steel o r C.I. quen t I y used. The p r i c e of the 1960's, PVC pipes i n the U.K. f i t t i n g s a r e fre- dropped b y more than 30% in whereas other p i p e m a t e r i a l s a r e c o n t i n u a l l y i n c r e a s i n g i n 182 cost. cast than In iron the U.K., for PVC pipes are less cheaper than than asbestos cement pressures and less pipes diameters 450 mm and 1 N/mmz. I t i s r a p i d l y r e p l a c i n g salt-glazed and asbestos-cement pipes f o r sewers a n d low pressure systems. At out least 5700 m i l l i o n was world. used The in figure ever is spent i n 1972 on p l a s t i c p i p i n g throughto r i s e considerably and also new as plastic the likely pipes are increasing proportions (see discoveries 1948; may yet r e v o l u t i o n i z e BVMA, 1964; P a u l , pipeline engineering Boucher, 1954). LINE VALVES There a r e many which types of v a l v e s f o r use i n p i p e l i n e s , the choice of The spacing of v a l v e s a n d the size w i l l smaller than side. In depends on the d u t y . depend on economics. the pipe diameter, Normally v a l v e s a r e sized s l i g h t l y installed with a reducer on and either waterworks the same practice i t level as i s p r e f e r a b l e to keep the s o f f i t of the v a l v e at soffit of the pipe, to prevent air being the trapped, be lined whereas up. in sewerage a n d sol i d s t r a n s p o r t , the i n v e r t s should I n choosing the cost it the of size, the be the cost of loss to the v a l v e should be it, although the full in weighed certain against head through circumstances may desirable maintain pipe bore ( t o prevent erosion o r b l o c k a g e ) . Isolating km, the valves are being of frequently a installed at of intervals and of 1 to 5 spacing Sections the be function economics operating problems. leaks waste valves profile. It around and the p i p e l i n e may water which have to be isolated to r e p a i r would h a v e to be d r a i n e d to volume of a would are f u n c t i o n of the spacing of i s o l a t i n g valves. Scour i n s t a l l e d at the bottom of each major d i p i n the p i p e l i n e i s sometimes a d v i s a b l e to in-line i n s t a l I smal I-diameter by-pass valves v a l v e s to equalize pressures across the gate a n d thus ( w h i c h may be manual o r by means of an e l e c t r i c facilitate opening o r mechanical a c t u a t o r ) . Sluice Valves Sluice v a l v e s , o r g a t e valves, a r e the normal type of v a l v e s used 183 for isolating or scouring. They seal well under high pressures a n d when f u l l y open o f f e r l i t t l e resistance to f l u i d flow. There spindle are two is types attached of to spindles the for raising does the gate: A rising which gate and not r o t a t e w i t h the screwed handwheel, attachment and a non-raising s p i n d l e which i s rotated i n a i n the gate ( F i g . 10.1). The r i s i n g s p i n d l e type i s easy to I u b r ica t e. The gate may be para1 lel-sided or wedge-shaped. the wedge-gate seals best b u t may be damaged b y g r i t . gunmetal sealing For low pressures r e s i l i e n t o r faces may be used b u t f o r high pressures s t a i n l e s s steel seals a r e preferred. Despite sometimes sluice valves' to simplicity operate. and positive a action, force they to are troublesome They need big unseat them a g a i n s t a high unbalanced pressure, minutes to t u r n open o r closed. a n d l a r g e v a l v e s t a k e many Some of the problems can be overcome b y i n s t a l l i n g a v a l v e w i t h a smaller bore t h a n the p i p e l i n e diameter. Fig. 10.1 Sluice v a l v e Butterfly Valves ( F i g . 10.2) Butterfly a n d occupy for sluice valves less are cheaper The than sluice valves for larger sizes space. sealing at i s sometimes not as e f f e c t i v e as pressures. They also offer a valves, especially high fairly h i g h resistance to flow even i n the f u l l y the flow open state, because the thickness of the d i s c obstructs even when i t i s rotated 184 90 degrees to the fully open position. Butterfly valves, as well as s l u i c e valves, the high gates and a r e not s u i t e d f o r operation in p a r t l y open positions as seatings to open would them erode rapidly. high As both types require have torques against pressure, they often geared handwheels o r power d r i v e n actuators. Fig. 10.2 Butterfly valve Globe Valves Globe v a l v e s have a c i r c u l a r seal spindle pipe and handwheel. The flow The seating connected a x i a l l y is a ring to a v e r t i c a l to the perpendicular axis. changes d i r e c t i o n through 90 degrees twice thus r e s u l t i n g i n h i g h head losses. bore pipework valve. a n d as taps, The v a l v e s a r e n o r m a l l y used i n small- a l t h o u g h a v a r i a t i o n i s used as a control Needle and Control Valves ( F i g . 10.3) Needle v a l v e s a r e more expensive than s l u i c e a n d b u t t e r f l y v a l v e s but are w e l l ing action suited for they t h r o t t l i n g flow. whereas They and have a g r a d u a l butterfly throttloffer as close sluice valves l i t t l e flow damage. springs, resistance u n t i l p r a c t i c a l l y shut Needle valves may or be used to with and may suffer c a v i t a t i o n counterbalance constant weights, pressure accumulators actuators maintain conditions e i t h e r upstream o r downstream of the v a l v e , a constant even axial at flow. o r to m a i n t a i n They a r e streamlined i n design a n d r e s i s t a n t to wear velocities. The cone method of i n t o a seat. sealing is to high flow push an needle o r spear-shaped There i s often a p i l o t needle which operates f i r s t to balance the heads before opening. A v a l v e w i t h a s i m i l a r h y d r a u l i c c h a r a c t e r i s t i c to the needle v a l v e 185 is the sleeve valve which is suitable seal for use discharging into the atmosphere or orifices spray, an open b a y . the tube They b y a sleeve which s l i d e s over around thereby and spread the flow i n a n umbrella-shaped valves are dissipating used as the energy. water Needle a n d sleeve a l s o occasionally to an electric for cone or hammer release v a l v e s when coupled (see Chapter working of the hydraulic actuator as the 4). They are require the the dismantling valve. sealing The maintenance valve is away a parts inside but of variation from the needle v a l v e instead cone rotates pipe axis being withdrawn a x i a l l y . Fig. 10.3 Needle v a l v e Spherical Valves ( F i g - 10.4) have Spherical it. valves a rotary opened p l u g with there an axial hole t h r o u g h as When the v a l v e bore i s equal is fully to that i s no resistance to flow the of the pipe. The v a l v e s close b y action rotating the sphere, a n d normally have a n offset to unseat them before r o t a t i n g the sphere into the open position. 186 Fig. 10.4 Spherical valve Reflux Valves Reflux, are used (Fig. 10.5) or to non-return, flow or check valves as they a r e also known, direction. Under stop automatically the gate in the reverse by normal the flow flow conditions i s k e p t open the flow, and when stops, the horizontally h i n g e d g a t e closes b y g r a v i t y o r w i t h the a i d o f s p r i ngs. to A counterbalance can be f i t t e d to the gate s p i n d l e fully open a t practically all flows, does or it could be keep the gate used to assist in r a p i d c l o s i n g when u s e d to a s s i s t c l o s i n g . which case the the flow stop. Springs are a l s o sometimes multi-gates, obstruct the in Larger reflux v a l v e s may h a v e partially difficult. thickness of the of e a c h g a t e w i l l pipeline may be flow, and swabbing Mounted in h o r i z o n t a l tend to flutter at pipes, t h e g a t e s of and for some t y p e s o f r e f l u x v a l v e s this reason an offset hinge low flows, w h i c h c l i c k s t h e g a t e open is sometimes used. AIR VALVES (see a l s o 1943). of air Lescovich, 1972; Parmakian, 1950; Sweeton, Two One types release valves air are normally used i n pipelines. is a small-orifice automatic release v a l v e a n d the other i s a large-orifice a i r vent v a l v e . A i r Vent V a l v e s When a p i p e l i n e i s f i l l e d , profile, thereby increasing a i r could be trapped a t peaks along the head losses a n d r e d u c i n g the capacity of 187 the pipeline. air in Air the into vent pipe the valves are normally installed by at peaks to permit also to escape when displaced the f l u i d . They the let air p i p e l i n e d u r i n g scouring o r when emptying pipeline. collapse, It Without or them vacuum may occur a t peaks a n d the p i p e could i t may not be possible to d r a i n the p i p e l i n e completely. u n d e s i r a b l e to hammer have a i r pockets in the p i p e as they during operation of may the is also cause water pressure fluctuations pipeline. is full, T h e s e a l i n g element i s seated i s a buoyant b a l l which, the top of when the p i p e When a g a i n s t a n opening a t the v a l v e . t h e pressure i n s i d e the p i p e f a l l s below the e x t e r n a l pressure the b a l l drops thereby p e r m i t t i n g a i r to be drawn i n t o the pipe. is being f i l l e d the valve will remain open u n t i l When the p i p e the the water f i l l s pipe and l i f t s the b a l I a g a i n s t the seating. The v a l v e w i l l not open a g a i n u n t i I the pressure fal I s below the e x t e r n a l pressure. Fig. 10.5 Reflux v a l v e The valve will tend to blow closed at high air velocities. It should be r e a l i s e d t h a t psi) will cause sonic a differential velocity of pressure of o n l y 0.1 through the valve N/mmz (13 air N/mrn2 (300m/s). Pressure differences close some air vent around valves. 0.027 The ( 4 p s i ) h a v e been found to closed may damage the slamming hollow b a l l seal. In practice a diameter approximately l/lOth of the p i p e diameter 188 is used, although larger diameters and duplicate installations the are preferable. The v a l v e i s r e f e r r e d to b y the size of i n l e t connec- t i o n diameter, The desired through same size a n d the o r i f i c e diameter i s u s a l l y s l i g h t l y smaller. of air vent of valve w i l l the pipe. depend on The the r a t e of r a t e of filling or of air scouring rate volume flow an o r i f i c e i s approximately difference, but ful I 40 times the flow of water f o r the vacuum pressure should not be pressure a1 lowed to develop. A i r vent relative Various during to v a l v e s should be i n s t a l l e d a t peaks i n the p i p e l i n e , the horizontal hydraulic should an air and relative to the hydraulic reverse normally in both gradient. gradients fitted the in possible scouring, with for gradients including They as are b e considered. release air valve, Combination sec t ion. Equations a is rule the of of discussed in be next sizing the of valves area are in at derived should Chapter 5. As Q thumb orifice air m2 Q/lOO where r a t e of free fitting flow air is in m 3 / s initial factor pressure. to The r a t e of though. all flow the most the difficult r a t e of determine of air During vent taken operations, equal evacuation the through valves as a l l will the r a t e of filling line. Care should be the a i r i s evacuated as the flow of water w i l l suddenly hammer i s possible. be stopped a n d water A i r Release Valves Air i s e n t r a i n e d in water in many ways; by vortices in the pump at air suction r e s e r v o i r o r pockets there or merely b y absorption a t exposed surfaces, suction reservoir. The air may be in the released when i s a drop i n pressure, e i t h e r a l o n g a r i s i n g main o r where the a r e s t r i c t i o n such as a p a r t i a l l y closed also cause a i r valves are to be released the velocity valve. from i s increased through An increase i n temperature w i l l Small orifice a i r solution. release i n s t a l l e d on p i p e l i n e to bleed o f f the a i r which comes out of solution. Smal I size, orifice air valves are designated by their i n l e t connection usually 12 to 50 mm diameter. This has n o t h i n g to d o w i t h the to 10 mm diameter. The a i r release o r i f i c e size which may be from 1 larger size. the pressure in the pipeline, the smaller need be t h e o r i f i c e the a i r (at The volume of a i r to be released w i l l which is on be a f u n c t i o n of the entrained the average 2% of volume of water 189 atmospheric p r e s s u r e ) , (see Chapter 5 ) . The small o r i f i c e release v a l v e s a r e sealed b y a f l o a t i n g b a l l , o r When a c e r t a i n amount of a i r has the p i p e , the the b a l l air. will drop needle which i s attached to a f l o a t . accumulated or the i n the connection on valve will open top of and needle release Small vent orifice valves release v a l v e s a r e often combined w i t h large orifice a i r on a common connection on top of the pipe. a double air valve, (see Fig. 10.6). The arrangement i s c a l l e d isolating sluice valve is An normally f i t t e d between the p i p e a n d the a i r valves. LAREE ORIFICE AIR VENT VALVE n SMALL ORIFICE FIlTINQ Fig. 10.6 Double a i r v a l v e Double a i r valves should be installed at peaks in the pipeline, b o t h w i t h respect to the h o r i z o n t a l a n d the maximum h y d r a u l i c g r a d ient. points grade They along line. should a It also be installed at the ends and intermediate l e n g t h of should be p i p e l i n e which borne in is parallel that air to the h y d r a u l i c may be dragged mind a l o n g i n the d i r e c t i o n of flow in sections falling slowly in i n the p i p e l i n e so may even accumulate relation to the hydraulic gradient. Double a i r v a l v e s should be f i t t e d every 4 to 1 km along descending sections, especially a t p o i n t s where the p i p e d i p s steeply. A i r release v a l v e s should a l s o be i n s t a l l e d on a l l long ascending 190 lengths of due to the pipeline where of air is likely to be released from solution especially at p o i n t s of lowering the pressure, again decrease discharge in g r a d i e n t . side of Other places a i r v a l v e s a r e r e q u i r e d a r e on the and at high points on large valves and pumps upstream of o r i f i c e p l a t e s a n d r e d u c i n g tapers. THRUST BLOCKS !See also Morrison, 1969) Unbalanced act ions: thrust results at a bend in a pipeline due to two (1) The dynamic force in thrust due to the change i n d i r e c t i o n of flow. is The in any direction proportional to the change momentum in that d i r e c t i o n a n d is: Fxl where flow = oqAVx (10.1) force, F is the p is the fluid mass density, q i s the i n the and A Vx x. the reduction of T h i s force the is, the component of velocity direction compared pipe. under normal conditions, to the internal negligible in the with force due pressure (2) The t h r u s t i n the d i r e c t i o n of each leg of the bend due to the pressure i n the p i p e i s : Fx2 = PA i s the i n t e r n a l pressure, (10.2) A i s the cross sectional area where p of p i p e flow a n d The 0 i s the a n g l e of d e v i a t i o n o f the p i p e ( F i g . outward thrust is the vector sum of the and is (10.3) 10.7). resultant forces i n both d i r e c t i o n s of the p i p e a x i s , Fr = 2pA s i n 0 / 2 The unbalanced t h r u s t may be counteracted b y l o n g i t u d i n a l tension in an all-welded pipeline, or by a concrete thrust block bearing against size of addition and the foundation m a t e r i a l . the to block I n the case of a j o i n t e d p i p e l i n e the In may be c a l c u l a t e d u s i n g s o i l mechanics theory. resistance on the the bottom there is of frictional the thrust block the circumference of the outer face of pipeline, a lateral resistance against the p i p e a n d block. The maximum r e s i s t i n g 191 pressure a soi mass w i l l o f f e r i s termed the passive resistance and i s (Capper and Cassie, f = 1969) 1 P 1 + sin@ + ~ s 1h - s i n @ + sin< 2cJ 1 - s i n @ where f @ is i s the r e s i s t i n g pressure a t depth h, y s i s the s o i l d e n s i t y , P the effective i n t e r n a l a n g l e of f r i c t i o n of the soil a n d c i s i t s If the thrust block extends from the surface to a depth H cohesion. below the surface, a n d i t s l e n g t h i s L, the total r e s i s t i n g t h r u s t i s HZ P = Ys2 1 This thrust maximum block i s a b l e to move i n t o the soil soil pressure is termed ponding minimum pressure, maximum pressure which y i e l d away from the s o i l mass. This i s Ifa = sin4 - ysh 1 + s i n @ "1 which i s considerably developed i f the force on which i t i s a c t i n g i s free to move away from the soi I e x e r t i n g the pressure. Fig. 10.7 T h r u s t a t a bend + ' - sin6 sin6 + kHLJ 1 + sin$ 1 - sin will only be developed (10.5) if the possible resistance mass s l i g h t l y . the passive The corresThe pressure. which may be may occur on the t h r u s t block developed if the thrust block i s the a c t i v e were free to $-sinm + sin4 (10.6) less than the passive pressure and w i l l o n l y be 192 Fig. 10.6 Thrust block I n p r a c t i c e the pressure which may be r e l i e d upon i s s l i g h t l y than the p a s s i v e pressure, as f u l l safety The movement of of at the p i p e i s less usually not permissible. the A factor of least 2 should be used w i t h the top of from H/20 a passive resistance formula. block to activate full i n w a r d movement of pressure 1972), thrust soft of passive varies for c l a y s to H/200 f o r dense sand, the excavation. These movements (CP where H i s the depth and the are seldom permissible, T h e "at varies "at of rest" coefficients a r e p r o b a b l y more r e a l i s t i c . soil rest" r a t i o horizontal stress to vertical soil stress from 0.4 for loose sands used of to 0.7 for very p l a sti c clays. An impact factor should be in a l l o w i n g for water hammer pressures. T y p i c a l values of a n g l e $ a n d cohesion c internal friction for v a r i o u s soils a r e indicated i n Table 10.1. 193 TABLE 10.1 Type of soil Strength of Soils - t y p i c a l values Angle of f r i c t i o n 4 Cohesion N/rnmz 0 Gravel Sand Silt Dense c l a y Soft s a t u r a t e d c l a y 35 O 30 28 O 5" 0 0.007 0.035 0.15 0 Exarnp I e Calculate pressures a t the size of a thrust block to r e s i s t the u n b a l a n c e d a 45O b e n d N/rnrnz. i n a 1 000 rnrn d i a m e t e r p i p e o p e r a t i n g a t a p r e s s u r e o f 2.0 L e n g t h of 1 p i p e l e n g t h = 10 r n , N/mmz. L a t e r a l f o r c e F = 2 x 2.0 depth = 3 x -If 1 m, @ = 30°, C = 0.005 4 s i n 2 2 i 0 = 1.20 MN. T r y a t h r u s t b l o c k 3 x 3 ~ 3rn: Weight of t h r u s t b l o c k 3 x 3 ~ 3 ~ 2 200x9.8/10 Weight of 10 rn l e n g t h of p i p e Weight of w a t e r 3 = = 600kN 40kN 80kN 130kN 850kN 250kN i n p i p e 0.785x1zx10x9.8x1 OOO/lO' = = Weight o f s o i l a b o v e p i p e l x l x 7 x l 8O0x9.8/1O3 Total weight F r i c t iona I resistance 0 . 3 ~ 8 5 0 L a t e r a l r e s i s t a n c e o f soi I a g a i n s t b l o c k : = = 1 ~-+ s i n $ 1 - - sin$ 1 + 0.5 1 - 0.5 = 32 ~ 1 ' ~ F = 18 0 0 0 ~ ~ ~ 3O3 +32/ ~ 5 ~ v3 3 3 L a t e r a l resistance of soil a g a i n s t p r o j e c t i o n of p i p e : (18 000x1 . 5 x 3 / 1 0 3 x 2 x 5 j 3 ) Total l a t e r a l resistance = = 889kN 1x6.5 = 640kN = 1770kN F a c t o r o f s a f e t y 1.77/1.20 1.48 A t h r u s t b l o c k s h o u l d b e d e s i g n e d so t h a t t h e l i n e o f a c t i o n o f the resultant the may pipe. best of the resisting forces coincides w i t h the l i n e of t h r u s t of This This w i l l prevent overturning or or by taking u n b a l a n c e d stresses. moments a b o u t be done g r a p h i c a l l y the centre of the p i p e . 194 Thrust horizontal not be blocks are of needed the not only at changes in vertical or alignment able to pipeline, b u t also a t f i t t i n g s which may forces, such as flexible i n s t a l led transmit longitudinal coupl ings. V i k i n g Johnson o r s i m i l a r coupl i n g s a r e frequently a valve the i n a v a l v e chamber, The opposite on one side of and removal of to f a c i l i t a t e i n s t a l l a t i o n of the valve chamber valve. wall would thus h a v e to be designed as a t h r u s t block. -li; Fig 10.9 Segment geometry bend. s t a n d a r d med i urn-rad i us 900 f a b r i ca t ed FORCES INDUCED BY SUPPORTS The There i n t e r a c t i o n of are many The a p i p e and and i t s supports tertiary i s a complex subject. and in displacements supported There is secondary are forces involved. above a effects on the general ly or by other or greatest isolated contract pipes ground, of plinths pipe to supports. tendency expand effects of longitudinally and circumferent i a l l y tial temperatures, under the temperature change, due differen- secondary strains to the Poisson r a t i o effect, 195 and pipe partial or total f i x i t y of supports which and impose iio forces on the support is vertically, longitudinally laterally. completely r i g i d a n d the more f l e x i b l e the support reaction i t imposes on the pipe. the less force or The stresses on the p i p e may be loosely c l a s s i f i e d as follows: Primary; circumferential due to due to internal pressure across diameter; across the cross section. longitudinal Secondary; across strains supports. Tertiary; internal pressure bending a t elbows, Temperature angle to branches, effects. changes i n section a n d Poisson Due ratio to counterof supports. at right primary strain. reaction l a t e r a l deflection due to l o n g i t u d i n a l expansion. the secondary and tertiary stresses are often not Al though accounted f o r i n p i p e design, they can be very s i g n i f i c a n t . Longitudinal Stress If the end of a p i p e i s b l a n k e d o f f a n d u n h e l d the l o n g i t u d i n a l is stress i n the p i p e w a l l i .e. The and 4 if the circumferential ratio ends effects are stress. tries to Poisson the and t reduce wall the length stress E by vLpd/2tE Ee = held the tensile becomes is the is Wpd/2t corresponding the wall force is e Vp-irdz/2 where the strain and elastic modulus, thickness, w Poisson's r a t i o (about 0.3 for s t e e l ) . Temperature stresses A pipe w i l l expand or contract by aAT where a i s the coefficient of expansion a n d LT the temperature change i n time. A where pipe the restrained coefficient longitudinally of expansion will for undergo a stress 12 x aEAT steel, a , is the 10 -6 per "C a n d for p l a s t i c , If there is a 50 x temperature gradient across pipe wall a Circumferential stress i s created equal to +_ aEAT/2(1-v). 196 Forces at Bends The force due to water is pressure along each a x i s at force acting outwards a p i p e bend sin (8/2) PA. The net resultant i s 2pA where with a 8 is the bend angle. block it I f the r e s u l t a n t force a longitudinal i s not countered in the pipes thrust creates force equal to 2pA s i n 2 ( 8 / 2 ) . Lateral Movement A straight a pipe of length big x fixed under at both ends due will to buckle temper- outwards a t u r e etc., dy since dy2 relatively amount expansion b y an amount (10.8) + (x/2)* = (x/2 + d ~ / 2 ) ~ dy = e.9. x = dy = I f the between to that loom, 400 x pipe -6 d x = xaAT = 100 x 12 x 10 0.02/2 is x 20 = 0.02m = lm. restrained twist prevent laterally or it could a try to force buckle equal supports required or to supports the exert lateral buckling. For example, dy, the deflec- t i o n of a simple supported ( l a t e r a l l y ) p i p e beam, under a force F is dy = = 48 1 = FL3/EI f o r above example. : . F 1 x 210 x lo9 2 8 is 1 13x.01/(1003x-~ 48 = 40 kN referred to as snaking and can cause The l a t e r a l deflection pipes to fa1 I o f f the side of supports, or bend the supports. an elbow will bend outwards A pipe fixed at both ends with under expansion by an amount: dy = d x / ( y / a where dx is + y/b) the net expansion in length of pipe with length ( a + b ) = c due to temperature, pressure etc. 197 Forces on Supports The equal pipe. Free to Slide: The longitudinal force of a freely sliding or This i s pW, highly where forces and on the to support the blocks or p i l l a r s or by the hangers w i l l supports on be the opposite forces exerted h e l d p i p e equals IJ the f r i c t i o n force on and the block. is the pipe f r i c t i o n coefficient on the block. W is i s the normal force also a lateral ( w e i g h t ) of to resist the There force snaking Fixed force pipe . Block: can The be resulting force is the smaller of to i ) maximum which and imposed on block (ii) sliding b y p i p e e.g. block, f r i c ion between or block, or resistance of or ( i i i ) resisttotal longiratio ance of tudinal support a t force in the other end, pipe due to ( i v ) maximum net change, temperature Poisson effect a n d bends. There i s thus a d i s t i n c t i o n between the f r e e to s l i d e case a n d the fixed case in that ( i ) or (ii) will apply to a "free to s l i d e " pipe a n d case ( i i i ) a n d ( i v ) w i l l g e n e r a l l y a p p l y to a p i p e r i g i d l y f i x e d to the support. Thus obviously the force as i f one end of be no force a p i p e i s free (see F i g . at that end, 10.9) then there w i l l support a n d beyond the f i r s t i s computed as above, a n d beyond the second support also lengths case ( i ) or of above etc. F o r the f i r s t few ( i i ) may these is apply less. a n d then case ( i i i ) or For case ( i v ) w i l l take over the other end" as one may ( i v ) the "force a t i n fact be that due to other support blocks. Unba Ianced Forces Generally balance out. it can be expected i n one that forces in welded pipework That i s forces direction a t one end a r e equal a n d opposite to those at however bends there may be the other end. moments. Along the length of the p i p e bending For instance a t elbows or there a r e net forces of l i q u i d on the p i p e w a l l inside a c t i n g to t r y to s t r a i g h t e n the bend. 198 During unbalanced instance hammer direction. length transient forces flow which closure at one the conditions could of of a a pull there the may pipe pocket may may force travel there however off in be large For water in one pipe supports. a pipe pipe following pressure vapour line end the Although pressure wave along are the and eventually forces which re-balance can forces, momentary unbalanced bends. cause s i g n i f i c a n t movement s t a r t i n g at 4 Support resistance length x + dx l a t e r a l movement dy Fig. 10.10 L a t e r a l movement due to temperature expansion total force F1 + F2 + F3 5" E L T Temperature Movement loose c o u p l i n g I f r i c t i o n on supports Fig. 10.11 L o n g i t u d i n a l forces i n p i p e w a l l created b y f r i c t i o n on supports FLOW MEASUREMENT Venturi Meters The with Venturi (Fig. meter head 10.12) offers loss. throat an It accurate is used method of mainly flow measurement minimum for large-diameter pipelines. The v e n t u r i has a converging section and g r a d u a l l y d i v e r g i n g section to minimize head losses. Flow measurement is based on the Bernoulli equation which is r e a r r a n g e d as 199 v22 29 V --291 2 - h , - h 2 = h (10.9) Solving f o r discharge Q = CdA2 , = / (10.10) (10.11 ) where d for and flow i s the diameter and C separation at V i s a velocity coefficient which allows the throat in the a n d includes a f a c t o r f o r upstream pipe. downstream in conditions A venturi meter should be calibrated pipe place a n d should have a s t r a i g h t very smal I t h r o a t / p i p e l e n g t h of a t least 5 diameters f o r diameter r a t i o s , increasing to 10 o r even 20 p i p e diameters f o r or double bends, is required l a r g e r throats, o r from branches (BS 1042). F u l l bore branches, p a r t l y impart s w i r l i n g motion may meter. The head need up loss in a before a closed valves a n d f i t t i n g s which to 100 p i p e lengths downstream v e n t u r i meter i s o n l y approximately O.1V ‘/2g. 2 Fig. 10.12 Venturi meter Nozz 1 es A contracted form of v e n t u r i a short meter i s the nozzle meter, which has bellmouth rounded i n l e t a n d a b r u p t expansion beyond i t . The equation is similar to that for the venturi meter but the discharge v e l o c i t y head recovery beyond i s very small. O r if ices An o r i f i c e consisting of a thin plate with a central ori f i c e i s a 200 popular method of measuring contraction flow in large which pipes. may There be as is low an as appreciable 0.61. orifice coefficient The discharge formula i s s i m i l a r to Equ. - 10.10 where The velocity it head recovery is low but the orifice has the a d v a n t a g e that straight pipe. i s short a n d can be i n s t a l l e d i n a short l e n g t h of straight p i p e r e q u i r e d on each side of The o r i f i c e should The lengths of the o r i f i c e a r e s i m i l a r to those f o r v e n t u r i meters. be c a l i b r a t e d i n place f o r accurate results. Fig. 10.13 O r i f i c e meter Bend Meters A g r e a t e r pressure i s exerted on the outside of a bend i n a p i p e than can on be the used inside, due to c e n t r i f u g a l force. The pressure difference in to measure the flow. The meter should be c a l i b r a t e d place, b u t the discharge coefficient f o r E q u . 10.10 i s approximately (10.13) Cd = r/2d where r i s the r a d i u s of c u r v a t u r e of the centreline. Mechanical Meters Flow to water consumers is invariably measured by mechanical meters which i n t e g r a t e the flow over a a p e r i o d of time. A common type Other has a r o t a t i n g t i l t e d disc w i t h types have r o t a t i n g wheels, s p i n d l e which rotates a d i a l . lobes o r propellers. 201 There is also a type of meter which reacts to the drag on a deflected vane immersed i n the flow. The meter records f o r p a r t l y f u l l conduits as well. The rotometer consists of increasing flow it in a calibrated vertical glass float tube which has a taper diameter the upwards. The A is suspended itself so in that the upward through tube. float positions the d r a g on ( w h i c h depends on the flow p a s t i t a n d the tube diameter) e q u a l s the submerged weight. The object may be e l t h e r a sphere o r to make i t r o t a t e a n d centre i t s e l f a tapered shape w i t h vanes i n the tube. Electromagnetic Induction By creating and a magnetic the field around a pipe of non-conducting an electrohas the material motive ionizing is I i q u i d by and no can be i n s e r t i n g electrodes, measured. head by the and The a force induced there can does is method of advantage including nique that l o s s of variety liquids tech- sewage also an be not measured obstruct this flow means. and A similar which of i s based on sonic developed. velocity The is velocity impressed shock wave, and i s also downstream being difference measured. between upstream sonic Mass and Vol ume Measurement The or most accurate To methods measure flow of the measurement mass or of flow of are fluid by mass volumetrically. a weight flowing The over certain flow time be the i s diverted from the i n t o a weighing volume filled in tank. a volume t ime. may measured certain TELEMETRY Automatic systems. ling data transmission a n d control i s often used on p i p e l i n e d a t a handautomatic Telemetry is systems a r e tending expensive and to replace manual less reliable than which more methods. Data Cables may be l a i d simultaneously w i t h the p i p e l i n e . which may be required of include water levels in reservoirs, or pressures, flows, opening valves, temperature, qua1 i t y pro- 202 perties mation of is the read fluid, by a pump speed or power consumption. linked by a The infor- standard instrument mechanical device to a local d i a l or c h a r t , or to a coder a n d transmitter. S i g n a l s may uous are analogue usually be sent waves out in from a t r a n s m i t t e r a series to of i n the form of continAnalogue but messages also less or digits. less accurate digital. (up 2 percent may accuracy) expensive uously With pulses of or than be The transmitter at are cores regular repeat messages contintermed scanning. electric level interrogated systems data intervals, to digital by converted or binary Every code relays, magnetic contacts. possible the measurand numbers. as bits. i s represented by Signals are a d e f i n i t e combination of in series via and in binary groups lines coded known or transmitted may One be The signals cables. transmitted of telephone is private bit, multiplex plus a pair conductors of u n i t s of needed for may be each sent common feed. A number data in r o t a t i o n v i a the same conductors. Alternatively over short hydraulic by or pneumatic Radio signals may be conveyed economic distances pipe. transmission becomes f o r systems w i th long transmi ssion distances. The linked from transmission to a decoder to a system or will send the messages to a be receiver decoded the digital and or comparater. vice by versa. of S i g n a l s can The decoder analogue to digital data on the (a feeds information play the bank dials, means or a servo motor can disor sound alarms at on readings of charts lights is extreme a or values measurand. Data picture) frequently the displayed with mimic dials diagram at the diagramatic of system tights p o s i t i o n of the u n i t being observed. rooms. be fed to These diagrams a r e mounted i n c e n t r a l control The stored may for be information on p a p e r or directly may also a data or to storage The system and magnetic or or at a tapes, later discs stage the for cards. a information to be used can those be fed computer decision-making programmed which would manipulat i n g a system, in data. L a r g e computers to optimize would result instance b y selecting pumping cost, or pumps which to minimum The turbines signals hammer match or power demand. operate computer could machinery or send water close valves hydraulic r e l i e f mechanisms. 203 Mini of digital computers systems. are They now are the most popular cheaper form than of control analogue computers. computat ions for telemetered but be sI ight ly than computers They can considerably programmed but cannot to be cheaper perform used larger digital or certain for be tasks other automatically which or they easily can computations are not programmed. They increased in c a p a c i t y l i n k e d to l a r g e r computers as t h e need a r i s e s . REFERENCES Boucher, P . L . , 1948. Choosing v a l v e s , K i Imarnock. B r i t i s h V a l v e M a n u f a c t u r e r s Assn. 1964. V a l v e s f o r the C o n t r o l of Fluids. BS 1042, Flow measurement, BSI, London. C a p p e r , P.L. a n d Cassie, W.F., 1969. The M e c h a n i c s o f E n g i n e e r i n g Soils, 5 t h E d . , Spon, London. CP 1972. L a t e r a l S u p p o r t i n S u r f a c e E x c a v a t i o n s , S.A. Instn. C i v i l Engs. L e s c o v i c h , J.E., 1972. L o c a t i n g a n d s i z i n g a i r r e l e a s e v a l v e s . J. Am. Water Works Assn., 64 ( 7 ) . M o r r i s o n , E.B., 1969. Nomograph f o r the d e s i g n of t h r u s t b l o c k s , C i v i l Engg., Am. SOC. C i v i l Eng. P a u l , L . , 1954. Selection of v a l v e s f o r w a t e r s e r v i c e s . J. Am. Water Works Assn., 46 ( 1 1 ) 1057. P a r m a k i a n , J., 1950. A i r i n l e t v a l v e s f o r steel p i p e l i n e s . T r a n s . Am. SOC. C i v i l Engs., 115 ( 4 3 8 ) . Sweeten, A.E., 1943. A i r i n l e t v a l v e d e s i g n f o r p i p e l i n e s . E n g g . News Record, 122 ( 3 7 ) . L I S T OF SYMBOLS A C - cross sectional a r e a soi I cohesion con t r a c t i o n c o e f f i c i e n t d i sc h a r g e coef f i c i en t velocity coefficient cC ‘d cV - d e i n t e r n a l diameter strain e l a s t i c modulus stress force gravitational acceleration E f F 9 h o r H - d e p t h below s u r f a c e f l u i d pressure flow r a t e r a d i u s of c u r v a t u r e wal I thickness temperature velocity normal force length direct ions I a t e r a I d i s p I acement temperat u r e c o e f f i c i e n t soil density f r i c t i o n coefficient Poisson's r a t i o s o i l mass d e n s i t y a n g l e of i n t e r n a l f r i c t i o n of s o i l 205 CHAPTER 1 1 LAYING AND PROTECTION SELECTING A ROUTE The bearing is selection of on the from a suitable route for cost and a p i p e l i n e has an costs. and important route plans, terrain, and capital aerial and operating A pipeline selected photos, any topographical data cadastral on the on-site inspections and local other In available a route, obstacles services. be is selecting Care the costs prcticability the ground have to considered. below the should be taken grade as peak If and line. to ensure (Low-flow as the profile should hydraulic as low the well conditions hydraulic above the be considered for rates, were gradient grade pumps also i s flattest line flows). input there a peak heads, between discharge obviously Peaks result level grade costs. Once surveyor. regular tions. in for may would have to be designed to pump over be p o i n t s of p o s s i b l e water column On the other as near t h i s peak. which separation i n water hammer overpressures. r o u t e should to h a n d the general to the h y d r a u l i c pipe of the pipeline as be kept lines possible minimize pressures a n d consequently a preliminary Pegs are put at to route in is selected, the it is pegged at out by a along centre-line 10 to 100 m deflec- intervals and pegs, changes i n g r a d e a n d at horizontal Offset 2 5 m from the centre l i n e pegs a r e also put The the l e v e l s of drawing at each pegs office, peg. a r e observed a n d the with Holes ground may levels, use d u r i n g is laying. in profile bed then and plotted depth levels indicated be augered along the r o u t e to tests may identify m a t e r i a l s which w i l l have to be excavated. samples to decide whether trench Strength be done on s o i l s h o r i n g w i l l be necessary. Underground at and this stage and or at overhead least services should to be accurately them. on located (Drains or before excavation to avoid underground cables may have be supported bridges, a heading c o u l d be hand-excavated under them). 206 L A Y I NG AND TRENCH I NG The type of p i p e to be used for although other will the any job will l a r g e l y be a matter life The the of the pipe of the of economics, and facilities affect on the for the type laying, decision. of pipe, materials delivered rigidity, pipes be be are factors depend lengths weight, pipes size of transport vehicles to 4 and method of jointing. Concrete often s u p p l i e d in 2 m m lengths, thin be w h i l e steel pipes may over 10 or in even 20 long, and walled p l a s t i c p i p e s may carefully should to be avoid stored be low- supplied to rolls. or Pipes pipe should or handled They damage and ered For may coatings on distortion. or transported i n t o the small be padded c r a d l e s sandbags. Pipes may trench by thick b e l t s l i n g s from mechanical booms or t r i p o d s . w a l l e d welded pipes, the trench, width of diameter at j o i n t i n g and wrapping 'snaked' done the The side of working the a n d the p i p e then i n t o the lines trench. required for excavation hand, construction of pipeand laying. be wide If the varies with method is done On excavation for small and laying by 3 m may enough diameter laying pipes. and the other hand for large mains where excavation, ally, of possibly to even s i t e coating m may be i s done mechanicReserve widths working widths up 50 required. 20 to 30 m a r e common, a n d allow f o r one or two a d d i t i o n a l pipe- l i n e s at a l a t e r stage. Once the the trench with i s excavated, centre line sight rails pipe may be set up across The trench the of the marked thereon. frames a r e set a d e f i n i t e height above the bed a n d the pipe l e v e l l e d 1970). w i t h the assistance of these (BSCP, Pipes m m are normally damage in by the laid with a minimum loads. frost cover of 0.9 m to 1.2 of 1 to is avoid superimposed A minimum cover necessary be reduced a concrete U.K. to prevent penetration. The depth i n which trench with pipes laying is may case i n rocky o r cover to may m steep be ground to minimize costs The pipe m necessary. than the width of normally widening 0.5 and m 0.8 more diameter, used for local over and deepening which for are joints. difficult (0.8 to is 300 m m diameter straddle while jointing). 207 The hesive shoring sides of or wet the open and trench for deep will h a v e to be supported for safety i n uncoThe soils trenches, reasons. should be designed to r e s i s t the a c t i v e the sides of should one be the trench may well l a t e r a l s o i l pressure. to a safe to a v o i d Alternatively angle. slips. Spoil At be b a t t e r e d back kept away from the excavation away is advisable. ground least trench a depth D r a i n s may be r e q u i r e d i n the bottom of dry to be while working, enable open the trench i n wet to keep the trench to reduce the p o s s i b i l i t y to of embankment s l i p s a n d D r a i n p i p e s should with frequent drains backfill and be compacted p r o p e r l y . bedded water. in In a stone wet jointed to filter ground cross-drains lead away very cutoff beside the trench may be necessary. Pipes bedding reduce shaped sandy gravel may is be bedded to on the flat trench bottom, of but a proper to preferable to the may minimize pipes. of deflections b e d of In f l e x i b l e pipes o r trench may a be damage to fit rigid The the the pre- profile pipe. rocky ground bed of material or be b u i l t up a n d trimmed to shape. stone up to Beds of sand, up to the crushed the 20 mm in as size, they brought haunches of settlement pipe, a r e often to used, do not e x h i b i t much and haunches o r and a r e easy compact. Concrete beds surrounds a r e sometimes used f o r Bedding should be continuous low-pressure r i g i d p i p e s a n d sewers. joints but haunches should stop Fig. under short of j o i n t s to f a c i l i t a t e r e p l a c i n g damaged pipes. typical types of bedding. (Refer to Chapter 7 to 11.1 shows factors bedding associated w i t h d i f f e r e n t types of b e d d i n g ) (CPA, 1967; ACPA, 1970). The best method of b a c k f i l l i n g a n d compaction depends on the type of soil. Soil properties limit may be described in terms of the p l a s t i c l i m i t index (PI), with liquid low (LL) and plasticity may often soils, be ( P I = LL-PL). compacted is For soils merely by i.e. PI'S fill For satisfactorily inundation. stampers o r of the high LL dynamic compaction required vibrators. B a c k f i l l densities may be Density. For large pipes specified i n terms it is practice to Proctor Standard compact the bed w i t h a w i d t h of at 100 least h a l f the p i p e diameter under The soil f i l l around the p i p e l a y e r s to 90 or 95% Proctor I t may the p i p e to 95 to should density be up % in Proctor density. 100 to 150 mm compacted to haunch level or to 3 / 4 of the depth of the pipe. 208 be necessary to s t r u t f l e x i b l e p i p e i n s i d e to prevent d i s t o r t i o n d u r i n g t h i s operation. The fill around the top half of the pipe, up to 300 m m above the crown should be compacted to 85 to 90% Proctor density. For b a c k f i I1 under roads, ed to the top while l a y e r s may have to be compactfor in runways open 90-95% Proctor is density, 110% may and be re- quired. 85% normally sufficient country densities as low as 80% a r e obtained i f control i s b a d ( R e i t r , 1950). fill around the p i p e should the trench To a v o i d damage to p i p e o r coatings, not h a v e stones to in it. Surplus for spoil may be spread over or width of compensate and settlement carted land away. Reinstatement and fencing topsoi I vegetation, p r o v i s i o n of drainage, o f f of w o r k i n g areas should be considered (see also Sowers, 1956). THRUST BORES To traffic soil be avoid on a excessively r o a d over lengths. jack or a deep pipe, hole up excavations, or to avoid disrupting the the p i p e may i s dug in one at each be j a c k e d through end of the for short A length to against of a the jacked. block Small A i s set hole w i t h i t s back thrust jack. timber a n d the p i p e set than up on r a i l s i n front may have a pipes (less 600 rnrn diameter) sharp head or tain the the pipe. shoe f i t t e d to the f r o n t the p i p e , the to ease the j a c k i n g as load a n d maindeviate with or d i r e c t i o n of the s l i g h t e s t obstacle w i l l Occasionally to outside Pushing of the should the pipe is lubricated stop for bentonite the is pipe dug is reduce f r i c t i o n . stick. auger With or never soil long the may by larger hand pipes ahead of the pipe The pipe out then and removed through pipe. pipe pushed i n f u r t h e r , the pipes in to the j a c k the bore a r e t r a c t e d a n d another and the a process shoe inserted The behind force repeated. be up jacking required if an push pipe a with may to 1 200 tons, but auger i s used, 100 ton j a c k may suffice. PIPE BRIDGES Pipes f r e q u e n t l y rigid jointed pipes h a v e to span r i v e r s o r may have sufficient gorges. For short spans, to support them- strength 209 Class A bedding Dt 200 v m mln Reinforced A,: RamforcedA, PI"," I 0% : M= 4 8 4 0 4%M. 3 M.28 0 IZ5H 150 mm l l i " 0 25 d I O O m m mm Plain or Reinforced bncr.1e 1 5 0 m k m i Compocted Gronulor t4 Y CONCRETE ARCH Class B bedding M= 19 Dens@ Compacted Bochf~l1 Class C bedding M : I ~ Lightly tO"'p0ct. Bocuftll 01251' CiKANULAK FOUNDATION GRANULAR I W U N U A I I ~ Class D bedding NOTE For rock or other incompresrible malert316,the trench should be ovaexcovoled 0 minimum of 150mm and refi1l.d wrlb gronulor mat.rm M-bedding factor Fig. 11.1 Types of beddings selves plus the the pipe fluid. For larger spans, it may be or necessary to support from an on trusses or concrete bridges, traffic bridge. h a n g the is to be pipe con- existing If a truss bridge 210 structed for the bottom, of Two the bridge cables hangers the or is pipe, the p i p e could act as the tension member at the compression one with the member a t the top. from may A n a t t r a c t i v e form suspension cables. and the pipe supported as to they a r e p r e f e r a b l e to one, attached at an helps angle be spaced a p a r t p l a n e through the v e r t i c a l pipe. and act T h i s arrangement reduces as an two or to support The lateral pipe the p i p e against could also would be be wind forces designed necessary to wind arch, vibrations. but again be support to act In pipe - either ing, p i p e s could stays designed be together all w i t h cross bracexcept if sup- cable on an could erected. the cases be ported independent steel. along bridge, should r i g i d jointed; preferably of welded joint T h i s means there w i l l the p i p e to prevent h a v e to be some form thermal stresses devel- expansion oping. UNDERWATER P I PEL I NES The it laying often is of pipes underwater In is very to expensive, nevertheless undersea beds is inescapable. addition Gas and river lines crossings, from laying or becoming common. oil undersea off-shore and t a n k e r b e r t h s a r e frequent. which pipes. discharge The There a r e also many sludge into industthe sea will bed ries towns effluent or through depend undersea on method used for as currents, underwater height, laying type of conditions such wave a n d length of (1) under-water pipe: In calm water the p i p e may up to Floating on shore, a n d Sinking: floated thus. out Care be j o i n t e d r n and is sunk. needed be Lengths in 500 have and to been laid on sinking the pipe line winches assist. barges should positioned along the (2) Bottom be Towing: Lengths land bed of pipe up to a up a few to kilometres 1 may and assembled along at is on the sea. i n strings, of each by km of long, a the towed the are air sea winch barge shore. tied pipe anchored The to pipe the Strings up by jointed in on the the together pipe sea or on by bouyed to buoys If the pipe, reduce f r i c t i o n bed. 211 i s f i l l e d with crete would line. coating be air to i t may get the to h a v e to be weighted down correct side buoyancy. and Too may by a cona pipe of light bend susceptible currents to or out The stresses by i n the p i p e due currents unit length the tension may and bending be and critical. currents caused The is underwater drag per waves to lateral due waves Cow (u + v ) ~ D/2g (11.1) (about 0 . 9 ) , wave w where C weight current pipe), D of i s the d r a g coefficient the water, (or u is the i s the s p e c i f i c and v is to the the velocity velocity their components perpendicular D is the outside diameter of the p i p e a n d g is gravi- t a t i o n a l acceleration. (3) Lay Barge: on (or a Pipes may be taken to sea in a pipe barge, down jointed an arm special stringer) lay-barge into a n d lowered continuously The barges place. proceed f o r w a r d as l a y i n g proceeds. (4) Underwater pipe has to Jointing: be Underwater jointing is difficult as each accurately aligned. A diver w i l l be r e q u i r e d , which l i m i t s the method to shallow depths (Reynolds, 1970) . to It i s usually necessary to b u r y the p i p e to a v o i d damage due currents. the Dredging i s d i f f i c u l t as sediment may f a l l before the pipe is laid. The trench or be washed into has to be trench normally over-excavated. bed fluidizer A novel way of (Schwartz, l a y i n g the p i p e i n soft beds i s w i t h a High-pressure jets of water fluidize 1971). the bed under the pipes a n d the p i p e s i n k s into the bed. passes of over a A number of the f l u i d i z e r a r e r e q u i r e d so that deep a the p i p e s i n k s g r a d u a l l y long length. Too trench may cause bending stresses i n the p i p e at the head of the trench. Most joints underwater be pipes are steel and with welded and joints. Pipes and is should well cwted lined cathodic protection d e s i r a b l e under the sea. 212 JOINTS AND FLANGES The of type the of joint to use on a pipeline on site, will cost, depand on the type of pipe, facilities and available watertightness following joint, strength flexibility requirements. The types of j o i n t s a r e used ( E E U A , 1968) ends :- (I) Butt-welded: bevelled joint right walls is The of the back, steel pipe a are trued root. and The approximately clamped with 30' leaving in 2 and mm and/or one or a tacked more weld places Large then with welded thick it is around may to runs. pass pipes also make require good inside, in although pipes less difficult the internal lining than 600 mm bore. (2) Sleeve to form welded: a of One end of a steel pipe edge may fillet the be flared to out the be socket the and the pipe. leading If welded barrel welded and other too. possible joint should inside (see F i g . lining, if 11.2). The e x t e r n a l should be p i p e coating made good the internal possible, at the weld a f t e r a l l s l a g has been wire-brushed Two welding essential methods and to of welding arc are available: off. gas is Oxy-acetylene welding metallic achieve welding. Top-class and high weld strength should avoid the cavities. welding. to the but A thorough testing testing to programme should be accompany where Destructive factory and confined on tests short may possible of sample welds lengths be pipe occasional including a field the destructive are cut necessary. Strips weld from the p i p e w a l l is ground a n d bent over and etched field to predetermined air radius. or The slag weld reveal pockets inclusions. X-ray, Normally tests w i I I be non-destructive: or e i t h e r by X-rays Gamma-ray, for magnetic ultra-sonic and useful the is methods. but are preferred equipment corners. inserted hi gh definiportable tion and contrast for Gamma-ray i s more With in the the otherwise inaccessible may the be large-bore p i p e and pipes, X-ray equipment around smaller a a film wrapped wall. p i p e to receive double, image from expo- single For pipes, overlapping 213 o m i t t e d for small bore pipes Fig. 11.2 Sleeve-welded joint Fig. 11.3 Push-in type j o i n t sures are made from outside, thereby exaggerating defects i n the near w a i l . Welding that for of high tensile steels. steels require better of the craftmanship pipe ends, low-tensile Pre-heating and post-heating f o r stress r e l i e f a r e n o r m a l l y desirable. and screwed ends and sockets are only (3) Screwed: Threaded used on small steel pipes. (4) Spigot quently and socket: Concrete, end cast iron and p l a s t i c pipes freend plain. The have one has a socketed sealing the and the other male end socket is rubber over gasket (see f i t t e d over Fig. i t a n d the Various forced ring. 11.3). shaped r u b b e r r i n g s a r e used. is to caulk Another way of sealing the j o i n t cement mortar, lead or i t w i t h bitumen compound, resin. to Joints f i t t e d w i t h r u b b e r r i n g s a r e often c a u l k e d as well the into can ring the in place, improve s e a l i n g and socket one or and joints two prevent with dirt hold getting rings joint. Spigot rubber of normally accommodate degrees def I ect ion. (5) Clamp-on jointing a rubber joints: plain seal Various proprietry They pipe joints normally are available for ended between pipes. each one involve a clamping sleeve. referred joints take barrel type of and joint cover (also Fig. to as 11.4 a illustrates Viking such or Johnson Dresser and coupling). be pipes These to accommodate several movement of easily, may designed or degrees If the the deflection is between resist pipe longitudinal may take be the movement. fixed to joint of to tension, by tiebolts to barrel each brackets tension. in the The b r a c k e t s cause local walls of bending a n d tension stresses the pipe a n d may cause damage unless carefour of the or even is fully designed. The the Normally diameter brackets to the two tie to bolts take are are the as The legs sufficient. tension close as bolts so selected the and designed barrel to that bolts possible are minimize e c c e n t r i c i t y . in The plan length with brackets welded the ing normal l y to the "U" pipe shaped axis. the parallel of the legs of bracket stresses all for should be such that are acceptable. stresses rings, tie-bolt In on longitudinal fact the it pipe shear a n d bend- i s impossible to e l i m barrel may with be brackets inate and for bending this reason the like flanges, to preferable wai I. The transferring coupling load iron the pipe Victaulic used f o r cast pipes, uses l i p s on the ends of the pipes to t r a n s f e r tension to the coupling. 215 Fig. 11.4 Slip-on type coupling. (6) Flanged: ends, Steel and cast iron pipes are often likely flanged at the especially Faces or if p i p e s or are fittings are and gasket according to be removed with frequently. rnrn machined insertion bolted together 3 rubber to other between. to the Flanges diameter are and drilled standard patterns working pressure. Ful I used for face gaskets, with holes for bolts cast a n d the iron bore, soft are high-pressure Joint inside rings joints an of and or metal less thick flanges. than steel raised Flanges are to the with outside diameter slightly diameter the b o l t holes a r e used f o r pipes. for to of Some use flanges with joint the flanges face used and inside with low-pressure the joint bolt have a circle rings. bolts rings tend dish when tightened the pipe though. The to the the The method attaching the flanges varies. but of of simplest method i s to s l i p leave pipe. pipe approximately the f l a n g e extending carried flange of the over the pipe end 10 is mm beyond around around inside the the the edges A and fillet at weld the then of the one for front pipe of back barrel. the for Alternatively may be both or flange high bevelled work is to welding. a lip A method preferred pressure have 216 on the flange projecting over the end of the pipe so that the bore at the j o i n t Jointing the standard and thrust w i l l be f l u s h a f t e r welding. are and fairly must thick, as indicated welded by flanges practice, codes of be securely to the p i p e or cast i n t e g r a l l y . Two other types of f l a n g e s a r e common:(1) Puddle of is as flanges are used on pipes The and which object they are of cast these not in walls water to retaining structures. flanges prevent as pipe leakage flanges stress, of water are are to necessarily longi- thick which although designed flange transfer be tudinal the should securely attached to the p i p e w a l l . (2) Blank ends. flanges Their at at at p is is are, as the name be implies, calculated i n s t a l l e d at to resist disc blank thickness should bending rigidity stress moments clamped occurs where and t the edges and centre. the the For a c i r c u l a r radial is equal edges perimeter fluid the maximum and d If bending to 3 bolts, pdZ/16t2 the pressure, thickness. stress i s the p i t c h c i r c l e diameter the edges were not at the rigidly and the the flange maximum clamped would occur centre would be 50% i n excess of t h i s amount. COAT I NGS Buried the p i p e during steel pipes are subject to corrosion and damage unless i s coated. Coatings should laying of the i d e a l l y be r e s i s t a n t to s c r a t c h i n g pipe, and to moisture, chemical and They transport attack, and biological should to to electric to currents prevent yet temperature during variations. be h a r d enough in the wall damage h a n d l i n g a n d due to the adhere well of stones the trench, and sufficiently enough to adhesive withstand pipe flexible flexing the p i p e w a l l ( P P l , 1975; Cates, 1953). The followed outer most by a common coating The coating for pipes with is is a thin adhesive possibly by is coat an wire then reinforced pipe or fibres and then wrapping. surface initially cleaned brushing, applied sandblasting by spray, acid pickling, or dipping a n d the prime coat pipe in a bath. brush the Bitumen 217 or coal the t a r enamel pipe may i s the p r e f e r r e d prime coating. be spirally This wrapped with After the p r i m a r y felt or coat woven impregnated followed by glass fibre matting. i s sometimes paper or asbestos f e l t whitewashed impregnated w i t h bitumen or coal to assist tar. The p i p e i s then in detecting damage a n d to s h i e l d the c o a t i n g may be a p p l i e d in the in the f i e l d a f t e r welding left of from the sun. the bare pipe for The coating or in and the joints, factory, in which case the ends a r e field. The total thickness jointing coated coating should be at least 5 mm. include an asbestos f i b r e bitumen mastic 3 paints, PVC or polythene tapes resins or plastics, Other types of coatings to 6 mm t h i c k , (either cement be self coal tar pitch, epoxy adhesive o r and zinc bedded on an adhesive), applied with by galvanizing. based mortar Exposed p i p e s may primed and painted bitumen aluminium or enamel (AWWA, 1962). mortar of 12 coatings offer additional resistance to buck1 i n g Cement in are the case usually l a r g e bore t h i n to 20 mm may walled pipes. 3/4 Cement mortar coatings (AWWA, pin 1954, 1962). by ($ be to inch) thick for flaws, Finished means of metal a coatings Holiday or checked An holes etc. in detector. electrical is run the conductor the form of An is brushes rolling is springs along the p i p e coating. a current electrical potential applied across coating and observed when f l a w s in the c o a t i n g a r e de ected. LININGS Steel friction pipes a r e losses. in l i n e d to r e s i s t steel In is the interna may corrosion and minimize the be oxidized by corrosive systems to in Unlined the fluid. pipe substances particular, corrosion. case of solids-conveying off leading be the oxide of rapidly scraped further by Corrosion water-conveying by adding pipes lime. may inhibited m a i n t a i n i n g a h i g h pH e.g. Lime on the other h a n d could cause carbonate s c a l i n g . The tar most popular (2 to 3 linings mm are bitumen Bitumen, (3 to 5 m m t h i c k ) o r coal is a by-product of enamel thick). which petroleum, Before i s t h e cheaper of the two. applying the lining the pipe wall is cleaned by sand- 218 b l a s t i n g or spray, other or methods and the lining i s then a p p l i e d by brush, dipping s p i n n i n g to o b t a i n smooth f i n i s h . bitumen, by a smooth surface. Coal tar it Spun enamel i s also more and pipe. to in particular resistant to provides a moisture subject enamel is than to although impact more b r i t t l e of the consequently Plasticised damage and flexing been coal tar enamels have, however, now developed overcome the problems of b r i t t l e n e s s . Epoxy careful to the in each paints are is also used successful l y to ensure of for I inings, although adhere with appl ication other. The necessary successive the lining coats recommended but it thickness varies type o f paint, layers. i s n o r m a l l y of tar they epoxy taint the o r d e r of 0 . 3 m m applied should be avoided for 2 to 4 Coal as linings the portable water pipes water. Lead based p r i m e r s should also be avoided as they Cement mortar is also to used for lining, large a r e toxic. by spinning lining the p i p e , is usually applied centrifugally bore pipes. thick. The Mortar applied 6 12 mm ( 1 / 4 to to pipes 3 in inch) l i n i n g s have been a p p l i e d successfully cleaned b y gally by a the f i e l d . or The o l d surface i s f i r s t thoroughly and then coated c e n t r i f u along the line (Cole, wire-brushing machine sand b l a s t i n g , propelled drawn or slowly 1956). On made pipes good over at about 600 mm bore, or most by factory linings may be field joints manually mechanical applicators. CATHOD I C PROTECT I ON Despite of steel the use often of protective coatings, flaws, corrosion pin-holes of or the at walls pipes occurs through exposed fittings. Corrosion i s due p r i m a r i ly to two causes; g a l v a n i c corrosion and stray current electrolysis (Uhlig, 1948). Ga I vanic Corrosion When lyte, two dissimi l a r may flow materials are connected to to the through an electrocurrent from one m a t e r i a l from or the other. the The r e s u l t i n g through the electric current flows the anode leave cathode electrolyte. Particles ions, anode causing corrosion. T h e cathode i s not attacked. 219 Such contact material osion action may take place (for when two dissimilar fittings form of metals are in in conductive soil instance of a different to the p i p e ) . Another more frequent w i t h pipes i n corrosive soils. in soi I w i t h or in v a r y i n g characteristics, water w i th gal v ani c corris particularly oxygen con- occurs The effect marked differential content action c e n t r a t ions sulphur. which which to add high chemical biochemical , especial l y in the s o i l Corrosion type of been to i s alSo caused by galvanic is a has lime a c t i o n r e s u l t i n g from b a c t e r i a . A method to counteract soil corrosion was used the successfully backfill. trench Stress concentration in the steel in an e l e c t r o l y t e may also lead to corrosion. The amount of corrosion due to the l a s t named two influences i s u s u a l l y small. Potential corrosive areas may tests or be detected by s o i l resistance tests, in the pipe. pipe - soil potential If the s o i l measurement of the c u r r e n t or i s a t a l l suspect, resistivity as a s t a n d a r d p r a c t i c e f o r major should be conducted. Soi I r e s i s t taken the pipelines, a ivity in-situ soi I survey i s measured using a i n ohm - centimetres. bridge drop. any circuit or by Readings a r e n o r m a l l y measuring are be a current and associated volt but Standard major probes available done by for an these exper- measurements, surveys should ienced corrosion engineer (Schneider, 1952). resistivity of A highly conductive soil may have a 500 ohm cm, a n d a poorly conductive s o i l , The potential in by difference more than 10 000 ohm cm. between a buried pipe and the soil is is important measured electrode frequently tial If the of the evaluating connecting contact as corrosive voltmeter the soil. conditions. between the The pipe potential and a a special cell is in with A copper sulphate conditions. half used the electrode under normal to 0.7 higher likely The poten- a p i p e i s 0.5 pipe is at a v o l t s below that of the s u r r o u n d i n g s o i l . voltage to flow than 0.85 volts below that of soil, currents are from p i p e to s o i l , thereby cor- r o d i n g the pipe. To by a prevent conductor 11.5). t h i s corrosion, to the pipe a in sacrificial the anode of may be connected corrosion vicinity possible (Fig. The s a c r i f i c i a l anode i s b u r i e d i n a conductive s u r r o u n d , below the water table and currents will tend to leave preferably 220 from to the anode If instead the of the is pipe, thereby limiting the from corrosion the steel need the are Maghigh the to anode. cause In to anode sufficiently no external may dissimilar electrical be pipe be galvanic fact, a the action potential in applied. resistor current. sometimes installed connection magnesium, nesium has I imi t and Common or alloys sacrificial of these iron, anodes metals. has of a zinc the aluminium, potential (ampere anodic greatest equivalent difference hours from electro-chemical and ions is fairly may per k i logram material) hydrogen actively polarkg. life resistant the to polarization. the ( A l a y e r of thereby is replace the metal ions leaving further anodes, This insulating ization). Magnesium against anodes attack. to termed Magnesium anodes give 200 1 200 ampere hours per for about a are normally designed 10 year b u t zinc anodes often l a s t 20 or 30 years. BOI Junction Wilh R o a l ~ t o ri f Required Fig. 11.5 S a c r i f i c i a l anode i n s t a l l a t i o n f o r cathodic protection T h e spacing requirements volts The below spacing to the of a n d size of bring soil the anodes pipe to will a be determined by the c u r r e n t safe potential length (at of in least the 0.85 potential along the entire pipe). con- sacrificial poorly anodes w i l l coated pipe vary to from 3 m m in poorly ductive soil and 30 highly conductive of estthe the soil provided the the p i p e required of a i s well coated. is The most r e l i a b l e way drain source current and imating pipe by current ground to actually d.c. from means bed and measure r e s u l t i n g p i p e to s o i l p o t e n t i a l a l o n g the pipe. 221 As a rule of thumb, the current required to protect a pipe a g a i n s t corrosion where and pipe i s i = 10/r in per square metre of b a r e d p i p e surface, r i is the of as current safety low as amps, i s the s o i l resistance The area i n ohm cm of exposed r i s i n g to a factor be of 3 is per incorporated. cent for a may 0.5 good coating, 20 p e r cent f o r a poor coating. Once the (less soils a total than with the required size ohm draw-off may cm) be large current per In km of pipe is known, soils in anode calculated. anodes highly may about to conductive be used 500 (20 k g ) than used but lower conductivities anodes (greater be 1 000 ohm cm) an adequate number of smaller should ensure c u r r e n t output. If use a an electricity supply is available, of it i s usually (Fig. be 11.6) cheaper instead to of an impressed current type protection sacrificial anode. A transformer-rectifier may i n s t a l led to pro- v i d e the necessary With corrosive. frequently ductive impressed Scrap used. and dc c u r r e n t . current iron, Steel for or i n s t a l l a t ions, graphite will the anode need not buried in coke in be selffill, are con- rods anodes this quickly corrode cast highly soils reason high s i l i c o n i r o n anodes a r e preferred. The omics. in the type of protection current as to use w i l l i n s t a l Iations depend on the are long-term the fewer the econ- Impressed long are run, frequently low and In cheapest instalcase may than of be a maintainance than for costs are lations required sacrificial a a anodes. high length impressed applied, sacrificial away may from have current which anode the to in in installations turn could. relatively longer voltage of fa1 I s a The pipe off high protects The voltage to pipe-soil though, a potential rapidly voltage applied be consequently long length. point applied protect vicinity pipe-to-soil not, of in potential general soi I ) . the immediate volts of the should exceed Larger 3 (the pipe may at potential b e i n g below that the voltages may be damage to 100 coatings. spacing Impressed depending current on the installations qua1 i t y ferable of to 1 km the p i p e coating. sacrificial anodes Impressed c u r r e n t if the soil installations are preis higher than resistivity about 3 000 to 5 000 ohm cm. 222 Considerable only "hot economic or savings are often to achieved by protecting and if spots", points can be subject aggressive this should attack, be occasional shutdowns tolerated considered. Stray Current E l e c t r o l y s i s The currents most severe a form pipe. of corrosion is often other caused users of by dc stray dc leaving Railways but if and current r e t u r n c u r r e n t s through as a steer p i p e nearby, instead of corroded The rails, there i s another conductor such a p r o p o r t i o n of the c u r r e n t may flow through the r a i l . at a rate Where the c u r r e n t of leaves the p i p e , per year per the conductor steel will of be 9 kg (20 Ibs) by ampere current. or current pipe/soi 1 may be detected actual current measurements recordings from be potent iat a day, measurements. as Continuous may fluc- should taken over the currents t u a t e w i t h time. B o r e d or S u b m r r g e d Hod8 Cothodic Rolotlv8 t o E l w . t r o l y t 8 Structure Iron or grophite 1 Fig. 11.6 Impressed c u r r e n t corrosion protection. The by to may would corrosion the associated pipe of at the along with the stray currents the may be prevented leaves it, connecting the point where with a in current destination the to low current, some on conductor. which The a the current current voltage bed and leave have pipe be to length, the pipe case impressed prevent to maintain A sufficiently current escaping. ground transformer r e c t i f i e r may be r e q u i r e d f o r t h i s protection. 223 When the a pipe i s cathodically joints are protected, c a r e should be taken by have welding to be a that cable mechanical them if electrically Branch bonded, may across necessary. pipes insulated from the main p i p e to control the currents. THERMAL I NSULAT I ON Fluid in the pipeline may often be heated or cooled by the surroundings. climates or from are the Ice formation sometimes interior of the a an i n a r c t i c climates a n d h e a t i n g i n t r o p i c a l serious exposed wall wall, problem. pipe and by and in Heat a is transferred ways: to by number of and a conduction layer face through pipe pipe wrapping boundary of of fluid the inside and the by r a d i a t i o n from the e x t e r n a l wind currents in the air pipe convection s u r r o u n d i n g the pipe. TABLE 1 1 . 1 Thermal c o n d u c t i v i t i e s Therma I c o n d u c t i v i t y Mater ia I k cal m sec B t u in C" 14 sq f t hr F o Water 0.000 4 Air Steel B i tum i n ized Wrapping Concrete Slag wool 0.000 005 0.014 0.15 420 0.000 0.0002 01 0.3 6 0.000 01 0. 3 EEUA, The is 1968. heat loss to by the conduction temperature through an homogeneous the pipe wall proportional gradient across wall a n d the heat t r a n s f e r r e d per u n i t area of p i p e w a l l per u n i t time i s -Q - - AT T k A0 (11.2) 224 where is the Q is the of amount pipe of heat conducted in kilocalories or time, wal I Btu, is A the area surface, across T the is the t duration is in the A0 temperature k is the difference wal I , thickness for and thermal conductivity, tabulated Table 11.1 various materials. An heat equation transfer has was developed by the wall to Riddick of a et at (1950) for the total The through pipe conveying water. equation been modified agree with relationships i n d i c a t e d by EEUA (1964) a n d i s converted to metric u n i t s here: Rate of heat loss of water kcal/kg/sec (0. - ' o ) / 250D I _ _ _ _ t, + t o + 1 + 1 (11.3) and since temperature k c a I/kg/sec the in specific degrees heat of water is unity, sec the r a t e of the heat drop loss in in Centigrade per equals , where temperature of water C " ambient temperature outside C " diameter m thickness of p i p e m c o n d u c t i v i t y of p i p e w a l l thickness of coating m c o n d u c t i v i t y of c o a t i n g kcal/m sec C o heat loss through boundary 0.34(1 layer = kcal/m sec C o + 0.020i)v0'8/D0'2 m/s kcal/m2 sec C" water velocity 100 kcal/m2 sec C o e m i s s i v i t y factor = 0.9 f o r b l a c k a s p h a l t a n d concrete 0.7 for cast i r o n a n d steel 0.4 for aluminium p a i n t 34f1 heat loss by convection = 0.000 kcal/m2 sec C" v = w i n d velocity km/hr + heat loss by r a d i a t i o n = 0.054 E('O 273 1 3 + 0.78V ( - 'i -90 0.25 D 1 225 The h e a t generation by fluid friction is usually negligible although i t theoretically i n c r e a s e s the t e m p e r a t u r e of t h e f l u i d . Example An thick water uncoated steel at an 300 mm diameter to a pipeline 10 km/hr 10°C. 1 000 m long with 5 mm of walls, initial exposed wind, conveys 100 C / s t e m p e r a t u r e of The a i r t e m p e r a t u r e i s 30°C. Determine t h e e n d t e m p e r a t u r e of t h e w a t e r . E V = = = 0.7 0.1/0.785 0.34 0.054 x 0.32 = 1.42 m/s Kf = Kr x 1.42°'8/0.30.2 x 0.7 = 0.67 ( 30 + 27313 10-3 = 0.001 tl kl = 0.005 ~0.014 - o.35 = 0.00103°C/sec = (30 - 1 0 ) / ( 2 5 0 x 0 . 3 ) 0.35 + 1/0.67 + (0.001 + 0.0029) T e m p e r a t u r e r i s e o v e r 1 000 m = 1 000 x 0.00103 1.42 The insulation of = 0.7"C industrial on pipework i t s own. carrying The cost of h i g h or low temp- erature fluids i s a subject t h e heat t r a n s f e r s h o u l d be b a l a n c e d a g a i n s t t h e cost of t h e l a g g i n g . Heat erature heat heat the used, transfer of the to or from buried which pipelines in depends is on the tempthe of If be surroundings, The turn and influenced by rate transfer. transfer temperature vary the with gradient and consequently to may of time are is difficult evaluate. 11.3 may temperature surroundings known, Equ. o m i t t i n g the term l / ( K + Kc). REFERENCES American Concrete P i p e Assn., 1970. Concrete P i p e Design M a n u a l , Arlington. AWWA S t a n d a r d C602, 1954. Cement M o r t a r L i n i n g of Water P i p e l i n e s in P l a c e , N.Y. 226 AWWA S t a n d a r d C203, 1962. C o a l T a r Enamel P r o t e c t i v e C o a t i n g s f o r Steel W a t e r P i p e 30 Ins. and O v e r , N.Y. AWWA S t a n d a r d C205, 1962. Cement M o r t a r P r o t e c t i o n L i n i n g and C o a t i n g f o r Steel W a t e r P i p e 30 I n s . and O v e r , N.Y. BSCP 2010, 1970. P a r t 2, D e s i g n and C o n s t r u c t i o n of Steel P i p e l i n e s in Land, B S I , L o n d o n . Cates, W.H., 1953. C o a t i n g f o r s t e e l w a t e r p i p e , J. Am. W a t e r W o r k s Assn. 4 5 ( 2 ) . 1956. D e s i g n o f s t e e l p i p e w i t h cement c o a t i n g and l i n Cole, E.S., ing, J . Am. W a t e r W o r k s Assn., 4 8 ( 2 ) . C o n c r e t e P i p e Assn., 1967. B e d d i n g and J o i n t i n g of F l e x i b l y J o i n t e d C o n c r e t e P i p e s , Techn. B u l . No. 10, T o n b r i d g e . Engineering E q u i p m e n t U s e r ' s Assn., 1964. Thermal I n s u l a t i o n of P i p e s and Vessels, H a n d b o o k No. 12, C o n s t a b l e , L o n d o n . Engineering E q u i p m e n t U s e r s Assn., 1968. P i p e J o i n t i n g Methods, H a n d b o o k No. 23, C o n s t a b l e , L o n d o n . 1975. P i p e l i n e p r o t e c t i o n r e v i e w , P i p e s and P i p e l i n e s I n t e r n a t i o n a l , 20(4). Reitz, H.M. 1950. S o i l m e c h a n i c s and b a c k f i l l i n g p r a c t i c e , J . Am. W a t e r W o r k s Assn., 4 2 ( 1 2 ) . R e y n o l d s , J.M., 1970. S u b m a r i n e p i p e l i n e s , P i p e s and M a n u a l . 3rd Ed. S c i e n t i f i c S u r v e y s , L o n d o n . and T o m a s s i , A., 1950. F r e e z i n g of Riddick, T.M., L i n d s a y , N.L. w a t e r in e x p o s e d p i p e l i n e s , J. Am. W a t e r W o r k s Assn., 42(11). S c h n e i d e r , W.R., 1952. C o r r o s i o n and c a t h o d i c p r o t e c t i o n o f p i p e l i n e s , J. Am. W a t e r Works Assn., 44(5). Schwartz, H. I., 1971. H y d r a u l i c t r e n c h i n g of s u b m a r i n e p i p e l i n e s , P r o c . Am.Soc. C i v i l E n g r s . 9 7 ( T E 4 ) Sowers, G.F., 1956. T r e n c h e x c a v a t i o n and b a c k f i l l i n g , J. Am. W a t e r W o r k s Assn., 4 8 ( 7 ) . 1948. The C o r r o s i o n H a n d b o o k , W i l e y , N.Y. U h l i g , H.H., L I S T OF SYMBOLS A AS - area a r e a of steel w i d t h of t r e n c h drag c o e f f i c i e n t B d D E f 9 inside diameter outside diameter thermal emissivi ty factor stress gravitational acceleration backfi I I a b o v e t o p o f p i p e - - H I c u r r e n t in amps 227 K C heat loss by convection heat loss through water f i l m heat loss b y r a d i a t i o n c o n d u c t i v i t y of p i p e wal I c o n d u c t i v i t y of coating bedding factor pressure amount of heat resistance i n ohms time thickness of p i p e w a l l t h i ckness of c o a t i n g component of wave v e l o c i t y p e r p e n d i c u l a r to p i p e mean water velocity, or component Kf Kr kl k2 M P Q r T tl t2 u V of current velocity p e r p e n d i c u l a r to p i p e v W w i n d velocity s p e c i f i c weight of water depth of bedding m a t e r i a l below p i p e temperature i n s i d e p i p e temperature outside p i p e Y 0. 0 0 228 CHAPTER 12 PUMP I NG I NSTALLAT IONS INFLUENCE OF The pumping pump as PUMPS I N P I P E L I N E DESIGN concerned forced The with pipeline lines. engineer That to is, a i s frequently the the design of the of pipe the vice to net by a is fluid fed is through design opposed with gravity pumping line line. pipe inter-related Pumes head, of the equipment losses selected in and versa. static must hence pipe overcome friction addition t h e p u m p i n g h e a d a n d p o w e r r e q u l .ement a r e a diameter. The pipe wall thickness is in function based on the turn interna I pressures. Therefore friction head a n d f l u i d velocity (which a f f e c t s w a t e r hammer h e a d ) a l s o a f f e c t t h e w a l l The other. engineer The system should therefore cannot design one v , hickness of the pipe. thout considering the must be designed in a n integrated manner. therefore their Addison pump size in Pipeline pumps, (1957), complete also the is engineers their IWt be aware of the and various costs. types of Stepanoff more I i m i t a t ions, (1969) and The characteristics (19551, and the for example, head give information. have pump, to be i.e. suction requirements w i l l The d e s i g n o f and considered the pumpstation design. or impeller In fact (1960), shape it optimum casing material, more the concern of such as the manufacturer. i s covered in books t h o s e b y K a r a s s i k and C a r t e r Similarly electrical power that is K o v a t s (1964) and KSB a n d control (1968). supply, motor design equipment by a r e so s p e c i a l i z e d engineers. It they should be selected o r designed pipeline engineer’s point of electrical from the view that the following i n f o r m a t i o n i s presented. TYPES O F PUMPS P o s i t i v e D i s p l a c e m e n t Types Least some used in pipeline practice are nowadays, positive but still used in industrial a p p l i c a t ions, displacement pumps. 229 The to to reciprocating move enter to on and a pump fro i s one such type. One-way exit A p i s t o n or ram i s forced liquid conduit i n a cylinder. stroke and v a l v e s p e r m i t the the receiving reverse into on a f o r w a r d stroke of the piston. The also p i s t o n can positive be replaced by a flexible These diaphragm. There are rotary displacement pumps. include s pi ral types a n d intermeshing gears. Centrifugal Pumps Rotodynamic pumps move pressure like by to it. a This action l i q u i d by may be is be i m p a r t i n g a velocity in the form along vanes of a an and hence axial flow through rotating propeller. There Liquid may pump the forced guide tabular the casing to blades. in casing reduce s w i r l . low heads. T h i s type of high heads i s most common f o r centrifugal pump l a r g e flows a n d Here For an i s preferred. r o t a t i o n of The in in impeller creates an o u t w a r d form is is the most common, accepted type of ( r a d i a l ) c e n t r i f u g a l flow. and as the centrifugal pump latter various forms universal ly This practical ly i s capable standard of hand- waterworks engineering. pump l i n g flows pumps by by an up to 20 cumecs. parallel is are For h i g h flows The head a n d to p e r m i t f l e x i b i l i t y , which can be generated water, but in common. to a impeller limited l i t t l e over 100 metres of assembling a number of impellers i n series a wide r a n g e of heads i s possible. lcllcr ,nes Fig. 12.1 Sectional e l e v a t i o n of v o l u t e t y p e c e n t r i f u g a l pump (Webber, F l u i d Mechanics f o r C i v i l Engineers, 1971) 230 The inlet c o n d i t i o n must and the be controlled to a v o i d c a v i t a t i o n or air entrainment to the permissible the maximum suction pressure i s r e i a t e d first pumping stage. In some cases delivery pressure of instead of connecting of impellers i n series on a common shaft a number T h i s permits more be driven by a independent pump u n i t s a r e i n s t a l l e d i n series. particularly if one of the units is flexibility to v a r i a b l e speed motor. The driving device i n a c e n t r i f u g a l pump i s termed the impeller. I t may be a series of vanes shaped to f l i n g the water from a c e n t r a l the the as outer periphery. nozzle. Here The it is directed of by this and eye a or volute of inlet towards into be casing pump discharge much as efficiency type motor may 90 percent although pump units together rarely h a v e efficiences installations can for above 80 percent except unusual duties as such as as 30 in large sizes. solids Pumping in pumping percent. suspension have efficiencies low Usually the inlet to the impeller eye is on one side, and the d r i v i n g shaft s i t u a t i o n s an to to the motor on the other side of the impeller. i n some i n l e t may be on each side pump. This i n which case i t i s r e f e r r e d a more expensive casing as a double e n t r y involves b u t i t r e s u l t s i n a balanced t h r u s t i n the d i r e c t i o n of the shaft. Fig. 12.2 Section through a s i n g l e e n t r y horizontal pump spindle centrifugal 231 Pump u n i t s may be mounted w i t h The the horizontal shaft with of a split the s h a f t is vertical the is most or horizontal. from deep be casing practical or a maintenance well is point view. a Where space spindle limited, suction required, is vertical arrangement may preferable. The motor then mounted on a p l a t f o r m above the pump. TERMS A N D DEF I N I T I ONS Head The water. head It in i t s general sense above is a the energy per u n i t weight of z, comprises elevation p l u s velocity certain datum, p l u s pres- sure head p / w head v2/2g. Total Head Total inlet 12.3). head and usually it is refers the to the excess by of discharge pumps head to head head generated the (see F i g . Fig. 12.3 D e f i n i t i o n of net p o s i t i v e suction head. 232 Net Positive Suction Head In order to avoid cavitation, air entrainment and a drop-off head. indi- in pumping efficiency The net by positive a a pump needs a c e r t a i n minimum suction head (NPSH) r e q u i r e d as as a function net can of u s u a l l y be r a t e of suction cated The It pump is manufacturer referred as to pumping. head. pres- requirement i s generally the positive above suction vapour expressed the absolute head s u r e r e q u i r e d a t the pump inlet. NPSH = Hp I t is c a l c u l a t e d as follows: - Pv/W f ( 2.1 - H e - = H r + H a - H s - H where H P = head PV/W to centre line of inlet, head. ( 2. 2) and at inlet, relative equal to absolute pressure head p l u s velocity PV W = vapour pressure = u n i t weight of water = suction r e s e r v o i r head above datum = atmospheric Hr Ha H S pressure head (about 10 m of water at sea l e v e l ) = = = elevation of centreline of pump suction above datum Hf He f r i c t i o n head loss between r e s e r v o i r a n d pump turbulence head loss between r e s e r v o i r a n d pump is a or NPSH requirement drop-off increases side of when in efficiency subjective increase It in figure noise as there at i s not a sharp It level this value. with discharge. i s p r e f e r a b l e to be on the conservative The NPSH requirement i s of the order considering NPSH. 10 percent of figure the head of should be the f i r s t obtained stage of from the the pump b u t a more manufacturer's tests. re1 i a b l e NPSH can tests firstly at al I (Grist, at be assessed by observing the NPSH c a v i t a t i o n o r from performance cavitation commences, 1974). As i s reduced flowrates away from best efficiency At due an to NPSH just less the flowrate but eventually that associated by with the flowrates. erosion than maximum impeller in cavitation head generated s t a r t s t o decrease. The head r a p i d l y decreases w i t h decrease in NPSH. A the 3 l i m i t of NPSH. times 3% decrease head to i s recommended for avoid cavitation For estabbe lishing at least The the NPSH r e q u i r e d 3% head drop should this NPSH, though. reason some degree of c a v i t a t i o n i s normally acceptable. 233 Specific Speed The pump's specific speed Ns of are a pump i s a useful i n d i c a t i o n of the two slightly different definitions of capabilities. There s p e c i f i c speed a n d the more general one i s g i v e n f i r s t : Specific relative speed a i s a c h a r a c t e r i s t i c velocity velocity of the of the r o t a t i n g element i.e. it is the to characteristic water, v e l o c i t y of the impeller r e l a t i v e t o that of water. The speed of the periphery of the impeller speed and is proportional is to ND where will N is be the impeller rotational D i t s diameter the water (units velocity introduced later). From B e r n o u l l i ' s theorum i s proportional proportional b is the to JgH where H i s the total head. Therefore But the discharge Ns vDb is t o ND/ JgH. width of Q is proportional to where impeller. so For a n y g i v e n geometric p r o p o r t i o n b i s p r o p o r t i o n a l t o D, Qa,&8D2 E l i m i n a t i n g D one a r r i v e s a t O- (12.3) NS NQf This / is a dimensionless form of Unfortunately express most in specific catalogues and per text books (12.4) speed p r o v i d e d the u n i t s omit not are the consistent. g term and N revolutions minute (rpm) r a d i a n s p e r second. One encounters the expression NS = NQi/H3/4 In S.1. (12.5) units Q is in gallons per minute and H i n feet. In imperial u n i t s Q i s i n cumecs The alternative ( c u b i c metres p e r second) a n d H in metres. of definition pump of against NS i s the speed in rpm of a geo- metrically similar (or gal. per one min) such size that i t would d e l i v e r one cumec 1 metre at (or 1 foot) head. Then by sub- stitution arrives directly the latter dimensionally dependent expression for N By of the is reviewing size of . the former definition of NS, one head. obtains In fact an a idea high impeller with relative a low a to pumping and Ns associated a low head fast low rotational speed speeds, to whereas that of NS implies thus high a head high and relative relative water (water has radial component to t a n g e n t i a l component). 234 Fig. N is 12.4 indicates the r e l a t i o n s h i p between (w = 271 head per stage and s p e c i f i c speed f o r a number of pumps selected from r e a l applications. i n r p m a n d w i n radians/sec 7 N/60). Lo Lo 0 \ 50 t@ W2 v u l t i - s t a g e 74- Ln 0, L $20 E I - \-- n \ 7 I \ T e d flow 5 1 12.4 the \ ' 20 50 < I I I Ns 500 specific 100 head 200 and 1000' speed for pumps Fig. Relationship between IMPELLER DYNAMICS The shape of the radiai flow the impeller blades which in i n a c e n t r i f u g a l pump influences the pump c e r t a i n charvelocities inside the pattern basic t u r n gives of acteristics. pump duty. Referring is u, A understanding relative i s therefore useful in selecting a type of pump f o r a p a r t i c u l a r to Fig. of 12.5 the the circumferential relative to speed the of the is impeller w velocity water i s v. impeller and the absolute water velocity Torque T o n the water i s force x r a d i u s But force = change in momentum 235 T h e r e f o r e i m p a r t e d T = c h a n g e i n moment of momentum = A(mvr) = (12.6) cos a dm - l r l v l 2 cos a dm 1 (12.7) 1 r2v2 Fig. 12.5 V e l o c i t y v e c t o r s a t i m p e l l e r of c e n t r i f u g a l pump. where dm is an element of mass discharge per unit time, and the integral i s o v e r a l l the vanes. where i s t h e r o t a t i o n a l speed Power P = T w (12.8) (12.9) .'. P = A (mvr) w u 2 /ulvl Now r w = u1 a n d r w = 1 2 P = 1 u 2 v 2 c o s a dm 2 A l s o P = pgHQ where Q 12.10) cosa drn .'. 1 12.1 1 ) 12.12) 12.13) 12.14) i s the d i s c h a r g e r a t e = .'. .*. P = gHJdm s i n c e p Q Jdm The term u,vl Now v Head H = ( u v c o s a - UIVl cosal)/g 2 2 coscll i s n o r m a l l y r e l a t i v e l y s m a l l . cosa2 = u 2 - t 2 cot B2 2 (12.15) where t 2 i s t h e r a d i a l component of v .*. H (u, - t 2 cot B 2 ) / g (12.16) (12.17) a n d Q = nDbt ... H 2 A - BQ cot and The B2 are constants, g is (12.18) gravity and p is where A 0 water mass density. blade angle B2 therefore affects in Fig. t h e shape of 12.6. the pump H-Q c h a r a c t e r i s t i c c u r v e , as i l l u s t r a t e d 236 1 Q 12.6 Effect of b l a d e a n g l e on pump c h a r a c t e r i s t i c s Fig. PUMP CHARACTER I ST I C CURVES The usually pumping and head-discharge produced system. of by This characteristic the of pumps and i s one to of the a curves viable manufacturer is used design size as relationship of useful in for pipe selection will be selection combinations pumps parallel discussed l a t e r . -BH Fig. 12.7 Pump c h a r a c t e r i s t i c curves. 237 Break and Fig. could pump horse power (BHP) or shaft power required by the pump (see efficiency The be duty E a r e often H-Q i n d i c a t e d on the same d i a g r a m with 12.7). also c u r v e may a l t e r any pump by the d r i v e speed a n d different impeller changed on fitting diameters. tant head The BHP a n d E curves would also change then. is The r e s u l is proportional to NZ a n d D2, whereas the discharge i s most e a s i l y p r o p o r t i o n a l to N a n d D. The ally. graph. required level and a required duty of a pump determined g r a p h i c - The pipeline Fig. c h a r a c t e r i s i t c s a r e p l o t t e d on a head - discharge Thus for a 12.8 illustrates assuming pipe, the (a) head a a (static plus friction) water level pipe. The from different new, a's, h i g h suction sump low suction to the an sump older line. and smooth and factor be (b) more pessimistic f r i c t i o n somewhere of between could applicable for A line selected can duty effect para1 lel i n g t w o or more pumps also be observed such a g r a p h . I 0flurves/ 2 in parallel llow sump and old pipe / \\ 0 pipeline a high sump level and new pipe Fig. 12.8 P i p e l i n e a n d pump c h a r a c t e r i s t i c s . 238 Pumps however, pipeline line pump to a to in series are pump more station difficult (Fig. to control. is Frequently, along a booster 12.9) required increase c a p a c i t y within a or to enable the f i r s t pressure. other, is In section of pipethe in operate are lower design the such cases for the pumps curves the added one at above any whereas i.e. parallel, discharge head added, abscissa i s m u l t i p l i e d by the number of pumps i n operation. Booster r e s e r v o i r or case one a pumps sump may on operate the in-line, side is of or with a break pressure suction volume grade the booster. in case be I n the of a latter at to certain The balancing hydraulic In the required trip down a station. l i n e must water also drawn due to reservoir level. former case hammer power f a i l u r e i s more d i f f i c u l t to p r e d i c t a n d allow f o r . Fig. 12.9 Location of booster pump station. 239 MOTORS The wheel speed driving power of a pump could an by be a steam motor. turbine, water or of most the The commonly pump pump is speed nowadays, controlled electric the The r o t a t i o n a l of alternating the frequency current. i s approximately N = 60Hz divided by number of per or p a i r s of Hz poles, is where N i s the pump speed in r e v o l u t i o n s frequency in cycles minute and Hertz. There the e l e c t r i c a l per second i s a correction can to be made f o r s l i p between the r o t o r ( f o r smaller motors). for driving pumps: and starter. Three Slip of be up t o 2 o r 5 percent motors a r e commonly used types AC a) s q u i r r e l cage induction motors (asynchronous) i n d u c t i o n motors (asynchronous) b ) wound r o t o r ( s l i p - r i n g ) c) synchronous i n d u c t i o n motors. Squirrel cage motors are simple They in design, robust, economic a n d than large require the minimum two maintenance. Their a r e general l y is that more e f f i c i e n t they require other types. disadvantage if this starting motor currents. However can be tolerated, offers the most a s q u i r r e l cage economical starting and not with d i rect-on-1 ine starter If reliable permitted, starters. combination it i s usual possible. to employ direct-on-I ine or is either star-delta auto-transformer A l t e r n a t i v e s t a r t e r s compare as follows:- Type of Starter S t a r t i n g Current ( p r o p o r t i o n of f u l l load) 4.5 to 7.0 S t a r t i n g Torque ( f u l l load = 1 ) 0.5 to 2.5 to 0.8 Direct - on Star - Delta Auto 1.2 t o 2.0 as r e q u i r e d 0.3 - transformer as r e q u i r e d Slip-ring starters up to and induction h a v e the speed with motors are started they by means of resistance brought are a d v a n t a g e that relatively low c a n be smoothly current. full starting They normal l y used when s q u i r r e l cage motors a r e impermissible. Synchronous the motors a are used on large They installations. may They have a d v a n t a g e of high load factor. be e i t h e r induction 240 motors speed. ance o r current. Variable constant although are used speed motors are Belt more expensive a n d drives or or salient pole be motors. by They run at constant synchronous resist- Starting reactor can direct-on-I ine, mainly auto-transformer, on the starters depending permitted s t a r t i n g less e f f i c i e n t units are than speed motors. on smaller possible motors now commutator as well. with used motors, Thyristor motor resistances on s l i p - r i n g and v a r i a b l e speeds motors. starters cost two for are being can used be savings for in small Pole c h a n g i n g cage motors. also selecting speeds for squirrel PUMPSTAT IONS The of cost of the structures While the to house pumps details concern and may exceed the cost the machinery. design to cannot himself delivery of be covered with of the here the as pipeline he engineer h a v e to with the will need the layout to will pump install suction The pipework each will control operation valves. capacity and the suction may more et sumps water effect of the system, in is the there be hammer protection of incorporated layouts stat ion. by A complete (1974). import- discussion The ant can pumpstation of the sump given inlet Twort al design and pump of pipework has an b e a r i n g on the capacity effect its operational reduce of a pipeline. Air of of Head losses i n t o the pump drawn the in by vortices or efficiency. the capacity turbulence The could pipeline entire considerably. system awareness the requirements the pumping therefore should be the d u t y of the p i p e l i n e engineer. REFERENCES H., 1955. C e n t r i f u g a l a n d Other Rotodynamic Pumps, 2nd Addison, Ed., Chapman a n d H a l l , London, pp 530. Grist, E . , 1974. Nett p o s i t i v e suction head requirements f o r avoidance of unacceptable c a v i t a t i o n erosion i n c e n t r i f u g a l pumps, Proc. C a v i t a t i o n conference, Instn. Mech. Engrs. London, p 153-162. I n s t i t u t i o n of Water Engineers, 1969. Manual of B r i t i s h Water Engineering Practice. V o l . I I , Engineering Practice, 4th ed. London, K a r a s s i k , I . J . a n d Carter, R., 1960. C e n t r i f u g a l Pumps, F.W. Dodge, N.Y. pp 488. 241 Kovats, A., 1964. Design a n d Performance of C e n t r i f u g a l a n d A x i a l Flow Pumps a n d Compressors, Pergamon Press, Oxford, p p 468. KSB, Pump Handbook, 1968. K l e i n , Schanzlin 0 Becker, F r a n k e n t h a l , p p 183. Stepanoff, A.J., 1957. C e n t r i f u g a l a n d A x i a l Flow Pumps, Theory, Design a n d Application, 2nd Ed., Wiley, N.Y., p p 462. Twort, A.C., Hoather, R.C. a n d Law, F.M., 1974. Water Supply, Edward Arnold, London, p p 478. 1971. F l u i d Mechanics f o r C i v i l Engineers, Chapman Webber, N.B., a n d H a l l , London, p p 340. L I S T OF SYMBOLS A,B BHP - constants break horsepower width di arneter efficiency g r a v i t a t ional acceleration head ( s u b s c r i p t a - atmospheric, e - turbulence, f - - b D E 9 - H friction, p - inlet and s - elevation). mass per u n i t time pump r o t a t i o n a l speed net p o s i t i v e suction head specific speed pressure power discharge r a t e radius torque r a d i a l component of velocity p e r i p h e r a l velocity velocity unit weight of water p 9. (9800 Newtons per c u b i c metre) u n i t mass of water a n g I es 242 GENERAL REFERENCES AND STANDARDS B I T I SH STANDARDS R Steel Pipes BS 534 778 1387 1965Ptl 2633 291 0 3601 3602 3603 3604 3605 Steel Pipes, F i t t i n g s and Specials Steel Pipes a n d Joints Steel tubes and t u b u l a r s f o r screwing But-welding pipe fittings. Carbon steel Class 1 a r c welding of f e r r i t i c steel pipes Radiographic pipe Steel pipes a n d tubes - carbon steel ex. welded circ. butt joints in steel - ordinary duties Steel pipes and tubes for pressure purposes Carbon steel : h i g h duties Steel pipes a n d tubes f o r pressure purposes Carbon a n d a l l o y steel pipes Low and medium a l l o y steel p i p e s Steel pipes a n d tubes for pressure purposes Austeni t i c stainless steel Cast I r o n Pipe 78-1 78-2 143 4 6 1 437 1 130 C C I spigot a n d socket pipes - p i p e s I spigot a n d socket pipes - f i t t i n g s I screwed pipes waste a n d vent pipes Malleable C C C I spigot a n d socket s o i l , I spigot a n d socket d r a i n p i p e s a n d f i t t i n g s C I d r a i n f i t t i n g s - spigot a n d socket Cast ( s p u n ) i r o n pressure p i p e s Malleable C C 121 1 1256 2035 4622 Wrought I screwed pipes I f l a n g e d pipes a n d f i t t i n g s Grey i r o n p i p e s and f i t t i n g s I r o n Pipe Wrought i r o n tubes a n d t u b u l a r s 788 243 1740 Wrought steel p i p e f i t t i n g s D u c t i l e I r o n Pipe L772 Ductile iron pipes a n d f i t t i n g s Asbestos Cement Pipe BS L86 582 P 201 O t4 A C pressure p i p e s A C soil, waste and ventilating pipes and fittings Design a n d construction of A C pressure pipes in l a n d 3656 A C sewer p i p e s a n d f i t t i n g s Concrete 556 4101 4625 Concrete pipes a n d f i t t i n g s Concrete unreinforced tubes a n d f i t t i n g s Prestressed concrete pipes ( i n c . fittings) Clay Pipe 65 539 540 1143 Clay d r a i n a n d sewer pipes Clay d r a i n a n d sewer pipes - f i t t i n g s Clay d r a i n a n d sewer pipes Salt glazed ware pipes with chemical l y resistant properties 1196 Clayware f i e l d d r a i n pipes P l a s t i c a n d Other Pipe 1972 1973 3284 3505 3506 3796 3867 4346 4514 4660 Polythene p i p e ( t y p e 3 2 ) for c o l d water services Spec. polythene pipe (type 425) for general purposes Polythene p i p e ( t y p e 50) f o r c o l d water services UPVC pipes ( t y p e 1420) f o r cold water supply UPVC p i p e f o r i n d u s t r i a l purposes Polythene p i p e ( t y p e 5 0 ) D i m s . of p i p e s O.D. Joints a n d f i t t i n g s for UPVC pressure p i p e UPVC s o i l a n d v e n t i l a t i n g p i p e UPVC underground a n d d r a i n p i p e 244 4728 Resistance t o c o n s t a n t thermopl a s t i c p i p e 2760 CP312 Pitch f i b r e pipes and couplings P l a s t i c pipework i n t e r n a l p r e s s u r e of l n s u l at i o n 1334 4508 CP3009 Thermal insulation Thermal l y i n s u l a t e d u n d e r g r o u n d p i p i n g systems Thermal l y i n s u l a t e d u n d e r g r o u n d p i p i n g systems Valves 8s 1010 1212Pt2 1218 & 5163(m) 1415 1952 & 51 54( m) 1953 2060 2591 3464 & 5150(rn) 3948 & 5151 ( m ) 3952 & 5155(m) 3961 & 5152(rn) 4090 & 51 53( rn) 4133 & 5157(rn) 431 2 5156(m) 5158(rn) 51 59(m) Taps a n d v a l v e s f o r water 8 a l l valves - diaphragm type S I ui ce v a I ves V a l v e s f o r domestic p u r p o s e s Copper a l l o y g a t e v a l v e s Copper a l loy check v a l v e s Copper a l l o y stop v a l v e s G l o s s a r y of v a l v e s C I wedge a n d d o u b l e d i s c v a l v e s C I parallel slide valves C I butterfly valves C I stop and check v a l v e s C I check v a l v e s F l a n g e d steel p a r a 1 l e l s l i d e v a l v e s Stop a n d check v a l v e s Screwdown d i a p h r a g m v a l v e s Plug valves Bal I valves 245 Jointing 10 21 1737 1821 1965 2494 3063 4504 Flanges a n d b o l t i n g f o r pipes etc. Threads Jointing m a t e r i a l s a n d compounds Oxy-acetylene B u t t we I d i ng Rubber j o i n t rings welding of steel p i p e l i n e s Dimensions of gaskets Flanges a n d b o l t i n g f o r pipes etc. Miscellaneous 1042 1306 1553 1710 205 1 29’17 3889 39 74 4740 Flow measurement Non-ferrous pipes f o r steam Graphical symbols I d e n t i f i c a t i o n of p i p e l i n e s Tube a n d p i p e f i t t i n g s Graphical symbol s Non destructive testing of pipes a n d tubes Pipe supports Control v a l v e c a p a c i t y SOUTH AFRICAN BUREAU OF STANDARDS Steel Pipe SABS 62 Steel pipes a n d f i t t i n g s up to 150 mm E l e c t r i c a l welded low carbon steel p i p e s Coated a n d l i n e d m i l d steel p i p e s 71 9 720 Cast I r o n Pipe 50 9 746 81 5 Malleable C I pipe f i t t i n g s water a n d vent pipes f i t t i n g s and j o i n t s C I soil, waste, Shouldered end pipes, Asbestos Cement Pipe 546 72 1 C I f i t t i n g s f o r A C pressure p i p e s waste and vent p i p e s a n d f i t t i n g s A C soil, 246 946 286 819 A A C C pressure pressure pipe pipes - constant - constant internal outside diameter diameter type type A C sewer p i p e s Concrete Pipe 676 677 975 902 R C pressure p i p e s Concrete non-pressure pipes Prestressed concrete pipes Structural pipelines design and i n s t a l l a t ion of precast concrete Glazed Earthenware Pipe 559 Glazed earthenware d r a i n a n d sewer pipes a n d f i t t i n g s P l a s t i c Pipe SABS 791 92 1 966 967 997 UPVC sewer a n d d r a i n p i p e f i t t i n g s P i t c h impregnated f i b r e pipes UPVC pressure p i p e UPVC s o i l , waste and vent pipes UPVC pressure p i p e s f o r i r r i g a t i o n I n s t a l l a t i o n of PE a n d UPVC p i p e s Black polyethylene p i p e s 01 12 533 Va I ves 144 191 C I s i n g l e door r e f l u x v a l v e s Cast steel g a t e v a l v e s 664 C I gate v a l v e s AMER I CAN WATER WORKS ASSOC I AT I O N A W W AC20 1 c202 C203 F a b r i c a t i n g e l e c t r i c a l l y welded steel water p i p e M i l l type steel water p i p e Coal-tar pipe enamel protective coatings for steel water C205 Cement mortar protective a n d over coatings for steel water p i p e of sizes 30" 247 C206 C207 C208 C300 F i e l d w e l d i n g o f steel water p i p e j o i n t s Steel p i p e f l a n g e s Dimensions f o r steel w a t e r p i p e f i t t i n g s R e i n f o r c e d c o n c r e t e w a t e r p i p e - Steel c y l i n d e r type C301 - not prestressed R e i n f o r c e d c o n c r e t e w a t e r p i p e - Steel c y l i n d e r t y p e - prestressed C302 R e i n f o r c e d c o n c r e t e w a t e r p i p e - Non-cyl i n d e r type - not prestressed C600 54 T C602 - I n s t a l l a t i o n of C I watermains Cement m o r t a r l i n i n g o f w a t e r p i p e l i n e s i n p l a c e ( 1 6" and o v e r ) AMER ICAN PETROLEUM INSTITUTE API Std.5A Std.5AC Std.5AX Std.5L Std.5LA Std.5LP Std. 5LR Spec. Spec. Spec. Spec. Spec. Spec. Spec. f o r Casing, T u b i n g and D r i l l P i p e f o r G r a d e C - 75 and C95 C a s i n g and T u b i n g f o r H i g h S t r e n g t h C a s i n g and T u b i n g for Line Pipe f o r S c h e d u l e 5 Alum. Alloy Line Pipe for Thermoplastic L i n e Pipe for Glass Fibre Reinforced Thermosetting Resin Line Pipe Std.5LS Std.5LX RP5C I RP5L I RP5L2 RP5L3 Bul.5C2 Spec. f o r S p i r a l Weld L i n e P i p e Spec f o r H i g h Test L i n e P i p e C a r e and Use o f C a s i n g , T u b i n g and D r i l l P i p e R a i l r o a d t r a n s p o r t of L i n e Pipe I n t e r n a l C o a t i n g of L i n e P i p e f o r Gas T r a n s m i s s i o n Conducting Drop Weight Tear Tests o n L i n e P i p e Performance Pipe Properties of Casing, Tubing and DrilI Bul.5T1 Non-destructive Testing Terminology 248 AMER I CAN SOC I ETY FOR TEST I NG MATER I ALS Concrete P i p e s ASTMC14 C76 Concrete Sewer, Storm D r a i n a n d C u l v e r t P i p e Reinforced Pipe C118 C361 C412 c443 Concrete P i p e f o r I r r i g a t i o n or Drainage Pressure Pipe Concrete Culvert, Storm Drain and Sewer R e i n f o r c e d Concrete Low-Head Concrete Cjrain T i l e Joints for Circular Concrete Sewer and Culvert Pipe w i t h Rubber gaskets c444 c497 P e r f o r a t e d Concrete P i p e Determining Physical Properties of Concrete Pipe or T i le C505 Non-reinforced Gasket J o i n t s C506 Reinforced Sewer P i p e C507 Reinforced Concrete El I i p t i c a l Culvert, Storm Drain Concrete Arch Culvert, Storm Drain and Concrete Irrigation Pipe and Rubber a n d Sewer P i p e C655 Reinforced Sewer P i p e Concrete D-load Culvert, Storm Drain and Steel P i p e s ASA 836.10 Steel p i p e s Cast i r o n Pipes A1 42 A377 A121.1 C C C I Pipes I pipes I pipes Asbestos Cement P i p e s C296 C500 C428 A C Pressure Pipes A C Pressure Pipes A C Pipes and Fittings for Sewerage and Drainage 249 Plastic Pipes D2241 U n p l a s t i c i s e d PVC p i p e s USDI BUREAU OF RECLAMATION S t a n d a r d Spec. f o r Reinforced Concrete P r e s s u r e P i p e 250 BOOKS FOR FURTHER READING Addison, London Albertson, H., 1964. A treatise on Applied Hydraulics, Chapman H a l l , M.L., Barton, J.R. and Simons, D.B., 1960. F l u i d Mech- a n i c s f o r E n g i n e e r s , P r e n t i c e - H a l I, American Pipe, Concrete Pipe 1960. 1970. Design Manual-Concrete Association, Arlington. Engs. and W a t e r Am.Soc.Civi I Pol In. Control Federation, M a n u a l 37, 1970. N.Y. Design and C o n s t r u c t i o n o f S a n i t a r y and Storm Sewers, Am.Water Works N.Y. 1963. Assn., 1964. Steel Pipe - Design and Installation, M a n u a l M11, Bell, H.S., (Ed.), Petroleum Transportation Handbook, McGraw H i l l , N.Y. Benedict, 531 pp. Bureau Criteria Of f i ce, Clarke, of for Public Roads, 1963. Reinforced Concrete U.S. Pipe Culverts R.P., 1977. F u n d a m e n t a l s of Pipe Flow, Wiley Interscience, - Structural DC. 1968. Design and Instal lation, Govt. Printing Was hi n g t o n , N.W.B., Buried Pipelines - A Manual of Structural D e s i g n a n d I n s t a l l a t i o n , M a c L a r e n and Sons, Colorado Proc. State Univ., 1971. Control of London. Flow in Closed Conduits, Inst., Fort Collins. and K i n g , Crocker, Hill. Davis, raulics, Holmes, S. R.C., 1967. P i p i n g Handbook, 5 t h Ed., McGraw C.V. and Sorensen, K.E., 1969. Handbook of Applied Hyd- 3 r d Ed., McGraw H i l l , N.Y. Handbook of Industrial Pipework Engineering, E., 1973. N.Y. Engs., McGraw H i l l , Instn. 4 t h Ed., Littleton, Martin, Nolte, cations, Rouse, Water 1969. Manual of British Water Engg. Practice, London. C.T., 1962. 1961. 1978. Industrial Piping, McGraw H i l l , 349 pp Pitman, London. Publi- W.L., C.B., H a n d b o o k of Optimum I n d u s t r i a l Pipework, Size Selection, Pipe Trans Tech 297 p p . H., 1961. Engineering Hydraulics, Wiley, N.Y. 251 Stephenson, Streeter, Hill, D., 1984. 1961. Pipeflow Analysis, (Ed), Handbook E l s e v i e r , 204 pp. of Fluid Dynamics, McGraw V.L., N.Y. A.C., Hoather, Twort, 2 n d Ed., Walski, R.C. and Law, F.M., 1974. Water Supply, A. A r n o l d , T.M., 1984. London. Analysis 275 pp. Design of of Water Distribution Systems. Van Nostrand Reinhold, Walton, N.Y. J.H., 1970. Structural Vitrified Clay Pipes, Clay P i p e Development Association, Watters, pipelines. Young, G.Z., 1984. London. and control of unsteady flow in Analysis 2 n d Ed. Butterworths. Trott, D.C. and J.J., 230 pp. 1984. Buried Rigid Pipes. Elsevier A p p l i e d Science, London, 252 APPEND I X SYMBOLS FOR P I P E F I T T I N G S GENERAL ELBOW SLEEVED TEE FILLET WELDEOTEE CROSS OVER BELLMOUTH TAPER JOINTS FLANGED ELECTRIULLY INSULATED FLEXIBLE SWIVEL 1 Jo. BEND JPtKETED FRONT VIEW OF TEE BACK VIEW OF TEE HANGER YMPLE SUPWRT CHANGE IN D I A --+_3_ A- 1 I I D E L E CT RICALLY BONDED BMT W E L D SCREWED SOCKET SPIGOT 0 SOCKET -4_f_ E X PANS ION S L E E V E COUPLING END CAP D VALVES __ EUl TERFLY ISOLATING WEDGE REFLUX ROTARY PLUG GATE NEEDLE GLOBE DIAPHRAGM RELIEF AIR MISCELLANEOUS HYDRANT FLOW INDICATOR SURFACE BOX DRAIN STRAINER SPRAY w VENT J-- --+ T t P L A T E BLIND HANDWHE E L + M 0 TOR 0 253 PROPERTIES OF P I P E SHAPES Ring AREA - F(D2-d2kTDt fa -11 I MOMENT OF INERTIA ABOUT DIAMETER = fi (0'- d') =TD" MOMENT O F INERTIA ABOUT CENTRE g ( D b - d L ) Z s D a t PROPERT I ES OF WATER Temperature C O Specific Mass kg/rn3 Kinematic Viscosity rn2/ s B u l k Modulus Vapour Pressure N/rnmz psi F" Ib/cu f t s q ft/sec N/rnm2 psi 0 1 0 32 1 000 1 000 62.4 62.4 62.3 62.2 1.79~10-~ 1 .93x 1 0-5 2 000 2 070 2 200 2 240 290 000 300 000 318 000 325 000 0.6~10-~ l.2~lO-~ 0.09 0.18 50 68 86 20 30 999 997 1 .31XI 0-6 6 1.01x100.81 x10-6 1.41~10-~ 1.09~10-~ 0.87~1 0-5 2 . 3 ~ 1 0 ~ ~ 0.34 3 0.62 4.3~10- PROPERTIES OF P I P E MATERIALS Coef. exp.per Clay Concrete Asbestos cernen t Cast Iron of O C Density kg/m' Modulus of elasticity N/mrn2 psi Y i e l d Stress N/rnrn2 psi Tensile Strength N/mm2 psi Poisson's ratio 5x10 6 2 600 2 500 14 000-40 000 24 000 100 000 210 000 2x106-6x106 3.5~10 6 15x10 -70 17 150 210 -10 1ox10-6 000 -2.1 -300 0.2 8 . 5 ~0-6 1 8 . 5 ~ 0-6 1 1 1 .9x10-6 6 2 500 22 000 30 000 225 330 23 000 48 000 7 800 7 850 0.25 0.3 M i l d Steet High Tensile Steel Pitch Fibre Polyethylene 3 1 ~ 1 0 ~ 1 1 .9x10-6 40x 1 0-6 1 60x 1 0-6 7 850 210 000 31x10 6 1 650 240 000 1730 250 000 900 138 20 000 3 400 14 2 000 Po I y e t h y l e n e (high density) PVC UPVC 2oox 1 o-6 50~10-~ 50~10-~ 1 8ox10-6 955 1 300 1 400 240 35 000 22 8 3 200 1 100 32 17 52 4 600 2 500 7 500 4 500 0.38 3 500 150 0.5~10 22 000 6 40 25 + 6 000 3 600 Po I y p r o p y I ene 91 2 30 256 CONVERSION FACTORS Length 1 i n c h = 25.4 mm 1 1 ft = 0.3048 m 644 mrn' 1 m i l e = 1.61 k m Area sq i n c h = 1 a c r e = 2.47 ha 1 sq ft 1 ha Vol ume = = 0.0929 mz mz = lo4 35.31 c u f t 1 US g a l . = = 1 m3 = 1 gal.(imperial) 4.54 I i t r e s = 3.79 I i t r e s 42 US gal. 35 i m p . g a l . 1 = barrel 159 I i t r e s = Speed 1 ft/sec 0.3048 m/s = 1 m p h = 1.61 k m / h r . Acceleration Discharge 32.2 f t / s e c 2 35.3 c u s e c 0 9 1 m/s' .8 = = g 1 mgd (imperial) = 1.86 cusec im3/s 13.2 g p m ( i m p e r i a l ) = 1 P / s Mass 1 I b = 0.454 k g 32.2 I b = 1 s l u g (US) 1 Ib. f o r c e = 4.45 N ( 1 Newton = Force 1 k g x 9.81 m / s ' ) = Pressure 145 p s i = 1 MPa 14.5 p s i = 1 b a r 778 f t 16. = 1 B t u 1 Btu 550 f t = 1 MN/m2 = 1 N/mmz Energy 252 c a l o r i e s 1 HP 1 c a l o r i e = 4.18 J o u l e s Power Ib/sec = 1 HP = 0.746 kW Kinematic Viscosity 1 sq ft/sec = = 929 s t o k e s 0.0929 m z / s Absolute o r dynamic viscosity Temperature 1 centipoise = 0 0 1 kg/ms .0 F o = 32 + 1.8C" 257 A b s o l Ute temperature R " (Ranki ne) A b s o l Ute temperature KO (Kelvin) 71 = FO(Fahrenheit1 + 460 = Co(Centigrade) + 273 = 3.14159 = e 2.71828 258 AUTHOR INDEX Abrarnov, N. 15 A d d i s o n , H. 228, 241, 250 A l b e r t s o n , M . L . 17, 35, 250 A n d e r s o n , O.A. 125 A v e r y , S.J. 105, 110 B a l l , J.W. 28, 35 B a r n a r d , R.E. 149, 157 B a r t o n , J.R. 17, 35 B e l l , H.S. 250 B e n e d i c t , R.P. 250 B e r n o u l I i , 16 B e r t h o u e x , P.M. 10, 15 B l i s s , R.H. 101, 111 B o u c h e r , P . L . 182 203 B u r a s , N. 49, 57 C a p p e r , P . L . 123, 125, 191, 203 C a s s i e , W.E. 123, 125, 191, 203 C a t e s , W.H. 176, 77, 216, 226 C h a p t o n , H.J. 177 C h e z y , 18 C l a r k e , N.W.B. 113, 125, 250 Cole, E.S. 218, 226 Col e b r o o k , 23 C r o c k e r , S. 173, 177, 250 Cross, H. 38,57 D a n t z i g , G.B. 51, 57 D a r c y , 21 D a v i s , C.V. 250 D e n n y , 9 . F . 101, 110 D i s k i n , M.H. 24, 35 D v i r , Y . 30, 35 Ervine, D.A. 105, 110 J a c o b s o n , S. 155, Johnson, S.P. 95 60 Joukowsky 157 , K a l i n s k e , A . A . 102, 104, K a l l y , E. 48, 57 K a r r a s s i k , I.J. 228, 240 K e n n e d y , H. 121, 125 K e n n e d y , J.F. 74, 95 K e n n i s o n , H.F. 129, 140 K i n g , C.L. 177 K i n g , R.C. 173, 177 K i n n o , H. 74,95 K n a p p , R. 28, 35 K o v a t s , A . 228, 241 L a i , C . 66, 95 L a m , C.F. 56, 57 L a w , F.M. 240, 250 L e s c o v i c h , J.E. 186, 203 L i t t l e t o n , C.J. 250 L u d w i g , H. 68, 95 L u p t o n , H.R. 64, 95 111 M a n n i n g , 18 M a r k s , L.S. 107, 1 1 1 Marston, A. 114, 125 M a r t i n , W . L . 250 M i l l s , K.G. 32, 43, 57 Moody, 21 M o r l e y , A . 154, 157 M o r r i s o n , E.B. 190, 203 N e l s o n , E.D. 177 N e w m a r k , 122 Newton, 16, 58 N i k u r a d s e , 21 N o l t e , C.B. 250 Osborne, J.M. 7, 15 108, 111, F o x , J.A. 109, 110 F e r g u s o n , P.M. 137, 140 110 Glass, W.L. G o o d i e r , J.N. 177 G r i s t , E . 232, 240 H a s s a n , D . R . 165, 177 Hazen-VJ i I I i ams , 18 H o a t h e r , R.C. 240, 250 Holmes, E. 250 Isaacs, L.T. P a r m a k i a n , J. 73, 95, 186, 203 P e a r s o n , F.H. 177 P a u l , L. 182, 203 P o i s s o n , 176, 195 P r o c t o r , 150 P r o s s o r , 1vl.J. 101, 111 R e i t z , H.M. 208, 226 43, 57 259 R e y n o l d s , 20 R e y n o l d s , G.M. 211, 226 R i c h , G.R. 78, 95 R i d d i c k , T.M. 224, 226 R o a r k , R.J. 174, 177 R o b e r t s o n , J.M. 104, 111 Rouse, H. 166, 177, 250 S c h a r e r , H. 176, 177 S c h l i c h t i n g , H. 20, 35 S c h n e i d e r , W.R. 219, 226 S c h w a r t z , H . I . 211, 226 S c h w e i g , 2. 48, 57 Sirnons, D.B. 17, 250 Sorenson, K.E. 250 Sowers, G.F. 208, 226 S p a n g l e r , M.G. 113, 125, 146, 152, 157 S t e p a n o f f , A.J. 228, 241 Stephenson, D. 56, 57, 69, 80, 9 5 , 110, 1 1 1 , 151 157, 165, 177, 25 1 S t r e e t e r , V.L. 66, 95, 251 Suss, A. 165, 177 Swanson, H.S. 162, 177 Sweeton, A.E. 186, 203 TSSYJ, Tirnoshenko, S . P . 134, 140, 158, T r o t t , J.J. 113, 125, 251 T u l l i s , J.P. 35 T w o r t , A.C. 240 Uhlig, H.H. 218, B. 226 51, 57 160, 177 Van d e r Veen, W a l s k i , T.M. 251 Walton, J.H. 250 Watson, M.D. 24, 35 W a t t e r s , G.Z. 251 Webber, N.B. 229, 241 Weisbach, 21, 109 W h i t e , 23 W h i t e , J.E. 9, 15 W i l k i n s o n , W.J. 177 W i n n , W.P. 33, 35 W i s n e r , P. 102, 111 W o i n o w s k i - K r i e g e r , S. 134, Wood, D.J. 43, 57 W y l i e , E.B. 66, 95 Young, Young, D.C. 113, 125, 251 G.A.J. 101, 110 140, 157 260 SUBJECT INDEX A b s o r p t i o n 99 A c t i v e s o i l p r e s s u r e 114, 149, 191 A c t u a t o r 92, 185 A d i a b a t i c 86, 107 Aesthetics 2 A i r pocket 89, 100 v a l v e s 106, 189 vessel 87 American Concrete P i p e Assn. 122, 125, 140 Anode, s a c r i f i c i a l 219 A p p u r t e n a n c e s 182 Asbestos cement 180 A x i a l e x p a n s i o n 176, 195 B a c k f i l l 113, 192 B a r g e , 211 Beam 213 B e a r i n g t e s t 128 B e d d i n g 115. 127 B e d d i n g f a c t o r 128, 207 Bend loss 27 meter 200 s t r e s s 173 B e n d i n g 144, 196, 213 B i n a r y n u m b e r 202 B i t u m e n 217 B o n i n g 206 B o u n d a r y l a y e r 22 B r a c i n g 161 B r a n c h 62, 68, 161 B r i d g e 208 B u b b l e 99 Buck1 i n g 152, 168 B u t t e r f l y v a l v e 27, 32, 184 B y p a s s 76, 79, 182 Cant i l e v e r 174 Capacity factor 4 Cash f l o w 1 1 C a s i n g 217 Cast i r o n 180 C a t h o d i c p r o t e c t i o n 218 C a v i t a t i o n 30, 97 C e l e r i t y 60 C e n t r i f u g a l f l o w 200 f o r c e 190 pump 229 C h a r a c t e r i s t i c method 66 pump 70, 73, 229 Chemicals 1 C l R l A 152 Clamp 212 C l a y 255 C o a t i n g , bi tumen 21 6 c o a l t a r 217 epoxy 217 g l a s s f i b r e 217 m o r t a r 23, 217 t a p e 217 Cohesion 191 Col l a p s e 148 C o l l a r 143, 161 Concrete p i p e s 127, 180 p r e s t r e s s e d - 129 180 p r o p e r t i e s 137, 255 Compound p i p e s 37 Compressibi I i t y 16, 60 Computers, a n a l o g u e 202 d i g i t a l 41, 202 Concrete P i p e Ass. 122, 125 C o n d u c t i v i t y 219, 223 Conductor 219 Cone v a l v e 30, 184 Consol i d a t i o n 149 C o n s t r a i n t 52 Container 2 C o n t r a c t i o n c o e f f i c i e n t 200 Convect i o n 224 Conversion f a c t o r s 256 Core 129 C o r r o s i o n , g a l v a n i c 218 Cost, p i p e 3 power 4, 12 p u m p i n g 4, 8 C o u n t e r b a l a n c e 186 C o u p l i n g 230 C r a c k 127 Creep 130 Cross section 253 C r o t c h p l a t e 161 C r u s h i n g 137 Current, electric219 impressed21 9 stray220 C y l i n d e r 129 D e f l e c t i o n 146, 150 Design f a c t o r 142 O i ameter 4 261 D i s c h a r g e c o e f f i c i e n t 200 t a n k 79 Discount r a t e 9 D i s s o l v e 99 D r a i n 207 D y n a m i c p r o g r a m m i n g 45 Economics 2 E l a s t i c i t y 64, 255 E l e c t r o d e 220 E I ec tro-chemi c a l e q u i v a l e n t 220 E l e c t r o l y t e 218 E l e c t r o m a g n e t i c i n d u c t i o n 201 El l i p s e 253 Embankment 1 1 6 Ernrnissivity 224 E m p i r i c a l 18 E n e r g y 16 E n t r a n c e l o s s 27 Epoxy 217 E q u i v a l e n t d i a m e t e r 37 Escher Wyss 177 E x c a v a t i o n 206 E x t e r n a l l o a d 115, 146 F a b r i c a t e d b e n d 194 F a c t o r o f s a f e t y 143 F i e l d p r e s s u r e 133 F l a n g e 212 b l a n k 216 p u d d l e 216 F l e x i b l e p i p e 142 F l o a t i n g 210 F i t t i n g s 182 Flow measurement 198 b e n d meter 200 e l e c t r o m a g n e t i c 201 mass 201 m e c h a n i c a l 200 n o z z l e 199 o r i f i c e 199 v e n t u r i 198 volume 202 Flow r e v e r s a l 75, 91 F l y w h e e l 76 F r i c t i o n 18, 68, 74 F r o u d e n u m b e r 104 G a l v a n i c a c t i o n 218 Gasket 215 Gate v a l v e 182 Globe v a l v e 184 G r a p h i c a l a n a l y s i s 14, 65 H a u n c h 128, 148 Head, loss 16, 37, 199, 232 v e l o c i t y - 16, 232 w a t e r hammer- 62 H e a d i n g 208 Heat loss 224 History 1 Hole 161 Hol i d a y d e t e c t o r 21 7 H y d r a u l i c g r a d i e n t 18, 68, 238 H y d r a u l i c j u m p 104 I m p a c t f a c t o r 121 I m p e l l e r 229 I n e r t i a 73, 94 I n f l u e n c e c o e f f i c i e n t 122 I n s u l a t ion, t herrna I 224 I n t e r e s t 10 I sotherrnal 86 J o i n t , b u t t - w e l d e d 212 clamp-on 214 f a c t o r 142 f l a n g e d 215 screwed 213 sleeve w e l d e d 212 s p i g o t a n d socket 130, 214 K i n e t i c e n e r g y 72 L a g g i n g 224 L a m i n a r f l o w 20 L a t e r a l s u p p o r t 149 L a y i n g 205 L i n e l o a d 122 L i n e a r p r o g r a m m i n g 52 L i n i n g , b i t u m e n 217 c o a l t a r 217 epoxy 218 m o r t a r 21 8 L i v e l o a d 120 L o a d c o e f f i c i e n t 114 soi I 113 superimposed 120 Longitudinal stress 21 3 Loop 38 Loss c o e f f i c i e n t 27 Losses 26 Mass, c o n s e r v a t i o n of 16 M a t e r i a l s 255 M e c h a n i c a l meter 200 134, 198, 262 Membrane t h e o r y 167 Meter b e n d 200 rnkchan i c a l 200 n o z z l e 199 o r i f i c e 199 r o t 0 200 v a n e 200 v e n t u r i 198 Model 165 M o d u l u s of e l a s t i c i t y 137, 255 M o d u l u s of s u b q r a d e r e a c t i o n 124 Mohr d i a g r a m 136 Momentum 16, 90 Motor 239 Needle v a l v e 91, 184 Network 38 Net p o s i t i v e s u c t i o n h e a d 232 Node 39 Non-l i n e a r p r o g r a m m i n g 56 Normal t h r u s t 190 Nozzle 199 O b j e c t i v e f u n c t i o n 56 Ohm 219 Oil 1 Operating factor 4 O p t i m i z a t i o n 8, 45 O r i f i c e 86, 199 P a r t l y f u l l p i p e 100 P a s s i v e s o i l p r e s s u r e 191 Pavement 123 P e r i m e t e r , w e t t e d 102 P i p e , asbestos cement 180, 255 c a s t i r o n 179, 255 c o n c r e t e 180, 255 p l a s t i c 180, 255 p o l y e t h y l e n e 180, 255 PVC 180, 255 p r o p e r t i e s , 255 s a l t g a l v a n i z e d c l a y w a r e 255 steel 179, 255 UPVC 180, 255 Planning 1 P l a s t i c 180 P o i n t l o a d 121 P o i s s o n ' s r a t i o 144, 195, 255 P o l a r i z a t i o n 218 P o l y e t h y l e n e 180, 255 P o t e n t i a l e n e r g y 90 Power 236 Present v a l u e 10 P r e s s u r e , e x t e r n a l 110, 146 i n t e r n a l 142 w a t e r hammer 58 P r e s t r e s s e d c o n c r e t e p i p e 129 P r o c t o r d e n s i t y 150, 207 Profile, pipeline 72, 106, 238 P r o t e c t i o n , c a t h o d i c 218 w a t e r hammer 69 P u d d l e f l a n g e 216 Pump, b o o s t e r 2, 9 c e n t r i f u g a l 75, 229 i n e r t i a 73 power 5 t y p e s 228 P u m p i n g c o s t s 3, 12 R a d i a l s t r e s s 142 R a d i a t i o n 224 R a d i o 202 R a d i u s o f s t i f f n e s s 124 Rail 1 Reducer 169 R e f l u x v a l v e 71, 81, 186 R e i n f o r c e d c o n c r e t e 1 , 127 R e i n f o r c i n g 127, 143, 162 R e l a x a t i o n o f s t r e s s 131 Release v a l v e 91, 184 R e s e r v o i r 14 R e s i s t i v i t y 219 R e t i c u l a t i o n n e t w o r k 37 R e y n o l d ' s n u m b e r 20 R i b b e d p i p e 154 R i g i d pavement 123 p i p e 113 R i n g g i r d e r 175 l o a d 149 s t i f f e n i n g 154 s t r e s s 142 t e n s i o n 142 Road 1 Roughness 21 Route 205 S a c r i f i c i a l anode 219 S a d d l e 174 S a l t g l a z e d 255 S a n d 192 Scale 6 S c o u r i n g 210 Screwed j o i n t 213 Sea 210 205, 263 Secondary s t r e s s 160 S e c t i o n m o d u l u s 174 S e r v i c e s 205 Settlement 118 Shape 253 S h r i n k a g e 135 S i n k i n g fund 9 S l u i c e v a l v e s 182 Snake 206 Socket j o i n t 130, 214 S o i l l o a d 115, 146 m e c h a n i c s 193, 208 p r o p e r t i e s 113, 192 Span 213 S p e c i f i c mass 254 S p e c i f i c speed 223 S p h e r i c a l v a l v e 185 S p i n d l e 182 S t a n d a r d s 242 S t a r t e r s 239 Steady f l o w 16 Steel, high t e n s i l e 136, 255 p i p e 180 p r e s t r e s s i n g 136 p r o p e r t i e s 255 S t i f f e n i n g r i n g s 154 S t r a y c u r r e n t e l e c t r o l y s i s 219 S t r e n g t h , l a b o r a t o r y 137 Stress, b e n d i n g 196, 213 S t r e s s , c i r c u m f e r e n t i a l 133, 142 Stress, l o n g i t u d i n a l - 134, 198, 213 t e m p e r a t u r e - 21 5 S t r u t t i n g 149, 154 S u l z e r 177 Superimposed l o a d 120 S u p p o r t 128, 148, 194 S u r f a c e l o a d 120 S u r g e 58 - t a n k 77 Symbols 252 Systems a n a l y s i s 44 Te I erne t r y 202 T e m p e r a t u r e 195, 215 T e n s i o n r i n g s 143 T e s t i n g 206 T h e r m a l i n s u l a t i o n 224 T h e r m o p l a s t i c 180 T h i c k n e s s 142, 162, 224 T h r o t t l i n g 28, 184 T h r u s t b l o c k 192 b o r e 208 T i e b o l t 214 T o r q u e 235 T o w i n g 210 T r a f f i c l o a d 121 T r a n s i e n t p r e s s u r e s 60 Transport and Roads Laboratory 152 Transportation, a i r 1 p r o g r a m m i n g 45 rail 1 road 1 waterway 1 T r e n c h 113, 206 T u r b i n e 77 Uncertainty 1 1 U n d e r w a t e r l a y i n g 210 U n i f o r m l o a d 122 Unp I a s t i c i z e d p o l y v i n y Ic h l o r i d e 180, 255 Vacuum 97, 153 V a l v e , a i r r e l e a s e 106, 188 a i r v e n t 186 b u t t e r f l y 183 cone 184 c o n t r o l 29, 184 g l o b e 184 n e e d l e 184 r e f l u x 71, 81, 186 r e l e a s e 91, 184 s p h e r i c a l 185 s l e e v e 185 s l u i c e 182 Vane, g u i d e 165 V a p o r i z a t i o n 90, 97, 153 V e l o c i t y 16, 58, 199 V e n t u r i m e t e r 198 V i c t a u l ic coup1 i n g 194 V i k i n g l o h n s o n c o u p l i n g 194 V i s c o s i t y 23, 255 V o l u t e 229 V o r t e x 89 W a l l t h i c k n e s s 142, 162, 224 Water hammer 60 p r o p e r t i e s 254 s u p p l y 14 Wave 60 Web 162 W e l d i n g 212 'Wetted p e r i m e t e r 148 W r a p p i n g 216 X-ray 217 Research Y i e l d s t r e s s 152, 255 This Page Intentionally Left Blank