How t h e S y s t e m WorksInput: Maintenance D e p a r t m e n t . . . . . . . Maintenance r e q u i r e m e n t s Job r e q u e s t s Failure reasons Labor estimates Material estimates Job p r i o r i t i e s Jobs completed 7' I output: Maintenance D e p a r t m e n t Visual Display Station (% i f 9 1 Optional . . . . . . . . Equipment s p e c i f i c a t i o n s Maintenance r e q u i r e m e n t s Job r e q u e s t s and e s t i m a t e s Work s c h e d u l e s and backlogs P a r t s availability Maintenance c o s t r e p o r t s Equipment h i s t o r x Special reports copies Acknowledgements The successful implementation of SMAP would not have been possible without the support and efforts of the Utah Copper Division Smelter Maintenance Department and Plant Management. The financial support and confidence of Utah Copper Division and Kennecott's Metal Mining Division management also contributed to the successful implementation of SMAP. A New Launder Design Procedure H. R. Green, D. M. Lamb, and A. D. Taylor Introduction The design of slurry launders has usually been based on strictly empirical concepts. An examination of the most common procedures reveals that they do not account for many of the variables that are recognized as significant for slurry transport. These may include flow rate, volume concentration of solids, solids specific gravity, solids size distribution, particle shape, launder geometry, and roughnes of the wetted surface. It was decided to develop a design procedure, which would accomplish two things: First: Take into consideration most of the known significant variables and systematize the procedure to assure consistent results. Second: Provide a rational basis for examining and utilizing operating data to refine and improve the system. To accomplish this, it was necessary to develop a basic design concept. This concept has been developed through a complex development history, and yet still appears workable and technically sound. That concept may be outlined as follows: First: The solids transport velocity is the fundamental basis for slurry launder design. Second: The stream configuration, hence the launder size, is integrated with the solids transport velocity so that the actual stream velocity exceeds the solids transport velocity. Third: The launder slope is that which will achieve the 1310 AUGUST 1978 SOCIETY OF February 1978. for various launder surfaces was derived from a family of curves published by the U. The above equation was solved for "k" and a tabulation of " k" values for various "n" and "R" values was produced on the HP9820A calculator. Lamb. San Francisco. The equation as H. D. It was then decided to revise the entire approach. Army Engineers in 1964. The equations used are shown in Table 1. is Chief Metallurgical Engineer. 1 and are used to determine the apparent viscosity of the slurry. Discussion of this paper must be submitted. also. It was planned to utilize a "slope adjustment factor" to increase the slope to compensate for the apparent viscosity of the slurry. The necessity of reference to the Moody curves for the Darcy friction factor is avoided by using the Colebrook and white3 equation. Dean. Preprint 78816. R = Hydraulic radius. 1978. This adjusted curve was assumed to apply to suspensions having panicles averaging 320 micrometers (50% wt. The camp2 equation is used for the solids transport velocity. The shape of this curve was similar to Thomas's but exhibited a steeper slope as the concentration increased. in duplicate. the present procedure is based on the DarcyWeisbach flow equation.. S. Mathematics The discussion which follows concerns the mathematical basis of the launder design procedure for pipe.183 m would apply to launder sizes most likely to be encountered. Taylor. Published "n" values for various types of surfaces and the derived n-k correlation resulted in the approximate "k" values shown in Table 3. CA. The intermediate curves were developed as a function of the ratio of increased particle surface area as the particles became smaller. A. Many papers have been published regarding the apparent viscosity of solid-liquid suspensions. The experimental data which formed the basis of these papers exhibit considerable scatter even though the experiments were carefully conducted. the symbols and units in Table 2. R. The mathematical treatment employed in this correlation reduced the scatter considerablv and minimized the effect of particle size and shape. Member SME. D. D. Manuscript. A nomograph. k = Effective roughness. which is rationally preferable to the Manning equation. Member SME. feet. and ~ 0 1 1 0 ~ 5 produced curves for other particle sizes. and Ushaped launders. feet. Errors introduced by this assumption are minimal. ~ h o m a s 4 correlated data from a large number of investigators. Effective roughness values. The apparent viscosity-volume concentration curve resulting from Thomas's work is used by many designers of slurry pipe lines where the particle size distribution is controlled. It was originally planned to utilize a series of charts and nomographs for the design procedure. An apparent viscosity-volume concentration curve for suspensions of 20 micrometer panicles was produced from unpublished data. Member SME. Bechtel Corporation. AlME Annual Meeting. Further data from a USBM paper by Schack.l was developed to determine the solids transport velocity. 1977. November 3. This failure was principally due to the complex relationship of viscosity to the required slope.6 The mathematical relationship given in the above paper is as follows: n = Manning roughness coefficient. The solids t r a n s y t velocity E q 1 was derived from an equation by Camp. A family of curves between the adjusted Thomas curve for 320 micrometer particles and the curve for 20 micrometer particles was then constructed. rectangular. CO. is Engineering Specialist. based on data given in Taggart's Handbook of Mineral Dressing. prior to November 30. this material has been assessed a page charge and is considered advertisement for postal purposes. Specifically. is Engineering Supervisor. passing). It is assumed an average hydraulic radius of 0. G. These curves are shown in the Fig. Camp's equation was for the self-cleaning or sediment transport velocity in sewers. Flgure I APPARENT VISCOSITY OF SLURRY MINING ENGINEERS MINING ENGINEERING 121 1 . Denver. Table 3. Green. The resulting mathematics require iterative solutions for several of the unknowns. For any particular hydraulic radius a correlation exists between the Manning "n" and the roughness value "k". These. the Thomas curve was adjusted to accelerate the slope increase as the solids concentration becomes greater.required actual stream velocity. All attempts to develop a suitable correction factor failed. The velocity thus determined was used with Manning charts to determine the launder slope and configuration as though the fluid were water. On the basis of these data and from examination of several other curves for apparent viscosity of solid-liquid suspensions. M. In accordance with the Postal Service Regulations. had slopes steeper than the Thomas curve in the high concentration region. and when less than one it is subcritical flow. The Darcy-Weisbach flow equation is usually stated: h = @ C ! D2g in consistent units h = Head low.5 Pipe Rectangular U-Shaped. and U-Shaped Equation -- 2 3 4 5 6 7 8 9 10 11 12 m m m 13 14 15 m - mlm 16 17 18 mls 1212 AUGUST 1978 SOCIETY OF . The mean hydraulic depth is equal to the area of the stream cross-section divided by the width at the water surface. L = Pipe length.originally expressed by Camp was as follows: V = Velocity. are derived directly from the Darcy-Weisbach flow formula. Rectangular. f = Darcy friction factor. 15. n S 0. the calculated velocity is that which will achieve adequate self-cleaning in sewers. Hydraulic radius. For more efficient use of programmed calculators and computers. The mean hydraulic depth. the flow is said to be supercritical. f = Darcy friction factor. is developed from the stream geometry and the definition of hydraulic radius. V = Flow velocity: g = Acceleration of gravity. Launders should never be designed with Froude numbers near one.5 U-Shaped. When constant "B" is 0 . when equal to one it is critical. ft/sec. g = Acceleration of gravity.. 16 and 18. and U-Shaped Pipe.5 Pipe Rectangular U-Shaped. and U-Shaped Pipe. respectively. Rectangular. n> 0. ft/sec. Rectangular. Rectangular. Eq. 8 as the particle motion constant. When flow velocities are close to the wave velocity. The solids transport velocity in this paper uses 0 . Moody.5 U-Shaped. Eq. n S 0. Rectangular and U-shaped Pipe Rectangular U-Shaped. 14. Eq. n S 0. the calculated velocity is that which will start motion of the particles. n> 0. 10 through 13. Rectangular. Camp stated that. L. TABLE 1 EQUATIONS Equation Number 1 Description Solids Transport Velocity Continuity Velocity Continuity Velocity Continuity Velocity Continuity Velocity Hydraulic Radius Hydraulic Radius Hydraulic Radius Hydraulic Radius Mean Hydraulic Depth Mean Hydraulic Depth Mean Hydraulic Depth Mean Hydraulic Depth Froude Number Darcy Friction Factor Launder Slope Reynolds Number Velocity as a function of R. the Colebrook and White equation. 8 . The Darcy-Weisbach friction factor is usually determined by reference to a family of curves based on the work of F. dimensionless. dimensionless. feet. n> 0. D = Pipe diameter. and U-Shaped Pipe. Slope and velocity.2 S = Specific gravity of particles. Dg = Particle diameter. 2 through 5. L f & & I mls mls mls mls mls m m m m Launder S h a ~ Pipe. is the ratio of the flow velocity to the velocity of elementary free-surface waves. The Froude number. when constant "B" is 0. is used to calculate the Darcy friction factor. The equations listed are derived from the stream geometry and the definition of mean hydraulic depth. S. Eq. 6 through 9.5 U-Shaped. Eq. When the Froude number is greater than one.5 Pipe. is used to calculate the Froude number. Four times the hydraulic radius is substituted for diameter to adapt the equation to open-channel flow. Eq.04. disturbances can cause extreme wave action and large variations of flow depth. is derived from the fundamental continuity equation Q = VA and the geometry of the stream crow section. dimensionless. Continuity velocity. B = Particle motion constant. and U-Shaped Pipe. no finish Float finish Trowel finish Pre-cast. it is reasonable to expect that the hydraulic transport of solids in launders would be subject to more uncertainties than in pipes flowing full under pressure.Reynolds number. the effect of varying flow rates in the now-fixed launder can be evaluated. uncoated Concrete construction: Formed only. TABLE 3 AVERAGE EFFECTIVE ROUGHNESS Launder Material Concrete pipe: Lined Unlined Asbestos-cement pipe Clay drain tile.000728 TABLE 2 NOMENCLATURE Wood stave pipe Steel pipe: Plain Rubber lined Plastic lined Plastic pipe: Welded joints Flanged or coupled joints Fibreglass pipe (FRP). This one.5.8 and 1.002292 . and physical dimensions may satisfy the requirements of a particular problem. Meters . In launder design. For each flow rate entered a new set of flow data is generated. it is appropriate to consider the limitations of such a basis.001350 . This is done by entering the desired flow rates in the calculations. This design system permits the evaluation of the flow data associated with the individual variation of physical dimensions and flow rate. The mathematical basis and the design procedure apply only to uniform flow sufficiently remote from junction boxes. unlined Rolled sections. plain Vitrified clay tile k. The calculation system does not apply to solid-liquid suspensions with solids concentration and particle size such that the slurry exhibits plastic or thixotropic characteristics.. The variety of conditions encountered in open-channel flow is greater than in pipe flow both because of the existence of the free surface and the alternative stages of flow having equal energy. Because of this. there is no absolute single answer. is stated in one of its many familiar forms. After a satisfactory set of flow data is obtained by entering new dimensions. with its free surface.quirements will assure adequate turbulence and avoid the unstable flow conditions associated with near critical flow. These re. feed points. 17. the slope is adjusted to conform to construction tolerance. Following a satisfactory slope selection. The formulae are stated in forms which apply to openchannel flow of liquids.15 times the solids transport velocity. as in many fluid flow problems.8 mls2) Effective roughness of launder surface Flow depth to launder diameter ratio Flow rate Reynolds' number Hydraulic radius Launder slope Specificgravity of pulp Specificgravity of solids Apparent viscosity of pulp Flow velocity as a Function of R. substitutes 4 times the hydraulic radius for diameter. flow depth to diameter ratio. An initial set of flow and launder size data is calculated from usually available information concerning the launder performance requirements. unlined Rubber lined Plastic lined Plastic construction. Many combinations of slope.001350 . It is assumed that the slumes behave essentially as true liquids. Eq. velocity. Entry of a new slope generates anew set of flow data. The nature of open-channel flow. S. This launder design system specifies that the Reynolds number must be greater than 5000 and that the Froude number must not be between 0.001350 . Entry of this new dimension creates a new set of flow data for analysis.000728 Description rad m m m Arc Cosine Launder diameter Particle diameter Mean hydraulic depth o flow f Froude number Darey-Weisbach friction factor Acceleration of gravity (9. extends the conditions that will satisfy a particular problem over that of pipes flowing full under pressure. The adjustment of diameter. Procedure The initial launder size is calculated so that the continuity (design) velocity is 1. This 15% safety margin is estimated to cover input data inaccuracies and launder construction variation. For pipe launders the flow-depth-to-diameter ratio must be less than one.flanged or coupled Cast iron pipe. & f Continuity velocity Solids transport velocity Launder width meter second pascal radian new ton - rad N MINING ENGINEERS MiNlNG ENGINEERING 1213 . Discussion Having selected the mathematical basis for the flow calculations.000728 . free formed . and other transitions to produce equilibrium conditions. rough joints Wood construction: Smooth planed surface Rough surface Steel construction: Welded sections. This initial set of data is used as a reference or starting point for the eventual design. Based on the initial set of data. the calculated launder size is then adjusted to dimensions consistent with construction tolerance and practice. again. 47 5.-------. 12. 11.-------...76 8.600 .. 11.TOR 1 0 . depending on launder 12.723+06 ... Step 7 is omitted.78 15. 6. SLOPE ADJUSTUENT FLOW RATE ADJ.a251 . can be done in any order desired but the sequence noted is the usual one.57 5.58 5. if not. 18).470+06 . 14..40 9.675+06 ...IFT..549+06 .. F t E T SOLIDS PARTICLF S I Z E . 14).58 1.440 . Calculate hydraulic radius (Eq.15 times the solids transport velocity. or 9.55 5. 7.. Calculate mean hydraulic depth (Eq..37 1. 5. 17). Design summaries of a typical problem for pipe.397 .58 1.58 5. 3. DATA IDENTIFICATION 14 15 and slope may be used to bring the Reynolds and Froude numbers to the desired values.01 1.------. Calculate hydraulic radius (Eq.64 5.600 . or 13. 10500. 1 . All values based on the slope adjustment have now been determined. If the continuity velocity is not equal to 1. 17).54 1. the calculation sequence noted for slope adjustment is used.627+06 . 8400. and rectangular launders are reproduced as Tables 4.. depending on launder geometry). 11.64 5.I563 . ..00 SLOPE IN...I250 . go to step 8.626+06 .65 7. RECHTFL COPPUKATIOR-YININC AND IIETALS DIVISIOII SLURRY LAUNDER DESICN PROCRAI! I?.70 1. 5.l-C-T..42 1. 6. PLOW RATE ADJ.73 6. Solve Eq.DLlL APPLICATION: TAILING LAlfNDBR . 7.-----.06 8.61 8.. 8. Usually any adjustment that will result in a higher flow velocity will also result in larger Reynolds and Froude numbers.00 28.. SOCIETY OF .20 1. 11.-------.63 1. SLOPE ADJCSTUENT FLOW RATE ADJ. and Darcy friction factor (Eq. 15 for "f". 6300. by trial and error. 14).94 8.49 1. 4. FLOW RATE ADJ. assign a new value to the flowdepth-to-launder diameter ratio and repeat steps 3 through 7.37 1.I563 . 8.0221 ..0233 ..a613 .62 11. HICRONS ' 9 9 % PASSING $02 P .91 9. The new diameter and flow-depth-to-launder diameter ratio is used in calculations 2 through 6 and 8 through 10 in the same manner as for the initial calculations. FLOW RATE ADJ. go to step 11.... LlSGPll *FLOW DEPTH TO LAUNDER DIAMETER RATIO *EFFECTIVE ROUGHNESS OF LAUNDER.719+06 ..413 . Calculate Darcy friction factor (Eq..00 30.486 ...34 ITEM -------.527+06 .331 19.00 28.558 ./SEC FLOW DEPTH TO DIAUETER RATIO DEPTH OF FLOW INCHES REYNOLDS NUUBER DARCY FRICTION FACTOR FROUDE NUIIBER DESlGN RISK DESIGN DATA ---. 8.57 16... and 6.69 5.49 1. Calculate the mean hydraulic depth (Eq.. 6.. 10500. Calculate launder slope (Eq. 7. DIAU 6 DEPTH ADJ.a227 .61 5.L67 . The slope is specified and the flow-depth-to-launder diameter ratio is calculated. 2. Calculate continuity velocity (Eq. 13.0228 .61 2 . 10500. 6. If the continuity velocity equals 1.752+06 .EXPANSIOU Z . Calculate solids transport velocity (Eq....00 28..54 1.525+06 . The calculation sequence for the initial launder size and flow data is: 1.43 7. 4200.2278 . PROJECT : X Y ..I250 . 1 1.00 16..l.00 28. Assume launder diameter. friction factor. If the continuity velocity equals the velocity calculated in step 6. In this sequence of calculations the launder size and flow rate are fixed. 1). 8400.I250 . Calculate Froude number (Eq. 8400.lSEC.00 28.654+06 .I250 .75 1..0242 ...631+06 . FLOW RATE ADJ. 4200. 15) by trial and error. The diameter and slope are held constant and the desired flow rate is assigned as step 1. 4.CENTIPOISES *PRII!ARY INPUT FOR DESICN CALCULATIONS ----------FLOW BATE USGPU LAUNDER DIAUETER INCHES 32.I19 .75 8... PRIMARY INPUT DATA -----------------*LAUNDER SHAPE *FLOW RATE. Calculate the Froude number (Eq. or 13. 10. 6300 4200... dependingon launder geometry).97 7.-----.. 10.a230 ..54 9.... 2.417+06 .520 ..00 28.a254 1. 9.I250 -1250 ..I563 DESIGN VELOCITY FT.00 28.00 30... If the value of the Darcy friction factor assumed in step 6 equals the friction factor calculated in step 9.. 3.67 6. FLOW RATE ADJ.00 28.300 .. 2. Calculate the Reynolds number (Eq. Calculate velocity as a function of hydraulic radius..32 7.. These summaries were produced using Bechtel's Fortran program on a time-share computer. .55 9.534 . 4200.00 28.49 5. 7.61 13.599 .31 14. .84 12..? L DATE : 020178 LAUNDER NO: 0 0 4 . 3.01 11. 6300.. . Assume a value for the flow-depth-to-diameter ratio. depending on launder geometry).15 times the solids transport velocity..25 18.. use the friction factor value calculated in step 9 as the assumed value in step 5 and repeat steps 6 through 10... depending on launder geometry). 1). 9.0259 .I563 . 4.Y..------------------. or 5. The sequence of calculations for this adjustment is as follows: 1. 10.CLIENT : ARC ENCINEERIhC COIIPANY ENGINEER: HRC. depending on launder geometry).I52 . The above sequence of design steps. assume another value for the launder dimension and repeat steps 2 through 7.. 6. The calculation sequence for launder size adjustment is nearly identical to the initial sequence.. Calculate continuity velocity (Eq. If it is required to determine the operating conditions at other flow rates.74 9. SOLIDS TRANSPORT VELOCITY FT... 8.0870 .600 'SOLIDS S P E C I F I C CRAVITY *SLURRY S P E C I F I C CRAVITY SLURRY SOLIDS CONCENTRATION WEIGHT X VOLUUE Z *APPARENT VISCOSITY OF SLURRY.I250 . or 5. slope.. 10.. Calculate Reynolds number (Eq.D251 ~0240 . C - PIPE LO500 . 4.03 14.32 8. At this point all values for the initial launder size and flow data have been determined. Then repeat steps 2 through 13 as above. or 9.a233 .. proceed to step 8: if not. Assign and input desired value for the launder slope.--------1 2 3 4 5 6 7 8 9 10 11 12 13 10500.. 2 .28 5.TABLE 4 ---------------------------------------------------------------------.I250 .00 30. The slope adjustment calculation sequence is different from the first two described above. 3. SLOPE ADJUSTMENT FLOW RATE ADJ.78 HIGH HIGH HIGH LW O LW O LW O LW O LW O LOU HIGH HIGH LW O LW O LW O LOU DESIGNREFERENCE DIAU 6 DEPTH ADJ.0240 .------.433+06 .49 1. U-shaped. 12. FLOW RATE ADJ.-----.00 30.413+06 . Calculate the solids transport velocity (Eq. Calculate Darcy friction factor. At this point the design of the launder is complete.-------. 10500. 16). except the reference one.27 .73 5.022L . Assume a value for the Darcy friction factor.a235 .57 8.08 30.. 5. . DEPTH ADJ. PLOY RATE A D J .-----.PRIHARY I N P U T FOR D E S I G N C A L C U L A T I O N S JOB NO DATE LAUIIDEP.. APPLICATION: TAILING L A U N D E R ~ ~~ TABLE 5 . D E P T H A D J ..DlIL T A I L I N G LAUNDER APPLICATIO!!: P R I H A R Y I N P U T DATA *LAUNDER S H A P E *FLOW R A T E ..B E C H T E L C O R P O R A T I O N . u s c p n 'FLOW D E P T H T O LAUNDER U I D T H R A T I O * C F F E C T I V E ROUGHNESS OF LAUNDER. : 1234 : 020178 NO: 0 0 6 CORPO1:ATIOI:-!!I!:IlCl AND L'CTALS D I I ' I S I O I I SLI!RRY L A U I I C E R L E S I G K PnocP.. 6300. HICRONS '99% PASSING 5 0 1 PASSING 'SOLIDS S P E C I F I C CRAVITY *SLURRY S P E C I F I C C R A V I T Y SLURRY S O L I D S C O N C E N T R A T I O N WEIGHT 1 VOLUME 1 *APPARENT V I S C O S I T Y OF S L U R R Y . 6300.. FLOW DEPTH TO WIDTH RATIO DEPTH OF FLOW INCHES REYNOLDS NUHBER DARCY FRICTION FACTOR FROUDE NUHBER DESIGN RISK HIGH HIGH LOW LOW LOW LOW LOW LOW LOW HIGH HIGH Loll LOU LOIJ LOV D E S I G N DATA ITEM --.68 1.. FLOW RATE A D J . -----.M I N I N G AND I i E T A L S D I V I S I O N SLURRY LAUNDER D E S I G N PROGRAM ----J O B NO : 1234 P R O J E C T : XYZ E X P A N S I O N : 020178 DATE : ABC E N G I N E E R I N G COtIPANY CLIENT LAUNDER NO: 0 0 5 E N C I N E E R : HRC .. 10500./SEC. FLOW RATE A D J . 9 10 II 12 13 14 IS I 6 11 MINING ENGINEERS MINING ENGINEERING 1215 .. FLOW RATE A D J .. SLOPE ADJUSTMENT FLOW BATE A D J .h!% TABLE 6 D E S I G N DATA SOLIDS TRANSPORT VELOCITY FT-ISEC. FLOW RATE A D J .51 1. 8400.33 1../FT.-.------ DATA I D E N T I F I C A T I O N ------------------- FLOW RATE A D J .---- -------.01 1. 4200...12 1./SEC.80 1.-----. C E N T I P 0 I S E S ...71 1. WIDTH...62 1. DEPTH ADJ. 10500. SLOPE ADJUSTHENT F L O l i R A T E ADJ.76 1. 10500. FLOU B A T E ADJ..--------.. 4200.. FLOW DEPTH TO WIDTH RATIO DEPTH OF FLOW INCHES ----------REYNOLDS NUMBER DARCY FRICTION FACTOR FROUDE MUHBER DESICN RISK HIGH HIGH HIGH LO11 LOU LOW LOW HIGH LOW LOW LOU LOW LOW LOW LOW LOW LOW ---. FLOW R A T E A D J .55 1. 10500.. P R I K A R Y I N P U T DATA U-SHAPED 10500 ...DIIL ~.66 1.-------.IERINC CO!IPANY CLIENT ENGINEER: HRC.-./FT. SOLIDS TRANSPORT VELOCITY FT.. FLOW RATE USGPM LAUUDEB WIDTH INCHES SLOPE IN. F L O U RATE A D J . F E E T S O L I D S P A R T I C L E S I Z E . 8400.95 1... BI:Cl!TEL ---------------------------------------------------------------------P R O J E C I : XYZ EXPANSION : ABC ENCI!.........00443 ' E F F E C T I V E ROUGHNES S O L I D S P A R T I C L E S I Z E . W I D T H .. 6300.TI WEIGllT I VOLUME X 'APPARENT V I S C O S I T Y O F S L U R R Y .-------. FLOW RATE A D J .66 1.... 8400.60 1. 4200. S L O P E ADJUSTMENT FLOW RATE A D J .. WIDTH.. IIICRONS '99% PASSING 50% PASSING * S O L I D S S P E C I F I C CRAVITY 'SLURRY S P E C I F I C G R A V I T Y SLURRY S O L I D S C O N C E N T R A .600 .71 1.-------ITEM 1 2 3 4 5 6 7 8 10500. DESICN VELOCITY FT./SEC....... D E P T H ADJ. 10500. SLOPE ADJUSTHENT FLOW RATE A D J .-O N ... SLOPE ADJUSTMENT SLOPE ADJUSTMENT FLOW RATE A D J I FLOW RATE A D J ... 4200..-----.45 1.12 DATA I D E N T I F I C A T I O N ------------------DESICN REFERENCE UIDTH. FLOW RATE A D J . 10500. C E N T I P O I S E S *PRIMARY I N P U T FOR D E S I C N C A L C U L A T I O N S ----------FLOW RATE USGPH LAUNDER WIDTH INCHES SLOPE IN. DESIGN VELOCITY FT.. John Wiley. Chilton. o Mineral Dressing. Army Engineers Waterways Experiment Station. T. however.. There is. R. 286. C. p. Bechtel has written programs for the Hewlett Packard HP 9820A programmable calculator and also in Fortran for use on a time share computer. References l ~ a g g a r t A. June. 1945.. Vicksburg. no problem with memory shortage if a shared time computer is utilized. 1942. John Wiley. 1965. and Kilpatrick. is amenable to optimization. Handbook . Bureau of Mines. 20-35. Vol. 4th ed. 1948. 6"~~draulic Design Criteria". SSchack. K. Wisler. The system.. 1975. and Woodburn. as further data become available.. New York. of course. p. 1957. 191. pp... "Measurement and Nature of the Apparent Viscosity of Water Suspensions of Some Common Minerals". . he calculations are extremely tedious to complete with a hand calculator. Hydraulics. jolt? AUGUST 1978 SOCIETY O F . Dean. This procedure was first programmed for the Hewlett Packard HP 9820A programmable calculator. W. 267-277. S. Those who plan to program this procedure will find that a machine with more memory will be idvantageous. New York. Bechtel Corporation Internal Paper.. 'A Guide to Hydraulic Design of Launders". C. d a m . Journal of Colloid Science. Further refinements. G. The Bechtel programs are confidential. R15334. can result in a better and better tool for the engineer charged with slurry launder design. Miss. 3-299. without major revision. 1963. G. May. 20. J. S. Nearly all of the available memory (429 registers) was used for a program covering one launder geometry. The described design procedure is an advance in the state-of- the-art of slurry launder design. S. U. and Molloy."Minimum Velocities for Sewers". 4Thomas. Engineers Handbook. .. There has not been sufficient operating experience with launders designed according to this procedure to guarantee the accuracy of the individual factors with a high degree of confidence. p. C.. M. H..Journal of the Boston Society of Civil Engineers. 5th ed. Use of these programs has demonstrated that the necessary design calculations are accomplished quickly and easily. Chemical . McGraw-Hill. 7 ~ e r r yR. Vol. H. "Velocities in Tailing Launders". N. New York.. 0. D.. S. that are anticipated as the system is used.. C.. 29. familiarity with them will demonstrate that the principles are straightforward and logical. but the mathematics presented in this paper will allow anyone with similar facilities to produce his own prigrams with little difficulty.Conclusion While the procedures described sound slightly formidable on first reading.. D. g ~ o c h e r B. A. S ~ i n gH. 1964. F. U. "Transport Characteristics of Suspensions: VIII A note on the Viscosity of Newtoniad Suspensions of Uniform Spherical Particles".