Vessel Volumes

August 21, 2000Rev: 2(05-05-03) The following are some guidelines and experienced hints for the design and utilization of process vessels. This information is never taught nor discussed in University courses or academic circles. It has been historically expected that graduate engineers will learn this information using their own efforts. Art Montemayor Vessel Design Tips 1) Always try to design around existing or available standard materials such as: a. Standard pipe caps. These are usually available off-the-shelf in carbon steel, as well as stainless, in sizes up to 42" and in various pipe schedule thicknesses. b. Standard seamless pipe. This is basic material that can be readily found available today. Always make this your first priority in selecting the vessel shell because of the convenience of eliminating any plate rolling, longitudinal weld seam, and reducing the possibility of stress relief. This option should be rejected only if required alloy, wall thickness, or diameter is not available. 2) Own a copy of Eugene Megyesy's "Pressure Vessel Handbook" as published by Pressure Vessel Handbook Publishing Inc.; P.O. Box 35365; Tulsa, OK 74153. This is probably the most useful and practical engineering book ever published in the USA. It clearly belongs on every process plant engineer's desk. Study it thoroughly and your project problems will start to fade away. 3) Ellipsoidal 2:1 heads have, by definition, 50% of the volumetric capacity of a hemispherical head with the same internal diameter. Ellipsoidal heads are designed and fabricated on the basis of using the inside diameter as their nominal diameter. These type of heads are used in preference to ASME Flanged and Dished heads for pressures in the range of 100 psig and for most vessels designed for pressures over 200 psig. Their inside depth of dish (IDD) is defined as half of the minor axis and is equal to 1/4 of the inside diameter of the head. 4) ASME F&D (also called Torispherical) heads are designed and fabricated in the USA on the basis of using the outside diameter as their nominal diameter. Flanged and dished heads are inherently shallower (smaller IDD) than comparable ellipsoidal heads. These heads (like the ellipsoidal) are formed from a flat plate into a dished shape consisting of two radii: the "crown" radius or radius of the dish and the inside-corner radius, sometimes referred to as the "knuckle" radius. Because of the relative shallow dish curvature, ASME F&D heads are subject to higher localized stresses at the knuckle radius as compared to the ellipsoidal type. The pressure rating of these heads is increased by forming the head so that the knuckle radius is made at least equal to 3 times the plate thickness. For code construction, the radius should in no case be less than 6% of the inside diameter. ASME F&D heads are used for pressure vessels in the general range of from 15 to about 200 psig . Although these heads may be used for higher pressures, for pressures in excess of 200 psig it may be more economical to use an ellipsoidal type. 5) The straight flange that forms part of each vessel head is part of the cylindrical vessel portion and should be accounted for as such in calculating the vessel volume. These flanges vary in length depending on the head thickness. A typical head flange length is about 1.5" to 2". 6) Try to stay away from the immediate area of the knuckle radius with respect to locating nozzles or doing other welding, cutting or grinding. The need to locate a nozzle, insulation ring, clips or other item near the knuckle radius should be consulted with a mechanical or fabrication engineer. 7) Be aware of the fact that the outside diameter of the cylindrical section may be bigger than that of the head if a flush fit is required between the two inside diameters. This occurs because the required head thickness for a given design pressure is usually less than for the corresponding cylindrical section. This is especially true in the case of Hemispherical heads. Page 1 of 75 Electronic FileName: 76469885.xls.ms_office WorkSheet: Notes & Experience August 21, 2000 Rev: 2(05-05-03) 8) Hemispherical heads are the strongest of the formed heads for a given thickness. A sphere is the strongest known vessel shape. However, the main trade-off here is that all spheres have to be fabricated as welded spherical segments. This requires more manual intensive work and results in a higher cost. Art Montemayor Vessel Design Tips 9) Always be cognizant of the need for vessel entry into a vessel as well as vessel internal parts such as trays, baffles, agitators, dip pipes, downcomers, separator vanes, demister pads, etc. Sometimes these items directly affect not only the height of a vessel, but also the diameter. A chemical engineer should take these factors into consideration even though they normally are not considered while doing process calculations and simulations. Often, if not in the majority of cases, these factors and items are the controlling parameters that practically establish the diameter and height of the fabricated vessel regardless of what the simulation program output states. 10) As you consider the physical dimensions of a process vessel, always keep in mind that you must have, as a minimum, certain required nozzles built into the vessel - besides those required for basic process operations. Many times some of these nozzles are not identified early in a project and their introduction later requires costly change orders or, worse, vessel field modifications after the vessel is installed. Some of these nozzles are: manways, inspection ports, drains, cleaning (spraying) ports, auxiliary level instrument nozzle, liquid temperature probe, sample(s) probe, top head vents, critical high and low level probes, etc. Process Chemical Engineers are the best qualified to identify this need and specify the location and size. Never expect to lift a vessel by its nozzles. Lifting lugs are required for this, and a qualified structural or mechanical engineer should be commissioned to design this critical need. 11) Do not forget to allow for insulation support rings. You must allow sufficient nozzle length so that any required vessel insulation can be applied in the field without obstructing nozzle flanges and bolts. It is always advisable for the process Chemical Engineer to participate in the specification of the ultimate insulation requirements and type since he/she are the most informed people of the temperature ranges and insulation types compatible with the vessel material, temperature, and service. Again, if this is not considered initially and is found to be required later, project timing and costs will suffer due to field vessel modifications that could involve an ASME "R" stamp procedure. 12) This Workbook was originally compiled to organize and utilize the techniques, formulas, basic data, and other information that I saved and used over the course of approximately 40 years of experience in Chemical Engineering. Users will probably find it useful for carrying out day-to-day process plant projects such as: 1. 2. 3. 4. 5. 6. 7. Calculating the maximum volume capacity of a vessel; Calculating the partial volumes of a vessel at different levels ("Strapping" a vessel); Calculating the required vessel size for a given partial volume; Calculating the surface area of a vessel for primer, painting and insulation purposes; Calculating the location of critical liquid levels on a vessel for alarms and shutdown; Calculating the weight of a process vessel for cost estimates or foundation work; Calculating the "Line Pack", or volume content, of a piping system with fittings. There are probably more uses or applications for this Workbook, but the above should suffice to indicate the utilitarian value of this information to a Process or Project Engineer - especially in an operating process plant in the field. Most of the basic information contained here was kept by me for years in notes, 3-ring binders, between pages of text books, in formal calculations, etc. Thanks to God for giving me the good common sense to save and document this information and for giving us the digital computer and a spreadsheet to organize and distribute it for use and exploitation by others. I hope this helps others - especially young, striving, and determined engineers who earnestly want to do a successful and safe project. Arthur Montemayor Page 2 of 75 Electronic FileName: 76469885.xls.ms_office WorkSheet: Notes & Experience Art Montemayor May 15, 1998 Rev:1(01/22/00) Partially-Filled Horizontal Vessels VOLUMES IN PARTIALLY FILLED HORIZONTAL VESSELS Steps: (1) Enter the required information in the YELLOW cells; (2) The calculated results appear in RED numbers. Name: Item No: Case: Tank Inside Dia. in = Cylindrical Length, in = Liquid Height, in = L/D = H/D = General Purpose Tank Vessel Volume 2:1 Flat Heads Unit T-C-15 Partial Vol 48.00 108,573 in3 137,526 62.83 470.0 ft3 79.59 595.4 gal 60 48.00 Hemi Heads Unit F & D Heads 1.3 1.0000 in3 166,479 Cylindrical radius = Chord Length = r CL = 24.00 = 0.0 Segment Area Aseg = 1,810 120,489 3 ft gal 96.34 720.7 = Ellip. Heads in. in. in2 3 69.73 521.6 U. S. Gallons Cylindrical Volume = Vcyl = 108,573 in 470.0 F & Dished Volume = VFD = 11,915 in3 51.6 Ellipsoidal Volume = Spherical Volume = Vell Vsph = 28,953 125.3 = 57,906 in3 in3 Page 3 of 75 250.7 Electronic FileName: 76469885.xls.ms_office WorkSheet: Partial-Filled HorizontalVessel Art Montemayor Horizontal Storage Tank November 11. dish (non-pressure) 2) Torispherical (ASME F&D) 3) Ellipsoidal (2:1) 4) Ellipsoidal (non-std) 5) Hemispherical Pressure < 15 psig < 200 psig > 200 psig Varies To Suit Head type selected: Inside depth of head (IDD): inches Head thickness: inches Number of calibration increments: Calibration curve for 90. (2) The calculated results appear in RED numbers.xls.000 7. x 2:1 Ellipsoidal Head Volume = 55. in.375 NOT REQUIRED FOR THIS HEAD TYPE 90.167 = = 7. If more than one option contains an "x". dia tank.0 90.000 (max 200) cu. heads 7. the program will use the first one it finds.ft. Tank Inside Diameter (ID) Tank length.5000 ft 86 inches Note: Place an "x" in only one of the 5 head options available. 1999 CALIBRATION DATA FOR HORIZONTAL TANK WITH FORMED HEADS Rev: 1(03/12/00) Volume Calibration Steps: (1) Enter the required information in the YELLOW cells.167 Page 4 of 75 ft tan/tan.22 20 NOT REQUIRED FOR THIS HEAD TYPE 0. tan/tan inches feet Tank HeadType 1) Std.ms_office WorkSheet: Horizontal Tank Strapping . 2:1 Ellipsoidal Electronic FileName: 76469885. 740 20 50.50 92.132.931.790.233 47 119.0 2.983 40 101.5 55 3 7.13 736.28 132.91 951.8 7.90 59.160 41 104.74 778.39 460.6 653 11 27.695 44 111.18 51.941 28 71.041.630 38 96.52 1.33 497.54 0.21 1.601.26 61.086.0 19 2 5.60 694.88 76.57 146.34 71.38 535.3 976 14 35.604 19 48.02 907.880 21 53.16 5.3 224 6 15.60 182.84 219.94 26.937 34 86.9 4.93 14.837.318.53 1.47 1.766 33 83.05 1.66 115.54 251.44 258.648. 1999 Rev: 1(03/12/00) Electronic FileName: 76469885.743.80 66.5 6.38 226.56 38.01 1.67 5.178.4 1.86 996.54 1.98 163.3 2.04 98.0 2.30 213.82 138.947 51 129.00 245.4 5.5 2.8 6.2 6.591 49 124.554.42 81.696.5 2.58 289.64 47.7 1.01 1.62 3.06 175.412 48 121.22 200.76 207.5 4.271.Art Montemayor Horizontal Storage Tank Volume Calibration Liquid Depth Liquid Volume Content Ft3 Inches Centimeters US Gals Liters 1 2.86 1.78 13.301 Page 5 of 75 November 11.4 3.054 46 116.108 35 88.14 1.32 16.65 199.124 52 132.094 15 38.7 3.68 194.5 7.455 37 93.20 121.14 188.598 32 81.02 172.412.224.8 3.9 3.12 109.2 1.365.46 228.9 756 12 30.70 7.6 2.3 1.02 34.338 42 106.87 321.8 6.90 1.47 78.32 1.36 144.91 1.44 157.769 50 127.0 159 5 12.1 5.0 102 4 10.60 42.86 19.266 30 76.9 6.5 1.5 1.74 126.5 864 13 33.884.43 820.29 1.08 257.96 87.92 232.57 424.28 99.471 25 63.024 22 55.4 463 9 22.806 39 99.08 1.15 653.24 10.48 30.506.5 6.77 1.32 122.782 27 68.281 36 91.319 24 60.4 4.ms_office WorkSheet: Horizontal Tank Strapping .2 4.19 863.215 16 40.1 2.87 389.59 1.6 4.90 151.341 17 43.30 1.6 3.40 23.46 238.60 27.2 5.80 613.625 26 66.470 18 45.30 354.517 43 109.0 1.102 29 73.10 42.7 5.58 103.72 56.431 31 78.5 297 7 17.8 4.xls.54 574.8 555 10 25.52 169.76 1.459.85 1.16 1.1 5.874 45 114.6 377 8 20.170 23 58.4 3. 5 3.778.227 10.5 2.5 2.6 2.652 7.42 375.203.1 3.72 350.32 162.67 182.46 223.Art Montemayor 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 Horizontal Storage Tank 134.9 3.005 12.841 9.82 413.848.948 12.74 407.0 2.013 11.34 365.367 10.15 144.40 306.73 180.766 10.91 170.731 11.131 11.98 423.1 2.088 12.59 215.24 282.0 2.5 2.3 2.2 3.944.9 2.04 388.86 300.39 228.116.90 419.xls.341 8.382.0 7.6 2.3 2.52 175.052 12.7 3.56 328.88 370.636 9.48 195.143.ms_office WorkSheet: Horizontal Tank Strapping .06 142.080.52 425.005 9.206.28 410.32 294.36 416.637 10.455 11.48 317.056.5 3.62 198.477 7.003.024.788 9.482 9.9 3.12 396.166 9.70 276.87 157.7 2.10 334.352 11.18 345.68 177.94 311.4 2.251.325 9.881.20 147.705.60 200.9 2.549.5 2.49 185.070.5 3.04 154.62 Calibration 263.19 187.124.810 11.030.02 323.16 218.20 149.589.339.937 10.16 269. 1999 Rev: 1(03/12/00) Electronic FileName: 76469885.2 2.974.80 360.509 8.41 203.628.46 220.676 8.92 139.19 193.26 172.2 2.1 2.78 288.50 384.504 10.103.883 11.63 160.74 210.552 11.4 2.78 213.0 3.467.74 Volume 137.5 2.913.107 November 11.826 7.0 2.13 226.3 3.46 167.4 3.160.49 208.978.20 404.5 2.60 427.814.171 8.424.197.64 339.58 392.06 426.06 Page 6 of 75 1.3 3.508.96 379.295.161.188.6 2.742.1 2.76 190.644 11.66 400.084 10.892 11.04 205.999 8.244 11.5 2.176.93 165.667.26 355.44 421.15 152. 1999 Rev: 1(03/12/00) Electronic FileName: 76469885.xls.Art Montemayor Horizontal Storage Tank Volume Calibration Page 7 of 75 November 11.ms_office WorkSheet: Horizontal Tank Strapping . 2001 Rev: 0 b D D/2 a D/2 H1 Horizontal Cylindrical Tank with Ellipsoidal or Hemispherical Heads Total tank volume = (Total volume in two heads) + (Total volume in cylindrical section) 3 2 = ( 1/6 p K1 D ) + ( 1/4 p D L ) K1 = 2b/D Ze = H1/D Zc = H1/D 3 2 Partial tank volume = ( 1/6 p K1 D ) ([f(Ze)]) + ( 1/4 p D L ) ([fZc)]) f(Zc) = Horizontal cylinder coefficient (from Doolittle tables) or. æ ö ç ÷ ç ÷ H1 a = 2 Atanç ÷ ç æç 2 H D ö÷ . æa -sin(a) cos (a)ö f (Zc) = ç ÷ p è ø f(Ze) = Ellipsoidal coefficient (from Doolittle tables) 2 or.ms_office WorkSheet: Partial Horizontal .H 2 ÷ 1 1 ÷ ç è 2ø è ø a is in radians For Ellipsoidal 2:1 heads.Horizontal Cylindrical Tank Partial Volume Determination Art Montemayor b L May 5.3 + ÷ D ø è D ø è Where. b = (1/4) D K1 = 1/2 Page 8 of 75 Electronic FileName: 76469885.xls. 2H1 ö æH ö æ f (Ze ) = -ç 1 ÷ ç . 2001 Rev: 0 Oct 31. Z = arccos(1-2h/D) h = height of liquid in the horizontal cylindrical tank D = diameter of the tank L = length of the tank Note that the result of the arccos-function has to be taken in radians.ms_office WorkSheet: Partial Horizontal .com The volume V of a liquid in a horizontal cylindrical tank is: V = LD2 (2Z-sin(2Z)) /8 Where. 1999 www.Horizontal Cylindrical Tank Partial Volume Determination Art Montemayor May 5.about. Bernhard Spang Page 9 of 75 Electronic FileName: 76469885.xls. 3 + ç 1 ÷ ÷÷ b è øø è Page 10 of 75 Electronic FileName: 76469885.Vertical Cylindrical Tank Partial Volume Determination Art Montemayor May 05. 2001 Rev: 0 D b H2 L H3 H3 H1 H1 b Vertical Cylindrical Tank with Ellipsoidal or Hemispherical Heads Total tank volume = (Total volume in two heads) + (Total volume in cylindrical section) 3 2 = ( 1/6 p K1 D ) + ( 1/4 p D L ) 3 2 Partial tank volume = ( 1/6 p K1 D ) ([f(Ze)]) + ( 1/4 p D H3) K1 = 2b/D Ze = (H1 + H2)/K1D f(Ze) = Ellipsoidal coefficient (from Doolittle tables) or.ç 1 ÷ è 2b ø 2 æ æ H + H2 öö çç . æ H + H2 ö f (Ze) = .xls.ms_office WorkSheet: Partial Vertical . 800000 0.850000 0.373530 0.000000 0. 1972.950000 1. Vol.200000 1.716x2 + 0.000000 1.311918 0.600000 0.900000 0.400000 0.094061 0.200000 0.600000 0. 1998 Rev: 0 Regression of Doolittle Partial Volume Coefficient 0.000000 0.436445 0.018692 0.4365x .000000 May 15.200000 H/D = Zc Page 11 of 75 Electronic FileName: 76469885.563555 0.800000 1.250000 0.150000 0.400000 0.100000 0.750000 0.857622 0.200000 -0.142378 0.0.800000 0.000000 0.600000 f(Zc) Zc 0.000000 0.700000 0.195501 0.947956 0.450000 0.650000 0.981308 1.804499 0.000000 Data Source: NGPSA Engineering Data Book 9th Edition.905939 0.200000 0.144x3 + 1.300000 0.550000 0.400000 0.052044 0.xls.050000 0.ms_office WorkSheet: Partial Cylind. 13-7 Coefficients for Partial Volumes of Horizontal Cylinders 1.350000 0. p.500000 0.252315 0.000000 y = -1.500000 0.747685 0. .Art Montemayor f(Zc) 0.626470 0.688082 0.0043 R2 = 1 0.200000 0. Art Montemayor Regression of Doolittle Partial Volume Coefficient May 15.xls.200000 Page 12 of 75 Electronic FileName: 76469885. Vol.ms_office WorkSheet: Partial Cylind. . 1998 Rev: 0 1. 20 0. Fraction 0.70 0.80 Volumetric Fraction Art Montemayor 0.12 0.9988 1.9896 0. To obtain the total volumetric capacity of a process vessel.90 0.34 0.9467 0.94 0. .9953 0.42 0.4100 0. 5th Edition.30 0.4700 0.6-87 Page 13 of 75 Electronic FileName: 76469885.0.58 0.92 0.52 0.04 0.7320 0.3230 0.14 0.6770 0.16 0.62 0.5600 0.02 0.20 0.40 0.60 0.5000 0.06 0.9603 0.9818 0.64 0.00 Liquid Depth/Head ID.1676 0.1913 0.xls.0047 0.0855 0.0533 0. P.0000 Doolittle Equation for Parially-Filled Vessel Heads May 27.88 0.1239 0.22 0.5900 0. (H/D) Reference: Chemical Engineers' Handbook.44 0.50 1.80 0.72 0.86 0.28 0.2420 0.00 0.6480 0.0001 R2 = 1 1.8549 0.0686 0. the volumetric capacity of the vessel headsHds must be calculated separately and added to the vessel's cylindrical volume.74 0.8324 0.5300 0.0026x3 + 3.78 0.8960 0.0397 0.46 0.18 0.4400 0.32 0.9145 0.68 0.10 0.3810 0.7840 0.40 0.84 0.0280 0.00 0.60 0.6190 0. Perry & Chilton.96 0.00 0.ms_office WorkSheet: Partial Vol.9314 0.00 Vol.0104 0.8087 0.8761 0.38 0.82 0.9720 0.0016x + 0.36 0.66 0.2160 0.24 0.54 0.1040 0.2680 0.7050 0.H/D 0.50 0.76 0.1451 0.2950 0.20 1.0012 0.7580 0.98 1.48 0.08 0.004x2 .26 0.0182 0.56 0. 1998 Rev: 0 Volume Fraction of Horizontal Vessel Heads y = -2.3520 0. Standard Mathematical Tables..h) ..May 27. in US gallons VHH = 2 VEll . since there are no existing standards for dished heads) 5.G.. h = depth of liquid content in the horizontal head..Volume of a dished-only head... Handbook. in..30) . Above this design pressure the 2:1 Ellipsoidal head is usually employed.. The ASME F&D head is usually restricted to pressure vessels designed for less than 200 psig.. 130-132. in US gallons VEll = 0. pp... Standard Dished (a misnomer.... Pressure Vessel Code...25d-0.. Zc = Cylindrical partial volume coefficient Ze = Heads' partial volume coefficient The cylindrical partial volume can be expressed by the following explicit analytical expressions: V1 = {r2cos-1[(r-h/r]-(r-h)(2rh-h2)0...00226 h2 (1.. The calculation of the partially-filled cylindrical portion of a horizontal vessel is straight-forward and can be done using the analytical expressions noted above. 1998 Rev: 0 To obtain the total volumetric capacity of a process vessel. the ....M.. Hemispherical 2.. To obtain the partially-filled liquid contents' volume of a horizontal tank requires the determination of the partial volume of the two vessel heads as well as the cylindrical partial volume..R. d = inside diameter of the horizontal head. L = total straight. 2:1 Ellipsoidal 3. Perry/Chilton...S..... Engrs. Hydrocarbon Processing...h) ..... V1 = in3 V2 = gal V3 = in3 r = vessel's inside radius. consequently.. in US gallons where..5}L ......0009328 h2 (1.. 5th ed.. 399. F.E... in.... the volumetric capacity of the vessel heads must be calculated separately and added to the vessel's cylindrical volume. a = 1/2 of the total angle subtended by the chord forming the liquid level. The partial volume of heads is open to inaccuracies and while the analytical equations are suitable for estimating..25d2arcSine(0.. It is restricted to pressures less than 15 psig.00433 L{pd2/8-[(0.. Page 14 of 75 Electronic FileName: 76469885. Chem.6-86) where. cylindrical.. h = depth of liquid content in the horizontal head..5d-h)(dh-h2)0. in.C... The contents of a partially-filled vessel are arrived at by adding the partial contents of the Cylindrical portion and both heads: Partial Volume = (Total Cylinder volume)(Zc) + (Total Heads' volume)(Ze) where. p...... does not comply with the A..ms_office WorkSheet: Hds Partial Vol.. Eng.5 + 0.. 6/11/73) V2 = 0.5d .5d ....... horizontal length...xls..(Kowal. p.. July 1968) 3) V3 = L r2[(a/57.(Caplan. F.Volume of Hemispherical head......... The equation given by Caplan (V2) should be very accurate since it is directly derived from an exact mathematical model presented in C.5h)]} .... July 1968) VDH = 0. degrees 1) 2) The partial volumes of horizontal-oriented heads (except for Hemi-heads) are not defined in a mathematically exact formula but can be expressed by the following analytical expressions: (From Caplan.sinacosa] . with the Hemipherical head reserved for those applications that require the maximum in pressure resistance and mechanical integrity. ASME F&D (Torispherical) 4.. in.Volume of 2:1 Ellipsoidal head. Conical The Standard Dished head is not suited for pressure vessels and. 12th Ed..(1959)..(Chem... Art Montemayor Doolittle Equation for Parially-Filled Vessel Heads The five types of formed vessel heads most frequently used are: 1. Hydrocarbon Processing.. in... (D) . p. r = inside radius of the horizontal heads. 322-323 (1928)] equation is used: Art Montemayor Doolittle Equation for Parially-Filled Vessel Heads Vpartial = 0. the method usually used is the Ze method for determining the liquid fraction of the entire head. Horizontal vessel diameter (D) Page 15 of 75 Electronic FileName: 76469885. in. Micro Motion Coriolis flowmeter). calculated by Doolittle's formula. The measurement may be made by weighing. and hemispherical heads with an error of less than 2% of the entire head's volume. the Doolittle [Ind. The Table or the resulting 3rd order polynomial equation. gallons h = depth of liquid in both heads. This fraction. is 142% in excess of the basic Doolittle relationship.. Ze = -2 (h/d)3 + 3 (h/d)2 . or by repeatedly filling small measuring tanks which have been calibrated by weight. ft When a tank volume cannot be calculated. calibration may be necessary. ft D = diameter of the large end. in. cu. This is done by draining (or filling) the tank and measuring the volume of liquid. For this purpose. Vc = total conical volume. His equation for an ellipsoidal head. (Note that this is the same equation offered by Caplan.0016 (h/d) + 0.0.e. Conical heads' volumes are defined by the exact mathematical expression for a truncated cone: Vc = p h (D2 + dD + d2) / 12 where. 21.00093 h2 (3r .xls. the equivalent volume can be quickly converted from the measured fluid mass. by a calibrated fluid meter (i. above.h) where. but the equation is satisfactory for determining the volume as a fraction of the entire head. Chem. 1998 Rev: 0 The partial volume of heads is open to inaccuracies and while the analytical equations are suitable for estimating. Vpartial = partial volume. although of the same form. ft.) Doolittle made some simplifying assumptions which affect the accuracy of the volume given by his equation. or when greater precision is required. is given in the Table listed above and regressed in the accompanying Chart.ms_office WorkSheet:minor Hds Partial axis Vol. torispherical (ASME F&D). ellipsoidal. Eng. h = height of the cone. for a dished-only head. ft d = diameter of the small end. From the known fluid density at the measured temperature.May 27.0001 can be used to arrive at a partial volume of standard dished. . This means that the Inside Depth of Dish (IDD) must be known. gallons (excluding flanged section) H = liquid depth in the dish.. "standard" dished heads at various depths is: V = 0. since no standards exist for dished heads) OD / 6 ID / 4 ID / 2 An analytical equation for the partial volume of vertical oriented.. For Vertical Vessel Heads: The H/D ratio corresponding to this orientation is the Liquid depth divided by the Minor Axis. note that the H/D ratio represents the Liquid depth divided by the Major Axis (internal diameter) of the Ellipsoidal heads... inches L = radius of the dish. Chemical Publishing Co. not the Major Axis (internal diameter) of the Ellipsoidal heads.(Chemical Processing Nomographs. Ze..004545 H3 . 1998 Rev: 0 minor axis (D) H H Horizontal Vessel Heads' orientation Vertical Vessel Heads' orientation The Doolittle relationship can be applied to Horizontal and Vertical-oriented Ellipsoidal (and F&D) vessel heads.xls. 276) where.... it is important to note that the H/D ratio that sets the fractional Coefficient.. For Horizontal Vessel Heads: In this case.. Refer to the above illustrations of Ellipsoids oriented horizontally and vertically. Davis. The IDD is the depth of the head at its center and includes the inside corner radius but not the straight flange or nominal thickness of the head.. p. is measured differently in both cases... minus 6 inches) Page 16 of 75 Electronic FileName: 76469885... inches (usually equal to the tank ID. However..ms_office WorkSheet: Hds Partial Vol. Characteristic IDD's for various types of heads are: Standard dished head: ASME F&D head: Ellipsoidal.Dale S..01363 H2 L ..Art Montemayor Horizontal vessel diameter (D) (major axis) Doolittle Equation for Parially-Filled Vessel Heads May 27. V = liquid volume in the dish..0. 2:1 head: Hemispherical head: OD / 7 (Note: This is only approximate..1969... 750 0.992750 1.216000 0.200000 y = -2x3 + 3x2 + 1.800000 f(Ze) Data Source: May 15.104000 0.281750 0. Vol.000000 0.650 0.574750 0.050 0. .100 0.007250 0.400000 0.150 0.600000 0.950 0.843750 0.850 0.not the volume for 1 head!! Coefficients for Partial Volumes in Ellipsoids & Spheres 1.Art Ze Montemayor f(Ze) 0.000 0.450 0.200 H/D = Ze Page 17 of 75 Electronic FileName: 76469885.000 1.500 0.600 0.156250 0.000000 0.400 0.352000 0.060750 0.648000 0.900 0.600 0.028000 0.425250 0.ms_office WorkSheet: Partial Ellip.000 0.718250 0. 13-9 NOTE: These capacity coefficients apply for the volume of 2 ellipsoidal or hemispherical heads…….156504905E-15x .200000 0.250 0.1.xls.800 1.000000 0.000 1.200 0.200 0. 1998 Rev: 1(02/25/01) Regression of Doolittle Partial Volume Coefficient 0.000000 NGPSA Engineering Data Book 9th Edition.800 0.300 0. p.350 0.939250 0.784000 0.896000 0..550 0.400 0.500000 0.972000 0. 1972.700 0.11143497E-16 R2 = 1 1. 61 27.12 254.55 71.22 67.78 2.81 70.25 0.1667 3.09 183.22 16.79 3.61 10.61 8.22 19.66 3.33 1.31 7.62 104.66 287.28 5.5000 14.40 2.09 90.14 4.0000 12.06 0.78 190.95 44.53 4.26 0.0000 8.Art Montemayor Internal Diameter Inches Ft 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 48 54 60 66 72 78 84 90 96 102 108 114 120 126 132 138 144 150 156 162 168 174 1.23 33.16 156.36 95.75 17.45 398.22 63.72 18.85 224.33 575.09 122.87 133.12 12.62 0.80 15.30 1.0000 10.88 1.18 59.13 0. 1998 Rev:1(08/21/00) Pressure Vessel Heads Volume of one head.54 102.41 1.04 9.64 3.72 156.93 28.34 7.00 4.28 36.60 62.04 42.33 4.23 42.90 55.78 28.38 22.26 1.75 75.07 72.5000 August 04.44 32.76 131.01 153.62 83.08 163.76 157.07 348.46 286.72 113.3333 1.09 23.1667 2.07 9.59 112.19 245.5000 13.99 2.05 71.45 19.87 71.36 3.44 13.39 0.0000 1.44 229.69 117.3333 2.88 92.59 7.43 50.93 0.27 25.76 33.64 35.18 45.06 359.13 0.61 0.09 4.73 11.09 3.12 2.0000 4.61 14.50 38.43 112.86 12.43 28.74 226.28 0.22 210.5000 2.02 20.88 330.49 127.55 9.04 11.28 7.69 5.42 0.26 16.88 6.13 0.20 0.31 0.68 0.53 174.ms_office WorkSheet: Hds Vol & Surf Area .73 169.61 2.78 3.29 163.27 39.50 96.1667 1.95 7.05 2.04 160.45 6.6667 1.26 7.82 11.0000 3.22 1.34 81.6667 2.28 6.01 10.24 165.19 255.38 9.40 144.17 644.81 39.26 Page 18 of 75 1.5000 12.06 1.23 44.xls.5000 11.62 14.96 53.60 5.92 39.48 2.75 51.58 5.66 2.09 2.13 132.28 307.70 8.94 195.52 92.08 173.80 303.5000 9.17 12.46 261.25 2.14 126.09 1.53 4.56 0.08 226.0000 7.18 3.5000 7.56 56.89 18.28 60.09 56.71 3.93 16.27 47.13 31.10 145.18 190.0000 6.44 265.31 9.55 66.05 56.36 7.21 1.76 23.55 0.19 399.19 182.81 1.5000 5.07 1.05 1.31 8.38 11.5000 4.77 2.14 182.45 1.65 1.90 23.67 0.45 205.11 110.04 22.12 718.66 111.45 6. Ft3 Internal Surface Area of one head.0000 9.57 2.80 4.0000 11.30 49.0000 2.03 122.23 141.03 30.59 322.05 0.97 88.48 52.16 4.70 1.90 89.13 Electronic FileName: 76469885.30 3.53 113.51 0.33 81.27 35.38 798.96 5.08 0.23 130.24 143.00 1.98 3.45 196.88 10.35 100.86 32.37 76.85 5.58 14.21 0.07 8.5000 6.33 0.86 78.5000 8.43 4.85 1.31 64.27 67.39 95.36 1.32 8.81 103.06 4.16 452. Ft2 Hemisphere Ellipsoidal ASME F&D Standard F&D Hemisphere Ellipsoidal ASME F&D Standard F&D 0.36 21.70 11.14 2.36 4.44 0.92 11.3333 3.80 110.5000 1.58 2.09 0.39 511.0000 13.90 2.8333 3.13 0.64 28.91 6.48 0.93 132.07 45.37 121.36 100.90 151.12 8.0000 5.58 1.70 5.43 0.57 18.14 15.99 144.42 169.84 1.02 1.37 8.65 3.79 1.18 0.25 2.8333 2.88 147.36 5.02 80.07 207.59 83.5000 10.0000 14.23 199.38 86.24 25.45 134.52 56.72 43. Young.20 281.57 974.14 668.38 300.5000 17.5000 20.34 287.22 1.Art Montemayor 180 186 192 198 204 210 216 222 228 234 240 15.55 289.H.0000 17. 1959 (3) A.64 397.10 371.53 298. Eugene F.72 252.02 375.60 1.81 897.38 402.Y.26 312.52 256.28 272.11 701.0000 August 04.68 1.02 643. Montemayor personal files Page 19 of 75 Electronic FileName: 76469885.xls.32 225.12 427.17 588. N.81 310.06 508. Megyesy.62 1.33 1.16 Note: The Volume and Surface Area attributable to a head's straight flange is not included in this data.526.81 268.21 2.72 188.65 453. therefore.24 447.51 486.047. 1998 Rev:1(08/21/00) Pressure Vessel Heads 883. (2) Process Vessel Design.09 410.40 380.094.53 254.286.10 237.0000 18.941.79 487.54 763.37 284.0000 19.87 317.59 324.5000 16.0000 16.04 1.83 226.06 597.36 342.45 536.06 213.69 572.94 537.30 628.65 314.44 208.90 199.81 1.072.ms_office WorkSheet: Hds Vol & Surf Area .98 240. References and Sources: (1) Pressure Vessel Handbook.60 219.94 223.96 481.91 1.55 240. Pressure Vessel Handbook Publishing. L.43 377.5000 19..795. 8th Edition.0000 15.38 367.63 361.94 342.78 263. Brownell & E.84 970. Inc. The Internal Diameter is used in calculating the Surface Area.176.E.41 828.61 567.08 1.60 339.32 306.44 176.97 528.403.40 441.22 353.657.44 428. John Wiley & Sons.69 201.00 180.80 283.73 619.67 400.81 335.80 353. the resultant Area is slightly less than the actual external surface area.5000 18.47 268.25 240. 636 211.722 50.793 36.890 217. Inc.672 9.768 345.741 1.960 1. 1997 Rev 0 Mfr's Hds' Vol Diameter Head Volume in Cubic Feet Head Volume in U.603 3.101 178.908 81.226 34.50 2. 7962M.182 3.541 671.045 1.703 9.084 1.072 56.002.188 839.672 39.667 138.389 379.980 0.909 89.727 413.510 402.225 2.248 30. Gallons ft Ellipsoidal ASME F&D Hemispherical Dished Ellipsoidal ASME F&D Hemispherical 1.983 Data source: Trinity Industries.228 58.xls.255 16.884 0.00 1.725 6.447 22.903 110.582 501.50 55.262 0.613 1.880 3.328 247.310 41.448 62.803 43.519 135.432 59.907 15.454 26.00 67.958.277 0.093 826.239 134.072 6.202.264 32.728 7.131 0.081 89.779 13.656 2.733 122.618 83.197 537.172 261.043 110.00 0.069 1.832 4.591 529.50 80.310 125.299 10.918 103.008 6.010 206.577 52.852 39.951 22.078 10.098 190.00 44.896 14.928 7.450 1.672 2.50 0.082 0.780 244.00 8.778 1.963 162.548 11.306 2.396 1.932 167.351 71.902 29.764 160.692 11.344 4.50 11.857 4.794 268.460 46.ms_office WorkSheet: Mfr's Hds' Vol .50 5.370 4.361 3.411 76.280 25.442 0.Art Montemayor September 12.819 7.463 5.877 17.756 3.477 335.378 5.237 70.S. Head Division Catalog No.095 0.047 0.025 43.217 6.50 112.298 10.679.393 Dished 0.842 15.430 7.535 2.613 3.394 50.881 442.276 18.218 170.271 713.260 607.041 27.797 18.209 1.00 16.119 261.188 423.00 28.00 130.871 979.366 67.767 23.053 0.444 16.613 2.427.800 5.988 27.778 33.50 35. Page 15 Page 20 of 75 Electronic FileName: 76469885.799 53.829 6.00 3.821 224.50 21.478 293.364 10.216 7.083 601.557 8.091 0.254 325.00 95.696 8.048 87.969 4.201 8.382 323. 99 186 3646.39 108 713.61 132 1303.52 78 268.09 5.89 90 413.000 4.000000133 R2 = 1 6.000 Volume. Head Division Navasota.907 Ft Reference: Trinity Industries.31 24 7..000566699x3.000 3.98 18 3.99 48 62.41 66 162.73 7261.30 36 26.43 162 2409.04 198 4398.000 1.ms_office WorkSheet: Ellipsoidal Curve Fit .26 126 1133. Gallons Art 12 0. Montemayor D.59 120 979.61 156 2151.63 192 4011. Inc.38 102 601.000 8.07 7834.39 180 3304.23 60 122.34 168 2687.000 0 0 50 100 150 Inside Diameter.12 96 501. inches Vol.000 2.03 6200.08 174 2985. gallons I.000 7.29 6716.67 54 89.92 72 211.26 Gallons = 200 250 300 3 130. TX Product & Services Catalog # 7962M (1996) Page 21 of 75 Electronic FileName: 76469885.21 5711.210 216 222 228 234 240 5248.33 144 1692.39 138 1489.06 Ellipsoidal Curve Fit 2:1 Ellipsoidal Head Volume September 12.16 150 1912.88 114 839.000 y = 0. inches Ellipsoidal Head Inside Diameter = 120 inches Volume of Single Ellipsodial Head = 979.44 42 41. 1997 Rev 0 9.95 204 4811.93 84 335.xls.83 30 15. 95 mm 329 Tangent Line 24.84 Inches 1723 mm mm 75 1905 Straight Flange (Varies) 2" Nom.xls.00 mm 1524 May 21. Note that this measurement convention is opposite to that of the ASME F&D head./4) 18. Page 22 of 75 FileName: 76469885. 51mm Inches mm 2:1 Elliptical Head NOTE: Ellipsoidal 2:1 heads are fabricated and measured using the Internal Diameter (ID) of the head.Art Montemayor Start of Knuckle Radius 2:1 Ellipsoidal Heads Inches 60. Inches Dish Radius 67.55 Note: Verify all dimension with vendor drawings 624 Key In the Head I.D.ms_office Worksheet: Ellipsoidal Heads .D.75 Inches 476 mm Knuckle Radius Inches 12. 2003 Rev: 1 Approximate area for nozzle attachment Inside Depth (= I. Any cylindrical shell fabricated to fit these heads must conform to or match the ID dimension. 204 3,078.42 210 3,324.02 216 3,582.12 222 3,853.00 228 4,187.61 234 4,700.90 240 5,025.88 Reference: Trinity Industries, Inc. Head Division Navasota, TX Product & Services Catalog # 7962M (1996) ASME F&D Curve Fit ASME F&D HEAD VOLUME September 12, 1997 Rev 0 6,000 5,000 y = 0.000292744x3.0378 R2 = 0.9996 4,000 Volume, gallons I.Art D.,Montemayor inches Volume, gal. 12 0.61 18 2.07 24 4.91 30 10.25 36 16.58 42 27.62 48 39.31 54 58.10 60 76.78 66 103.25 72 135.19 78 167.20 84 217.54 90 261.09 96 323.45 102 379.74 108 442.08 114 529.78 120 607.21 126 714.90 132 809.04 138 934.15 144 1,015.27 150 1,227.02 156 1,361.28 162 1,504.82 168 1,712.89 174 1,879.89 180 2,057.21 186 2,312.53 192 2,515.83 198 2,730.51 3,000 2,000 1,000 0 0 50 100 150 200 250 300 Inside Diameter, inches ASME F&D Head Inside Diameter = 84 inches Volume of Single ASME F&D Head = 205.29 Gallons = 27.443 Ft3 Page 23 of 75 Electronic File: 76469885.xls.ms_office WorkSheet: ASME F&D Curve Fit Art Montemayor May21, 2003 Rev: 0 ASME Flanged and Dished Heads Flanged and Dished Head (ASME) Area for nozzle attachment O.D. - (R2+T)x2 Wall Thickness "T" Knuckle Radius "R2" Inside Depth of Dish "IDD" Tangent Line All Dimensions are in Inches (mm) Verify all dimension with vendor drawings Straight Flange (Varies) 2" Nom. 51mm Dish Radius "R1" Outside Diameter (O.D.) NOTE: ASME F&D heads are fabricated and measured using the Outside Diameter (OD) of the head. Note that this measurement convention is opposite to that of the Ellipsoidal head. Any cylindrical shell fabricated to fit these heads must conform to or match the OD dimension. Not all wall thicknesses are shown. Interpolate for approximate inside depth O.D. dish IDD Inches (Flanged & Dished Head ASME Table) Millimeters (Flanged & Dished Head ASME Table) "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) O.D "T" "R1" "R2" IDD ASME O.D 0.38 24 1.63 4.50 10 610 41 114 0.50 24 1.63 4.44 26" 13 610 41 113 26" 0.63 24 1.88 4.50 660 16 610 48 114 0.75 24 2.25 4.69 19 610 57 119 0.38 26 1.75 4.81 10 660 44 122 0.50 26 1.75 4.75 28" 13 660 44 121 28" 0.63 26 1.88 4.75 711 16 660 48 121 0.75 26 2.25 4.94 19 660 57 125 0.38 30 1.88 4.88 10 762 48 124 0.50 30 1.88 4.81 30" 13 762 48 122 30" 0.63 30 1.88 4.81 762 16 762 48 122 0.75 30 2.25 5.00 19 762 57 127 0.38 30 2.00 5.56 10 762 51 141 0.50 30 2.00 5.50 32" 13 762 51 140 32" 0.63 30 2.00 5.38 813 16 762 51 137 0.75 30 2.25 5.50 19 762 57 140 0.38 34 2.13 5.56 10 864 54 141 0.50 34 2.13 5.50 34 13 864 54 140 34" 0.63 30 2.13 6.00 864 16 762 54 152 0.75 30 2.25 6.06 19 762 57 154 0.38 36 2.25 5.94 10 914 57 151 0.50 36 2.25 5.88 36" 13 914 57 149 36" 0.63 36 2.25 5.81 914 16 914 57 148 0.75 36 2.25 5.75 19 914 57 146 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) O.D "T" "R1" "R2" IDD ASME O.D 38" 40" 42" 48" 0.38 0.50 0.63 0.75 0.38 0.50 0.63 0.75 0.38 0.50 0.63 0.75 0.38 0.50 0.63 0.75 36 36 36 36 40 40 36 36 40 40 40 40 42 42 42 42 2.38 2.38 2.38 2.38 2.50 2.50 2.50 2.50 2.63 2.63 2.63 2.63 3.00 3.00 3.00 3.00 6.50 6.44 6.38 6.38 6.63 6.56 6.94 7.00 7.19 7.13 7.06 7.00 8.00 8.75 8.69 8.63 38" 965 40" 1016 42" 1067 42" 1219 Page 24 of 75 10 13 16 19 10 13 16 19 10 13 16 19 10 13 16 19 914 914 914 914 1016 1016 914 914 1016 1016 1016 1016 1067 1067 1067 1067 60 165 60 164 60 162 60 162 64 168 64 167 64 176 64 178 67 183 67 181 67 179 67 178 76 203 76 222 76 221 76 219 FileName: 76469885.xls.ms_office Worksheet: ASME F&D Heads Art Montemayor 0.38 0.50 54" 0.63 0.75 0.38 0.50 60" 0.63 0.75 O.D "T" 0.38 0.50 66" 0.63 0.75 0.38 0.63 72" 0.75 0.88 0.38 0.50 78" 0.75 1.00 0.38 0.63 84" 0.88 1.00 0.38 0.50 90" 0.75 1.00 0.38 0.50 96" 0.88 1.25 O.D "T" 0.50 0.75 102" 1.00 1.13 0.50 0.75 108" 1.00 1.13 0.50 0.75 114" 1.00 1.25 0.50 0.88 120" 1.25 1.63 0.50 0.88 126" 1.25 1.38 0.75 0.88 132" 1.25 1.63 O.D "T" 0.63 1.00 138" 1.38 1.75 0.63 1.00 144" 1.38 1.75 0.75 1.13 156" 1.50 1.88 54 48 48 48 60 60 54 54 "R1" 66 60 60 60 72 72 72 66 78 72 72 72 84 84 84 84 90 84 84 84 96 90 90 90 "R1" 96 96 96 90 102 102 102 96 108 108 108 108 114 114 108 108 120 120 120 114 126 120 120 120 "R1" 132 132 132 132 132 132 132 132 144 144 144 144 3.25 3.25 3.25 3.25 3.63 3.63 3.63 3.63 "R2" 4.00 4.00 4.00 4.00 4.38 4.38 4.38 4.38 4.75 4.75 4.75 4.75 5.13 5.13 5.13 5.13 5.50 5.50 5.50 5.50 5.88 5.88 5.88 5.88 "R2" 6.13 6.13 6.13 6.13 6.50 6.50 6.50 6.50 6.88 6.88 6.88 6.88 7.25 7.25 7.25 7.25 7.63 7.63 7.63 7.63 8.00 8.00 8.00 8.00 "R2" 8.38 8.38 8.38 8.38 8.75 8.75 8.75 8.75 9.38 9.38 9.38 9.38 ASME Flanged and Dished Heads 8.94 10 1372 83 227 9.75 54" 13 1219 83 248 9.75 1372 16 1219 83 248 9.63 19 1219 83 245 10.00 10 1524 92 254 9.88 60" 13 1524 92 251 10.69 1524 16 1372 92 272 10.63 19 1372 92 270 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) IDD ASME O.D 11.00 10.94 11.75 11.63 12.00 11.88 11.88 12.63 13.00 13.81 13.69 13.50 14.00 13.88 13.75 13.69 15.13 15.81 15.69 15.56 16.13 16.88 16.63 16.44 IDD 17.88 17.69 17.56 18.50 18.88 18.75 18.56 19.44 19.88 19.75 19.63 19.50 20.88 20.69 21.44 21.25 21.88 21.69 21.50 22.31 22.81 23.69 23.44 23.25 IDD 23.94 23.75 23.56 23.38 25.88 25.63 25.44 25.19 27.75 27.50 27.31 27.06 66" 1676 72" 1829 78" 1981 84" 2134 90" 2286 96" 2438 ASME O.D 102" 2591 108" 2743 114" 2896 120" 3048 126" 3200 132" 3353 ASME O.D 138" 3505 144" 3658 156" 3962 Page 25 of 75 May21, 2003 Rev: 0 10 1676 102 279 13 1524 102 278 16 1524 102 298 19 1524 102 295 10 1829 111 305 16 1829 111 302 19 1829 111 302 22 1676 111 321 10 1981 121 330 13 1829 121 351 19 1829 121 348 25 1829 121 343 10 2134 130 356 16 2134 130 353 22 2134 130 349 25 2134 130 348 10 2286 140 384 13 2134 140 402 19 2134 140 399 25 2134 140 395 10 2438 149 410 13 2286 149 429 22 2286 149 422 32 2286 149 418 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) 13 2438 156 454 19 2438 156 449 25 2438 156 446 29 2286 156 470 13 2591 165 480 19 2591 165 476 25 2591 165 471 29 2438 165 494 13 2743 175 505 19 2743 175 502 25 2743 175 499 32 2743 175 495 13 2896 184 530 22 2896 184 526 32 2743 184 545 41 2743 184 540 13 3048 194 556 22 3048 194 551 32 3048 194 546 35 2896 194 567 19 3200 203 579 22 3048 203 602 32 3048 203 595 41 3048 203 591 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) 16 25 35 44 16 25 35 44 19 29 38 48 3353 3353 3353 3353 3353 3353 3353 3353 3658 3658 3658 3658 213 608 213 603 213 598 213 594 222 657 222 651 222 646 222 640 238 705 238 699 238 694 238 687 FileName: 76469885.xls.ms_office Worksheet: ASME F&D Heads 75 51 4318 295 883 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) IDD ASME O.13 48 3658 257 791 31.63 12.13 168" 1.00 1.25 180" 1.69 204" 5182 210" 5334 216" 5486 228" 5791 Page 26 of 75 22 32 41 51 25 35 44 57 25 35 44 51 25 35 44 51 4318 4318 4318 4318 4318 4318 4318 4318 4318 4318 4318 4318 4572 4572 4572 4572 311 311 311 311 321 321 321 321 330 330 330 330 349 349 349 349 May21.00 13.81 19 3658 257 808 31.00 1.13 10.69 43.88 0.81 41.63 12.00 1.25 12.00 4572 41 4318 276 787 30. 2003 Rev: 0 1005 1000 995 989 1062 1057 1049 1041 1124 1118 1110 1105 1183 1176 1170 1161 FileName: 76469885.88 1.63 "R2" 12.88 10.88 10.63 11.50 1.56 39.25 180 32 4318 276 794 31.25 12.63 41.00 44.06 45.63 11.75 2.00 144 144 144 144 170 170 170 170 170 170 170 170 "R1" 170 170 170 170 170 170 170 170 170 170 170 170 180 180 180 180 10.94 41.56 46.13 10.00 13.75 13.31 41.88 10.25 204" 1.38 210" 1.25 44.25 192" 1.38 228" 1.75 13.00 O.50 168" 29 3658 257 800 31.D 39.31 46.94 4877 41 4318 295 887 34.25 1.63 2.13 10.19 38.75 2.13 10.50 46.63 11.38 216" 1.00 43.63 13.88 11.88 1.75 ASME Flanged and Dished Heads 31.19 192" 32 4318 295 894 34.D "T" 0.25 12.63 12.38 39.00 13.44 22 4318 276 799 31.88 1.75 1.xls.44 22 4318 295 900 35.00 0.31 4267 38 3658 257 795 31.63 2.63 2.Art Montemayor 0.00 1.81 51 4318 276 783 35.ms_office Worksheet: ASME F&D Heads .00 1.25 12.75 13.00 13.75 2. 095 2.9997 R2 = 1 250 200 Volume.225 4. TX Product & Services Catalog # 7962M (1996) HEMISPHERICAL HEAD VOLUME 300 y = 0. Head Division Navasota.ms_office WorkSheet: Hemispherical Curve Fit .778 9. Inc.00 6.797 7.00 190.725 5.447 8.000 inches 3 261.548 6.00 Hemispherical Head Inside Diameter = Volume of Single Hemispherical Head = 2.50 11.00 89.1 Gallons Page 27 of 75 Electronic FileName: 76469885.50 160.00 0.00 56.50 23.799 September 12. ft Volume.00 Inside Diameter.00 134. cu. CuFt Internal Hemispherical Diameter.50 0.50 4. Ft.00 16.00 7.857 5.262 1. 1997 Rev 0 Hemispherical Curve Fit 150 100 50 0 0.959.50 43.00 2.00 10.091 3.00 32.900 Ft = 1.00 12.xls.2619x2.896 7. Ft 8.756 4.50 224. 1.46 10.Art Montemayor Reference: Trinity Industries.00 120.00 261.041 8.069 3.852 9.884 2.50 71.557 6.50 110.00 4. 1997 Rev 0 12.xls.Art Montemayor Hemispherical Curve Fit September 12.ms_office WorkSheet: Hemispherical Curve Fit .00 Page 28 of 75 Electronic FileName: 76469885. 963 6. TX Product & Services Catalog # 7962M (1996) DISHED HEAD VOLUME 60.50 46.00 120.00 3.00 Dished Head Inside Diameter = Volume of Single Dished Head = 2.000 20.842 3.50 2.00 0. Ft3 1.454 3.000 inches 3 53.00 10.ms_office WorkSheet: Dished Curve Fit .000 y = 0.271 9.000 10.636 6.000 0.582 8. ft Volume.Art Montemayor Reference: Trinity Industries.00 11. Head Division Navasota.60 Ft = 401.50 14.182 2.733 5.50 0.000 0.727 8.310 4.0 Gallons Page 29 of 75 Electronic FileName: 76469885.188 10.083 9.000 Volume.00 18.477 7.00 27.00 Inside Diameter.053 1.00 53.00 12.00 1.50 33.00 39.448 4.794 7. 1997 Rev 0 Dished Curve Fit 30.00 6. CuFt Dished Internal Diameter.909 5.00 6.0536x3.50 4. Ft 8.000 50.430 2.50 8.xls.50 0.50 22. Inc.00 0.871 September 12.00 4.0033 R2 = 1 40. 63 0.63 0.50 0. dish IDD Inches (Flanged & Dished Head Table) Millimeters (Flanged & Dished Head Table) "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) O.38 0.25 5.50 0.50 0.38 0.81 6.81 5.75 "T" 0.00 5.25 5.31 5.75 "R2" 1.75 4.13 6.25 1.88 2.50 4.00 7.88 2.38 0.13 1.75 IDD 5.63 5.00 5.38 6.D 26" 28" 30" 32" 34" 36" O.50 0.50 1.50 1.75 0.88 2.D 38" 40" 42" 48" 0.31 5.88 2. Any cylindrical shell fabricated to fit these heads must conform to or match the OD dimension. 2003 Rev: 0 Flanged and Dished Heads Flanged and Dished Head Area for nozzle attachment O.D.38 0.00 5.88 7.50 0.06 6.13 1.50 4.50 5. Interpolate for approximate inside depth O.19 5.D.13 1.13 4.63 4. .50 1.94 4.63 5.63 4.75 0.25 4.50 0.50 1.50 0.38 24 24 24 24 26 26 26 26 30 30 30 30 30 30 30 30 34 34 33 30 36 36 36 36 "R1" 36 36 36 36 40 40 36 36 42 42 42 40 48 48 48 48 54 1.06 5.13 1.38 0.63 0.88 2.75 0.D "T" "R1" "R2" IDD O.63 4.D.13 1.75 0.00 5.81 5.25 1.69 4.38 0.94 4.63 0.75 0.38 0.75 0.75 4.69 26" 660 28" 711 30" 762 32" 813 34 864 36" 914 O.88 6.50 4.69 6.) NOTE: F & D heads are fabricated and measured using the Outside Diameter (OD) of the head.50 4.50 0.00 6.94 6.19 7.63 0.44 6.63 4.38 0.63 0.38 0.25 1.38 4.25 6.19 5.44 5.81 5.31 5.75 0.44 6.63 0.63 0.63 0.ms_office Worksheet: Dished Heads .38 7.xls.63 0. 51mm Dish Radius "R1" Outside Diameter (O.44 5.D 38" 965 40" 1016 42" 1067 42" 1219 Page 30 of 75 10 610 29 108 13 610 38 111 16 610 48 114 19 610 57 119 10 660 114 114 13 660 118 118 16 660 121 121 19 660 125 125 10 762 114 114 13 762 118 118 16 762 122 122 19 762 127 127 10 762 127 127 13 762 132 132 16 762 135 135 19 762 140 140 10 864 127 127 13 864 132 132 16 838 138 138 19 762 154 154 10 914 133 133 13 914 138 138 16 914 143 143 19 914 146 146 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) 10 13 16 19 10 13 16 19 10 13 16 19 10 13 16 19 10 914 914 914 914 1016 1016 914 914 1067 1067 1067 1016 1219 1219 1219 1219 1372 29 38 48 57 29 38 48 57 29 38 48 57 29 38 48 57 29 148 152 156 160 148 151 170 175 154 159 162 173 175 178 183 187 195 FileName: 76469885.50 4.06 5.25 4.00 5.75 0.25 1.(R2+T)x2 Wall Thickness "T" Knuckle Radius "R2" Inside Depth of Dish "IDD" Tangent Line All Dimensions are in Inches (mm) Verify all dimension with vendor drawings Straight Flange (Varies) 2" Nom.50 5.19 5. Not all wall thicknesses are shown.50 0.Art Montemayor May 21.38 0.50 0.00 5.75 0.81 6.50 1.19 5. 31 9.69 21.88 1.75 102" 1.38 1.25 "R2" 1.00 3.50 15.88 2.63 3.00 3.00 8.88 2.44 13.06 15.50 66" 0.D "T" 0.ms_office Worksheet: Dished Heads .19 8.38 0.44 9.25 O.94 23.13 24.D "T" 0.88 1.25 1.63 3.00 1.75 "R2" 1.75 10.25 15.75 0.25 7.50 0.13 1.75 108" 1.63 12.81 11.88 2.63 0.13 20.75 14.63 78" 0.63 3.88 2.13 1.38 16.81 8.00 19.50 0.81 19.50 0.D 102" 2591 108" 2743 114" 2896 120" 3048 126" 3200 132" 3353 O.63 0.38 0.75 96" 1.50 2.13 1.25 3.81 8.31 13.50 2.50 2.88 2.75 1.50 5.50 1.88 1.88 138" 1.25 3.75 54 54 54 60 60 60 60 "R1" 66 66 66 66 72 72 72 72 78 78 78 78 84 84 84 84 90 84 84 84 96 96 96 96 "R1" 102 96 96 96 108 108 102 102 114 114 108 108 120 120 120 120 126 120 120 120 132 132 132 132 "R1" 132 132 132 132 144 144 144 144 144 144 144 144 170 1.88 0.88 2.38 17.63 2.13 0.38 1.38 10.88 120" 1.63 3.38 4.50 2.75 O.88 144" 1.63 0.50 0.25 0.63 9.xls.50 2.00 20.63 0.63 8.38 0.38 4.50 18.69 11.75 1.25 19.31 20.13 1.50 0.88 2.25 0.38 4.13 0.19 11.25 3.75 1.50 1.88 126" 1.D "T" 0.88 2.88 2.19 17.Art Montemayor 0.81 15.06 17.13 23.06 15.50 24.88 12.50 11.25 3.50 "R2" 1.63 0.13 1. 2003 Rev: 0 10 1676 29 236 13 1676 38 240 16 1676 48 245 19 1676 57 248 10 1829 29 256 16 1829 48 264 22 1829 67 272 29 1829 86 279 10 1981 29 276 16 1981 48 284 22 1981 67 292 29 1981 86 300 10 2134 29 297 16 2134 48 302 22 2134 67 313 29 2134 86 321 10 2286 29 318 16 2134 48 349 22 2134 67 356 29 2134 86 363 13 2438 38 341 19 2438 57 349 25 2438 76 357 32 2438 95 365 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) 13 2591 38 362 19 2438 57 394 25 2438 76 400 32 2438 95 408 13 2743 38 383 19 2743 57 391 25 2591 76 421 32 2591 95 427 13 2896 38 403 19 2896 57 411 25 2743 76 441 32 2743 95 448 13 3048 38 424 22 3048 67 435 32 3048 95 447 41 3048 124 459 13 3200 38 445 22 3048 67 478 32 3048 95 489 41 3048 124 500 16 3353 48 468 22 3353 67 476 29 3353 86 483 38 3353 114 495 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) 16 22 29 38 16 22 29 38 19 29 38 48 19 3353 3353 3353 3353 3658 3658 3658 3658 3658 3658 3658 3658 4318 48 511 67 519 86 526 114 537 48 508 67 516 86 524 114 537 57 602 86 613 114 622 143 633 57 588 FileName: 76469885.75 114" 1.88 2.25 1.88 1.69 11.25 3.75 1.69 18.50 13.63 3.63 3.13 20.63 84" 0.50 O.50 1.59 18.50 54" 0.38 1.44 20.13 1.13 1.75 4.13 156" 1.75 4.44 18.25 0.63 0.50 2.00 1.63 3.D 66" 1676 72" 1829 78" 1981 84" 2134 90" 2286 96" 2438 O.50 0.94 IDD 9.06 14.88 16.63 0.13 0.50 8.38 0.50 2.75 0.00 3.63 0.50 1.75 16.50 60" 0.88 1.75 19.75 14.69 24.50 0.69 17.38 0.63 90" 0.50 0.38 4.13 0.13 Flanged and Dished Heads 54" 13 1372 38 198 1372 16 1372 48 203 19 1372 57 208 10 1524 29 216 60" 13 1524 38 219 1524 16 1524 48 224 19 1524 57 227 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) O.38 0.63 3.D 138" 3505 144" 3658 156" 3962 Page 31 of 75 May 21.63 72" 0.88 132" 1.13 1.00 14.56 16.38 IDD 14.63 3.00 3.31 12.63 21.00 1.63 16.13 17.25 1.06 10.25 1.88 1.50 IDD 20.38 1.50 1.00 10.13 1.00 1.88 11. 25 31.00 35.88 0.88 1.63 39.00 2.00 2.00 23.63 2.00 46.31 35.00 0.88 6.00 41.D 204" 5182 216" 5486 228" 5791 240" 6096 Page 32 of 75 22 32 41 51 22 32 41 51 22 32 41 51 22 32 41 51 4318 4318 4318 4318 4318 4318 4318 4318 4572 4572 4572 4572 4572 4572 4572 4572 67 95 124 152 67 95 124 152 67 95 124 152 67 95 124 152 May 21.50 39.06 39.63 3.ms_office Worksheet: Dished Heads .00 2.25 240" 1.75 4.00 170 170 170 170 170 170 170 170 170 170 170 "R1" 170 170 170 170 170 170 170 170 180 180 180 180 180 180 180 180 3.25 41.75 42.63 3.88 1.13 27.44 46.00 O.63 2.75 4.25 228" 1.xls.75 4.25 46.63 2.88 1.75 4.00 2.63 IDD 34.88 6.56 24.00 30.88 31.50 41.19 26.06 24.63 46.50 1.00 0.56 28.25 216" 1.00 0.25 180" 1.63 3.69 27.50 30.63 3.88 6.75 4.63 3.88 6.63 2.88 6.25 204" 1.63 2.88 1.88 1. 2003 Rev: 0 880 889 897 905 992 1003 1010 1016 1048 1054 1060 1067 1175 1180 1184 1189 FileName: 76469885.D "T" 0.63 35.81 Flanged and Dished Heads 168" 29 4318 86 598 4267 38 4318 114 611 48 4318 143 614 22 4318 67 678 180 32 4318 95 689 4572 41 4318 124 700 51 4318 152 711 22 4318 67 775 192" 32 4318 95 784 4877 41 4318 124 794 51 4318 152 803 "T" (mm) "R1"(mm) "R2"(mm) IDD(mm) O.Art Montemayor 1.25 192" 1.38 4.75 4.13 168" 1.00 "R2" 2.88 6.63 2.88 1.63 3.75 40.00 0.50 5.63 2. 703 3. Perry & Chilton.878 1.705 57.777 30.expressed as Gallons of Liquid Content per inch length of Cylinder.164 1. p.047 11. Diam.341 48.285 102 10. Diam.926 14.572 1.334 32.618 19.050 25.298 46 47 48 7.373 36.5 22.406 4.5 24.760 22.0 0.500 8.5 27.750 47.640 26.0 1.000 35.499 1.817 28.511 7.571 49 50 51 8.5 16. 15.960 50.5 1./in.479 2.041 41 42 43 44 45 5.0 27.5 2.060 56 Gal.460 59.649 44.859 54 2.xls.810 15.885 74 76 78 80 82 18.666 52 2.886 64.926 29.605 52.0 15.0 23.227 1.287 6.5 0.0 25.102 1.502 72.0 18.983 30 Gal...657 41.715 5.0 21.870 29.0 16.653 34.978 55.930 4.429 1.835 12.774 17.861 126 128 130 132 134 53.5 21.914 100 10.165 57 58 59 60 62 11.438 11.722 16.194 7.329 136 138 140 62.240 13.146 26.721 1. 2.551 98 9.685 21. Source: Chemical Engineers' Handbook.557 70.843 90 92 94 27.660 17.990 25.998 6. 6-86 Diam.140 42.202 39.765 28. in.626 116 118 120 122 124 45.0 19. 5th Edition.662 104 Gal.0 20.762 53 2.0 2.171 5.267 3.5 0.0 Gal.ms_office WorkSheet: Cylindrical Tank Volume .959 55 3./in.5 23.834 84 86 88 23.638 20..440 64 66 68 70 72 13. 1998 Rev:1(06/06/01) Cylindrical Vessel Volume Relationship Cylindrical Volumes of Vessels --.5 26.582 6.5 17.5 1.5 19.041 1.749 66. 0.473 Page 33 of 75 Electronic FileName: 76469885./in.388 2.241 61..474 74.482 3.958 2.125 2.042 142 144 146 148 68.5 18.186 20.799 1.540 28.360 1.655 4. 9.646 36 37 38 39 40 4.070 106 108 110 112 114 38. 31.0 0. Diam./in. in.910 5.293 31 32 33 34 35 3.163 8.194 96 9.211 2.0 24. in.Art Montemayor May 27. in.278 22. 042.9 11.995.116.1 628.47 Nominal 90o Elbows Pipe Size.9 9.322.7 40.391.1 6.7 46.6 8.764.759.6 1.061.0 90o Elbows: Page 34 of 75 Electronic FileName: 76469885.8 9.432.532.1 69.917.702.1 24.4 2.8 13.8 2.4 12.8 18.365.7 52.0 87.8 31.2 4.7 63.9 19.091.5 3.8 0.882.4 2.707.6 736.026.155.997.322.8 22.130.4 1.1 27.6 1.1 4.2 367.5 94.182.752.7 1.0 471.5 27.238.8 12.0 245.0 36.189.3 4.415.598.9 4.8 108.049.366.2 2.482.0 2.5 6.8 9.4 30. 1999 Rev: 0 Art Montemayor VOLUMETRIC CAPACITY FOR BUTT-WELDED FITTINGS All volumes expressed in cubic inches Reference: Piping Engineering.720.809.7 130.6 62.4 10.7 119.0 14.914.0 23.261.5 108.5 295.634.1 69.5 40.8 10.0 145.1 40.3 1.5 3.3 31.3 5.0 5.6 413.260.0 34.6 1.3 3.1 184.0 4.2 430.0 684.9 47.188.260.221.2 9.5 52.3 54.3 65.054.9 9.250.451.5 9.700.1 7.1 59.5 46.4 9.4 110.8 1.5 1.301.813.9 544.344.1 14.4 239.5 13.7 23.6 517.135.xls.964.2 15.730.7 816.9 4.476.3 6.0 Tees Full-size outlets Standard X-Strong 0.3 88.5 19.7 3.6 1.8 2.2 20.289.3 13..4 14.020.329.0 4.163.853.816.316.493.3 18.2 77.3 3.8 3.8 40.712.0 144.054.1 2.2 17.9 1.936.3 1.1 61.471.2 31.490.6 94.8 30.1 811.4 7.449.4 0.658.125.6 21.0 35.545.2 20.9 28.1 879.7 11.0 1.064.879.701.763.2 3.1 1.8 123.516.1 368.3 11.2 58.1 62.6 5.5 176.594.4 31.6 0.9 272.1 68.834.2 35.971.935.9 3.376.085.3 23.014.899.0 41.5 12.179.5 1.441.2 4.9 204.5 8.8 18.9 8.7 0.6 132.4 180o Returns Long Radius Short Radius Standard X-Strong Standard X-Strong 1.1 3.6 1.480. Standard X-Strong Standard X-Strong 1/2 3/4 1 1-1/4 1-1/2 2 3 4 6 8 10 12 14 16 18 20 22 24 26 30 34 36 42 48 0.0 1.128.2 19.8 15.4 6. Nov.526.713.3 3. 1971.856.6 104.9 11.8 4.7 14.7 13.110.347.243.4 4.4 81.195.3 8.836.0 3.3 216.9 26.8 2.0 82.4 3.5 2.7 2.013.538.3 408.054.0 11.9 7.7 65.644.2 29.2 6.7 66.351.520.4 1.3 0.7 7.449.642.8 6.5 6.7 3.3 62.8 8.6 1.1 72.621.4 0. Long Radius Short Radius in.7 4.6 2.6 7.733.2 46.092.707.260.1 881.0 14.5 2.256.7 5.5 34.273.077.675.010.2 143.429.1 1.5 5.9 2.8 23.6 23.991.1 8.912.8 1.0 2.ms_office WorkSheet: Fittings' Volumes .784.327.3 148.4 2.681.906.207.810.1 3.676.2 0.4 26.2 198.145.108.209.9 0.161.9 62.4 0.8 93.7 62.953.9 4.648.443.804.0 47.4 572.8 6.224.7 135.6 159.0 93.172.5 8.1 1.157.6 967.041.030.9 490.2 13.2 3.2 15.June 02.8 13.297.9 2.396.0 196.0 18. Tube Turns Division of Chemetron Corp.203.9 52.3 860.1 928.1 7.350.602.5 6.130.745.3 5.985.5 34.6 3.3 942.4 8.5 55.7 4.0 110.0 2.945.353.3 1.323.0 9. p.8 10.249.664.1 45o Elbows Long Radius Standard X-Strong 0.348.6 23.2 11.2 1.884.1 1.8 54.695.442.967.8 79.758.0 Caps Standard 0.647.2 6. D3/3 V = Volume D = Inside diameter C= Center to end of run M = center to end of branch Page 35 of 75 Electronic FileName: 76469885.June 02.ms_office WorkSheet: Fittings' Volumes . 1999 Rev: 0 Art Montemayor V = P2D2A/8 V = Volume D = Inside diameter A = Center to face distance A 180o Returns: V = P2D2O/8 V = Volume D = Inside diameter A = Center to center distance 45o Elbows: V = P2D2A/8 V = Volume D = Inside diameter A = Center to face distance Full Size Outlet Tees: V = (PD2/2) (C + M/2) .xls. t .ms_office WorkSheet: Fittings' Volumes .xls.(2/3)D3 V = Volume D = Inside diameter C= Center to end of run M = center to end of branch Concentric & eccentric reducers: Page 36 of 75 Electronic FileName: 76469885.D/12) V = Volume D = Inside diameter E = length t = wall thickness Crosses: V = (PD2/2) (C + M) . 1999 Rev: 0 Art Montemayor Pipe Caps: V = (PD2/4) (E .June 02. xls. 1999 Rev: 0 Art Montemayor Page 37 of 75 Electronic FileName: 76469885.ms_office WorkSheet: Fittings' Volumes .June 02. 6 5.3 2.6 114.2 9.0 911.4 3.0 20.0 110.3 264.9 100.5 1.0 1.1 9.9 123.6 111.2 788.2 Stub Ends Lap Joint Standard X-Strong 0.157.5 2.8 46.371.1 375.3 354.189.6 9.868.9 19.1 44.9 4.081.5 15.4 0.6 9.0 1.8 Electronic FileName: 76469885.2 15.9 4.9 25.171.1 3.9 334.061.2 0.7 8.9 55.4 6.0 Crosses Full-size outlets Standard X-Strong 9.9 10.938.2 108.1 400.2 13.9 5.5 17.5 3.1 8.363.9 15.255.xls.9 103.1 3.5 501.5 52.1 58.3 1.8 2.3 1.8 6.402.5 5.8 158.311.7 16.3 49.4 313.4 1.4 50.802.8 2.0 1.6 7.0 208.0 4.3 2.6 8.7 4.4 441.1 7.8 147.0 6.8 3.5 29.6 3.9 1.9 17.5 1.5 166.8 65.4 37.0 346.5 10.7 6.4 5.1 340.0 8.5 6.3 121.9 51.6 69.804.131.5 41.634.8 3.June 02.3 746.811.1 2.592.7 321.920.7 2.666.6 54.8 307.7 72. Reducers in.7 9.654.2 2.6 18.5 10.5 0.8 52.6 6.0 3.0 5.4 2.4 Nominal Pipe Size.7 4 6 3/8 1/2 3/4 1/2 3/4 1 1/2 3/4 1 1-1/4 3/4 1 1-1/4 1-1/2 1 1-1/4 1-1/2 2 2-1/2 1-1/2 2 2-1/2 3 3-1/2 2-1/2 3 3-1/2 4 5 Page 38 of 75 1.3 41.4 3.884.8 2.5 37.7 4.7 99.120.6 3.4 475.723.7 26.2 361.1 20.7 125.313.5 7.144.6 2.006.7 80.043.985.4 21.8 39.492.9 5.3 6.5 6.084.9 3.6 5.7 122.8 10.0 983.8 48.1 5.4 20.368.7 13.6 3.2 21.1 175.5 27. 1999 Rev: 0 Art Montemayor Caps X-Strong 0.6 16.1 11.9 1.4 22.6 108.0 8.3 8.7 1.7 2.4 8.1 12.191.6 1.5 132.9 4.5 46.ms_office WorkSheet: Fittings' Volumes .4 76.4 45.9 2.6 97.7 134.9 119.3 33.094.8 16.3 1.682.0 2.0 11.9 152.6 3.3 9.4 113.8 2.4 9.5 301.6 2.0 3.1 17.4 1.0 1.0 640.4 231.4 62.7 24.1 5.3 12.3 17.4 47.010. Concentric & Eccentric Large end Small end Standard X-Strong 1 1-1/4 1-1/2 2 3 22.9 55.7 Tees with Reducing Outlet Standard X-Strong 2.5 365. 0 2.382 201.598 3.745 11.430.701 4.4 697.7 690.0 1.9 428.902 4.226 12.250.288 2.973 4.419 1.567.0 2.7 235.7 606.4 1.022 2.321 2.150 7. 1999 Rev: 0 Art Montemayor 8 10 12 14 16 18 20 22 3 3-1/2 4 5 6 4 5 6 8 5 6 8 10 6 8 10 12 6 8 10 12 14 8 10 12 14 16 8 10 12 14 16 18 10 12 14 16 Page 39 of 75 221.496 1.414 8.360 6.0 1.248 6.027 12.175 3.373.0 1.212 2.337 Electronic FileName: 76469885.6 309.0 2.620 655.841 716.747 9.915 2.0 1.3 476.xls.974 9.5 719.426.5 661.289 2.976 2.June 02.717 7.8 215.8 947.646 1.9 722.920 3.621 3.396 3.0 2.348.291 3.916 11.029 3.985 5.506.8 586.204 7.552 2.877 10.0 401.110 12.952 2.993 6.6 730.976 6.323.656 3.104 4.695 3.0 993.803 4.4 444.922 7.8 1.8 779.0 1.054 4.191 4.0 2.458 6.6 753.944 12.214 5.413 3.394 12.2 385.0 2.0 1.4 658.318.7 1.6 269.0 2.318 4.855 6.468.0 668.013 5.0 791.147 7.163 12.180 5.1 1.432.0 2.657 9.329.922 2.9 362.587 2.606 8.059 6.891 5.0 1.711 5.488 2.7 827.129 7.333 8.283 3.741 4.0 245.821 4.0 1.010 6.350.8 546.300.221 7.404 6.849 4.ms_office WorkSheet: Fittings' Volumes .992 2.8 280.396.816 3.0 639.738 2.532 3.224.055 7.041 2. 779 45.385 44.848 9.565 30.879 46.606 20.265 45.458 34.345.006 30.710 8.287 19.603 10.813.795 9.745 12.233 20.070 20.094 16.141 16.102 44.837 20.851 46.116 44.487 22.622 12.979 8.172 8.353 52.919 21.972 10.242 52.519 14.711 8.449 20.058 50.600 45.ms_office WorkSheet: Fittings' Volumes .701 53.768 30.392 30.526 14.637 9.334 8.587 54.June 02.520 30.xls.164 29.283 30.386 31.098 53.062 20.958 52.869 31.936 33.364 48.221 14.628 10.548 47.429 36 Page 40 of 75 Electronic FileName: 76469885.693 47.465 20.668 19.018 49.445 32.652 33.995 9.571 51.724 44.846 21.701 14.316 21.841 53.184 45.351 48.177 12.887 22. 1999 Rev: 0 Art Montemayor 22 24 26 30 34 18 20 10 12 14 16 18 20 22 12 14 16 18 20 22 24 14 16 18 20 22 24 26 28 16 18 20 22 24 26 28 30 32 16 18 20 22 8.583 43.325 16.908 31.477 16.389 49.419 12.451 10.131 32.474 1.964 32. 954 Electronic FileName: 76469885.710 80.972 78.358 125.xls.899 79.842 59.317 123.378 135.462 131.874 124.031 126.256 54.561 130.561 33.685 139.113 132.375 40.635 111.151 130.June 02.305 103.940 76.693 127.172 77.311 85.432 138.540 81.462 82.377 126.419 133.207 133.902 40.276 125.927 122.031 33.071 31.044 107.947 55.610 56.594 59.185 75.878 55.053 38.742 140.341 83.540 38.521 134.354 83.143 89.746 77.574 80.760 129.047 101.245 129.365 123.710 135.923 133.617 31.128 54. 1999 Rev: 0 Art Montemayor 36 42 48 24 26 28 30 32 34 20 22 24 26 28 30 32 34 36 22 24 26 28 30 32 34 36 38 40 42 44 46 Page 41 of 75 30.229 42.314 34.825 76.667 126.402 134.176 30.960 138.344 128.650 79.253 76.132 37.753 106.660 137.050 118.639 78.044 129.840 42.163 98.425 82.653 57.337 127.723 77.173 141.959 113.636 81.144 97.866 36.539 32.700 56.831 33.404 58.984 88.622 54.ms_office WorkSheet: Fittings' Volumes .693 116.698 32.736 128.186 125.359 57. Spherical Radius and Diameter. Two typical Torispherical profiles are shown below in Red.Profiles of Torispherical Dished Heads The volume calculator assumes the head profile to be a perfect ellipse. Torispherical heads can have different profiles depending on the relationship between: . The error will depend on the relationship between: . and the true ellipse for the same diameter and head height is shown in Blue. Treating a Torisphere as an ellipse for volume calculation will generally give a slight under estimate of the volume. which is correct for a semiellipsoidal head but only approximate for a Torispherical profile. .Knuckle radius.Knuckle radius. Spherical Radius and Diameter used. Knuckle .a semihave different ameter. me diameter and ill generally een: . 3762x3 + 1.b ) -1 Sin (a / R ) ß= i x = Ri Cos ß . Head Volume = 84.0664x R² = 0.45 245 c b Ri x a h z + p / 3 * x ((D/2)2 + (D/2)a + a2) approximate calculation for knuckle section 412.2 mm ß 1.ri a = b Ri / (Ri .4 litres = Volume of partially filled Torispherical head: Liquid Height Level in End dish: "h" (mm) "z" 0% 0 0 10% 37 37 20% 74 74 30% 111 111 40% 147 147 50% 184 184 60% 221 221 70% 258 245 80% 295 245 90% 332 245 100% 368.3 210.134 mm = 6. Vertical Torispherical Tank Head Volume 100% Volume of Fill 80% y = -0.9999 60% 40% 20% 0% 0% 20% 40% 60% 80% 100% Level of Fill Page 44 of 75 FileName: 76469885.c .7 mm = 368. 2003 Rev: 1 Volume of a Partially Filled Torispherical Bottom Head VERTICAL TANK BOTTOM TORISPHERICAL HEAD VOLUME CALCULATION Tank Internal Diameter(3) Crown Radius % Knuckle Radius Knuckle Radius D Ri 2.ri) 2 2 ½ c = ((Ri .63 inches 14.x h= x+z = = 5.ri) .xls.045 283 669 84% 1.8 mm = ri b = D/2 .1 + 798.6 mm ri 0.000 41 427 54% 1.2 mm 992.91 US gals Sector Area Volume (1) "r" 0 0 395 9 556 36 678 80 779 142 867 221 946 316 992 386 992 386 992 386 992 386 "x" 0 0 0 0 0 0 0 13 50 87 124 Knuckle Area Total Head Volume Volume (2) "r" litres % 992 0 0 0% 992 0 9 1% 992 0 36 5% 992 0 80 10% 992 0 142 18% 992 0 221 28% 992 0 316 40% 1.4 mm = 9.134 mm = 2.51 inches p / 6 * z (3a2 + z2) Approx.Art Montemayor July 20.7 mm = 4.55% 139.c z = Ri .87 inches 244.02 inches 386.4453x2 .7 ° 123.765.022 160 546 68% 1.4 100% Notes: (1) Sector volume = PI / 6 * "z" (3 * "r"2 + "z"2) (2) Knuckle volume = PI / 3 * "x" ("r"2 + "r" * a + a2) (3) Torispherical (also called ASME F&D) heads are designed and fabricated in the USA on the basis of using the outside diameter as their nominal diameter.ms_office WorkSheet: F & D Partial Volume .02 inches 84.067 412 798.0.50 inches 927.484 radians 27. 2004 Rev: 0 Vertical Tank Bottom Torispherical Head Volume = = Knuckle-Radius (kD) = dish-radius parameter (fD) = 5.9075 = 5. k f kD fD a a1 a2 D1 s t u(h) September 30.35 Gallons FileName: 76469885.xls.6383 = 5.ms_office WorkSheet: Vertical F&D Head Volume .22 234.9075 8.87 Gallons h = V = h Top 24 in 3 102.4538 inches = 78.D.420 in = 9.04 inches = 84 inches 84.35379 in 3 58.00 h = V = h 9.77 252.0 inches 0.7706 inches = 4.77 15.90 Gallons h = V = h 14.583195 Sin a = 0.468085 Asin a = 0.22 15.Art Montemayor I.062004 = 9.487 radians Acos a = 1.883683 = 0.508792 Limits of the Equation 0.06 inches 1 Cos a = 0.255 in = Page 45 of 75 14.35379 in 3 54.565584 = 8.183 in = 442. A guppy head is a conical head with its apex level with the top of the cylindrical section of the tank. 2002. and then by adjusting those results using appropriate correction formulas. spherical or torispherical heads where the fluid height. For a spherical head. pp. and a dish-radius parameter. Parameters for Horizontal Cylindrical Tanks with Conical. An ellipsoidal head must be exactly half of an ellipsoid of revolution. as shown in Fig.June 15.no “segment” of an ellipsoid will work. A torispherical head is an American Society of Mechanical Engineers (ASME-type) head defined by a knuckle-radius parameter. These equations allow rapid and accurate fluid-volume calculations. guppy. as shown in Fig. only a hemi ellipsoid is valid .ms_office WorkSheet: Reference Article . 2 graphically illustrate horizontal tank variables. as is true in the case of a spherical head that can be a spherical segment. Guppy or Spherical Heads 1. Exact fluid volumes in elliptical horizontal or vertical tanks can be determined by calculating the fluid volumes of appropriate cylindrical horizontal or vertical tanks using the equations described above. spherical or torispherical heads. Ellipsoidal. and Fig. ellipsoidal. 1 and Fig. 2. 1.D. All variables defining tank shapes required for tank volume calculations are defined in the “Variables and Definitions” sidebar. For concave conical. k.E. 2003 Art Montemayor Determining Vessel Volumes Rev: 0 The following article appeared in "Chemical Processing" magazine on Novermber 17. h. radius R (R > 0) and length L (L > 0) Page 46 of 75 FileName: 76469885. Cylindrical tube of diameter D (D > 0).. |a| < L/2. Ph. depending on fluid height and the shape of the heads (ends) of a horizontal tank or the bottom of a vertical tank. |a| < R.xls. 46-50: Computing Fluid Tank Volumes Updated equations allow engineers to calculate the fluid volumes of many tanks quickly and accurately By Dan Jones. Above diagram is for definition of parameters only. Both heads of a tank must be identical. Horizontal cylindrical tanks Fluid volume as a function of fluid height can be calculated for a horizontal cylindrical tank with either conical. Fig. Calculating fluid volume in a horizontal or vertical cylindrical tank or elliptical tank can be complicated. 3 and Fig. ellipsoidal. P. All volume equations give fluid volumes in cubic units from tank dimensions in consistent linear units. guppy. Figure 1. 4 graphically illustrate vertical tank variables. where R is the radius of the cylindrical tank body. Exact equations now are available for several commonly encountered tank shapes. is measured from the tank bottom to the fluid surface. 2. f. Af This is the cross-sectional area of the fluid in a horizontal tank's cylindrical section.e. of the ellipse defining the cross section of the body of a vertical elliptical tank. r > R and |a| < R 3. 2003 Rev: 0 Art Montemayor Determining Vessel Volumes For spherical head of radius r. However. DA & DB These are the major and minor axes. 7. convex (a > 0) or concave (a < 0). For convex head other than spherical.5 for torispherical heads. i.xls. R This is the radius of the cylindrical section of a horizontal of vertical tank. L > 2|a| for a < 0 Ellipsoidal head must be exactly half of an ellipsoid of revolution 0 < h < D. if a horizontal cylindrical tank has a conical head on one end and an ellipsoidal head on the other end. r This is the radius of a spherical head for a horizontal tank or a spherical bottom of a vertical tank. D > 0. and average the results to get the desired fluid volume. The heads of a horizontal tank can be flat (a = 0). |a| < L/2 for concave ends. 0 < h < 2R for all tanks. L This is the length of the cylindrical section of a horizontal tank. Variables used in Volumetric Equations and their Definitions a This is the distance a horizontal tank's heads extend beyond (a>0) or into (a<0) its cylindrical section or the depth the bottom extends below the cylindrical section of a vertical tank. D This is the diameter of the cylindrical section of a horizontal or vertical tank. h This is the height of fluid in a tank measured from the lowest part of the tank to the fluid surface.ms_office WorkSheet: Reference Article . 0 < a < a . 6. of the ellipse defining the cross section of the body of a horizontal elliptical tank. 0 < k < 0. L > 0.. a = 0. respectively. f > 0. Page 47 of 75 FileName: 76469885. f This is the dish-radius parameter for tanks with torispherical heads or bottoms. fD is the dish radius. The following variables must be within the ranges stated: • • • • • • • |a| < R for spherical heads. one with conical heads and the other with ellipsoidal heads. 4. kD is the knuckle radius. Both heads of a horizontal cylindrical tank must be identical for the equations to work. respectively. for concave head a < 0 L > 0 for a > 0. For instance. For a horizontal tank with flat heads or a vertical tank with a flat bottom.5 for torispherical heads. 5.June 15. calculate fluid volumes of two tanks. DH & DW These are the height and width. if one head is conical. the equations can be combined to calculate the fluid volume of a horizontal tank with heads of different shapes. k This is the knuckle-radius parameter for tanks with torispherical heads or bottoms. the other must be conical with the same dimensions. 041. Figure 2. and Af is the cross-sectional area of fluid in the cylindrical body of the tank in square units consistent with the linear units used for R and h. 2. The fluid volumes are 6.for a conical.72 gal for guppy heads.06. of fluid depth h.. L = 156 in.. each head extending beyond the ends of the cylinder 42 in. ellipsoidal. spherical and “standard” ASME torispherical (f = 1. 2. L = 156 in.939.288 in.06) heads. 4 for tank configurations and dimension parameters. In the Vf equation for torispherical heads. for conical.ms_office WorkSheet: Reference Article . k = 0.931.06.54 gal for conical heads.028. “a” is not required input. 1.96 gal for spherical heads and 2. Find the volumes of fluid. (example 1) and 84 in.11 gal for guppy heads. h = 84 in. The fluid volumes are 2. the parameters are D = 108 in. Vertical cylindrical tanks The fluid volume in a vertical cylindrical tank with either a conical. June 15. (except torispherical).. 6. spherical or torispherical bottom can be calculated.63 gal for torispherical heads. and torispherical heads (use radian angular measure for all trigonometric functions and D/2 = R > 0 for all equations). For these torispherical head examples. in horizontal cylindrical tanks 108 inches [in. h = 36 in.96 gal for ellipsoidal heads.935. where the fluid height. f = 1 and k = 0. 7. ellipsoidal. in a horizontal or vertical cylindrical tank.103. For example 1. spherical and torispherical head.. h. guppy.. For example 2.Art Montemayor Determining Vessel Volumes Vf This is the fluid volume.. ellipsoidal. The equation for Af is given by: Horizontal cylindrical tank examples Two examples can be used to check application of the equations. for fluid depths in the tanks of 36 in. a = 42 in.380. 3 and Fig. Parameters for Horizontal Cylindrical Tanks with Torispherical Heads Page 48 of 75 FileName: 76469885. In the horizontal tank equations. For torispherical heads.] in diameter with cylinder lengths of 156 in.xls. See Fig. it can be calculated from f..90 gal for torispherical heads. and 5.19 gallon (gal) for conical heads.303. f = 1 and k = 0.. which also are defined in the “Variables and Definitions” sidebar.45 gal for ellipsoidal heads. Calculate five times for each fluid depth .180. k and D. is measured from the center of the bottom of the tank to the surface of the fluid in the tank. a = 42 in. the calculated value is “a” = 18.. (example 2). the parameters are D = 108 in. use + (-) for convex (concave) heads. ellipsoidal. guppy.16 gal for spherical heads. 5. 2003 Rev: 0 Horizontal tank equations The following are the specific equations for fluid volumes in horizontal cylindrical tanks with conical. guppy.954. in gallons. Vf is the total volume of fluid in the tank in cubic units consistent with the linear units of tank dimension parameters. spherical. Ellipsoidal or Spherical Bottoms Vertical tank equations The specific equations for fluid volumes in vertical cylindrical tanks with conical. f = 1.60 gal for a spherical bottom and 904. |a| < R. as shown in Fig. Parameters for Vertical Cylindrical Tanks with Conical. a < R for a spherical bottom. • 0 < k < 0. for each example. and the dish radius will be fD.07 gal for a Page 49 of 75 FileName: 76469885. For a spherical bottom. ellipsoidal.06.Art Montemayor June 15. spherical and torispherical bottoms are provided in the Vertical Tank Equations sidebar (use radian angular measure for all trigonometric functions. 583. calculate the fluid volumes for conical. The following parameter ranges must be observed: • a > 0 for all vertical tanks.. where a is the depth of the spherical bottom and R is the radius of the cylindrical section of the tank.67 gal for a conical bottom. spherical and torispherical bottoms.5 for a torispherical bottom. Figure 3. a = 33 in.ms_office WorkSheet: Reference Article . The knuckle radius then will be kD. 783. • f > 0. and k = 0. For example 1. h = 24 in. 2003 Rev: 0 Determining Vessel Volumes A torispherical bottom is an ASME-type bottom defined by a knuckle-radius factor and a dish-radius factor. and D > 0 for all equations). D = 132 in.xls.. ellipsoidal. Parameters for Vertical Cylindrical Tanks with Torispherical Bottoms Vertical cylindrical tank examples Two examples can be used to check application of the equations for vertical cylindrical tanks. Figure 4.. • D > 0. 4. An ellipsoidal bottom must be exactly half of an ellipsoid of revolution.5 for a torispherical bottom. The fluid volumes are 250.36 gal for an ellipsoidal bottom. spherical and torispherical heads with the following measurements: DH = 100 in. Figure 5. In certain cases such as those with torispherical heads and bottoms and spherical heads and bottoms.calculate the volume of a horizontal cylindrical tank with D = DW and a fluid height h' = h(DW/DH) using the equations for horizontal cylindrical tanks with the appropriately shaped heads.Art Montemayor torispherical bottom. it is necessary to distinguish which elliptical axis defines the head or bottom shape and which axis has been proportionately stretched or compressed from the cylindrical tank shape to form the elliptical tank shape.. Page 50 of 75 FileName: 76469885.036. h = 60 in.. the calculated value is a = 22.) of horizontal elliptical tanks with ellipsoidal.251.. Multiply the volume found by DW/DH to get the elliptical tank fluid volume. 2. a = 33 in. 5. L = 156 in.83 gal for an ellipsoidal bottom. this distinction will be made for all cases for the sake of consistency. 2. and D.calculate the volume of a horizontal cylindrical tank with D = DH using the equations for horizontal cylindrical tanks with the appropriately shaped heads. For a torispherical bottom.. parameter "a" is not required input.1 for torispherical heads. but can be calculated from the values of f.46 gal for a spherical bottom and 3.658. and head parameters of each tank defined (1) in a horizontal plane through the tank centerline and (2) in a vertical plane through the tank centerline. DW = 120 in. The heads of horizontal elliptical tanks and the bottoms of vertical elliptical tanks may be any of those described above for the corresponding cylindrical tanks.xls. Horizontal and vertical elliptical tanks The cross-sections of tank bodies of horizontal and vertical tanks with elliptical bodies are ellipses. f = 1. Examples for horizontal elliptical tanks Find the fluid volumes (in gal.8 and k = 0. f = 0. To calculate the fluid volume in a horizontal elliptical tank with the elliptical body oriented in one of the two orientations shown in Fig..06. k. For these examples. not necessity.where the head parameters are defined in the vertical plane through the tank centerline (plane goes through DH) .ms_office WorkSheet: Reference Article . a horizontal elliptical tank must be one of two possible configurations. D = 132 in. therefore.353 in. Multiply the volume found by DH/DW to get the desired elliptical tank fluid volume. for ellipsoidal and spherical heads. 5 . June 15.where the head parameters are defined in the horizontal plane through the tank centerline (plane goes through DW) . fluid height h = 48 in.76 gal for a torispherical bottom.. For this article. The fluid volumes are 2.. where the major and minor axes of the elliptical cross-sections are either vertical or horizontal. shown in Fig. a = 25 in. 5 . 2003 Rev: 0 Determining Vessel Volumes For example 2. Cross-sections of Horizontal Elliptical Tanks To calculate the fluid volume in a horizontal elliptical tank with the elliptical body oriented in one of the two orientations shown in Fig. and k = 0.18 gal for a conical bottom.902. with the assumption that the heads and bottoms are "deformed" proportionately to the deformation of the cylindrical body to form the elliptical body. . (for conical and spherical bottoms). and multiply the volume found by 72/96. f = 0. To calculate the fluid volume in a vertical elliptical tank. For example 2. calculate horizontal cylindrical tank volumes with D = 100 in.ms_office WorkSheet: Reference Article .8 and k = 0. To calculate the fluid volume in a vertical elliptical tank. fluid height h = 53 in.June 15. DB = 72 in. a = 34 in..2 (for the torispherical bottom). f = 0. Use the equations above for a vertical cylindrical tank with the appropriately shaped bottom. x 120/100).2 for the torispherical bottom.554 in. For example 2. respectively. and h = 48. and multiply the volume found by 96/72. a = 34 in. use D = DA.. for ellipsoidal and spherical heads. for example 1 and 22.8 and k = 0. calculate horizontal cylindrical tank volumes with D = 120 in. calculate vertical cylindrical tank volumes with D = 72 in. a = 25 in. Multiply the volume found by DA/DB to get the desired elliptical tank volume. Multiply the volume found by DB/DA to get the elliptical tank volume. f = 0.. and multiply the volume found by 120/100. spherical and torispherical bottoms with the following measurements: DA = 96 in.065 in..2 (for the torispherical bottom). 2003 Rev: 0 For example 1. CP Page 51 of 75 FileName: 76469885. a = 34 in.9 and k = 0.. Use the equations above for a vertical cylindrical tank with the appropriately shaped bottom. and 22. and h = 57..684 in. f = 0. where the bottom parameters are defined in the plane through both the tank centerline and through DB.. and multiply the volume found by 100/120. for conical and spherical bottoms.554 in.xls. where the bottom parameters are defined in the plane through both the tank centerline and through DA. L = 156 in. use D = DB. Examples for vertical elliptical tanks Find the fluid volumes (in gal. The results are summarized in the following table: Calculated values for "a" in the torispherical-bottom cases are 25. for ellipsoidal and spherical heads.1 for torispherical heads. of the ellipse defining the cross-section of the tank body.1 for torispherical heads. a = 25 in. The results are summarized in the following table: Art Montemayor Determining Vessel Volumes The values for "a" in the above torispherical head cases are 27. For a vertical elliptical tank. For example 1.6 in.9 and k = 0. L = 156 in. calculate vertical cylindrical tank volumes with D = 96 in. (for conical and spherical bottoms). for example 2. (48 in.) of vertical elliptical tanks with conical. Head parameters of each tank defined (1) in a plane through the tank centerline and DA and (2) in a plane through the tank centerline and DB. and h = 53 in.. f = 0. for examples 1 and 2.9 and k = 0. and h = 53 in.. respectively. define DA and DB to be the major and minor axes. 2 M 1 .M  where.K ) for ø R  h  2R æ 1 ö 2 K = cos -1 M + M 3 cosh -1 ç ÷ .Art Montemayor June 15. èM ø M = R-h R Ellipsoidal Heads h ö æ V f = A f L + p a h 2 ç1 ÷ 3R ø è Guppy Heads (Eccentric Cone) Page 52 of 75 FileName: 76469885.ms_office WorkSheet: Reference Article . 2003 Rev: 0 Determining Vessel Volumes Horizontal Tank Equations Conical Heads æ 2a R 2 ö ÷÷ (K ) for 0  h  R V f = A f L + çç è 3 ø æ 2a R 2 öæ p ö ÷÷ç ÷  for h = R V f = A f L + çç è 3 øè 2 ø æ 2a R 2 V f = A f L + çç è 3 ö ÷÷(p .xls. 2çç w r ý R(w . 2003 Rev: 0 Determining Vessel Volumes V f = Af L + 2 a R2 h ö 2a æ cos -1 ç1 .r 2 .r ) R(w + r ) r çè R úû è 3 ø z 3 ï è r ø ÷ø êë þ 5.R2 úû For the above 5 spherical heads equations: r= ( a2 + R2 2a  where.R.÷ + 2 R h .ms_office WorkSheet: Reference Article .01D é R 2 2 -1 ê2 r .3 R )(h + R ) 3 R 9 R è ø Spherical Heads 1. For the condition where: p a V f = Af L + 6 (3R 2 2.xls. For the condition where: V f = Af L + h  R.h 2 (2 h . and a  0. For the condition where: h = R and a  R + a2 ) h = D (3R 2 + a2 h=0 or and a  R ) a = 0. R.R. R. For the condition where: V f = Af L + p a 3 3.2 + ç ÷ cos êcos ú .) for convex or (concave)heads w= R-h y= 2 R h . R. For the condition where: a V f = Af L + a ìï 2 r 3 í ïî 3 2 2 é -1 R 2 .x2 dx A z f ú r 2 .R 2 ) + or (. . a  0. and a =  r .01 D a a h  R. .R2 Page 53 of 75 FileName: 76469885.r w ù æ 2 w3 ö z æç y 4 w y z üï æ R ö ö÷ -1 R + r w -1 w ÷÷ tan -1 + + cos .x tan êë w ( ) ù R2 .R æ h ö ÷÷ V f = A f L + p a h 2 çç1 è 3R ø 4. or . and a  0. D. a  0. D.Art Montemayor June 15.h2 z= r 2 . a  0 . R2 June 15.ms_office WorkSheet: Reference Article . Contact him at Dan. La. Garyville. 2003 Rev: 0 Determining Vessel Volumes Torispherical (ASME Flanged & Dished) Heads Jones is a senior process chemist for Stockhausen Louisiana [email protected] z= r 2 .xls.w= R-h Art Montemayor y= 2 R h . Page 54 of 75 FileName: 76469885. Art Montemayor Determining Vessel Volumes Page 55 of 75 June 15.ms_office WorkSheet: Reference Article . 2003 Rev: 0 FileName: 76469885.xls. xls.ms_office WorkSheet: Reference Article . 2003 Rev: 0 FileName: 76469885.Art Montemayor Determining Vessel Volumes Page 56 of 75 June 15. 2003 Rev: 0 FileName: 76469885.Art Montemayor Determining Vessel Volumes Page 57 of 75 June 15.ms_office WorkSheet: Reference Article .xls. xls. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article .Art Montemayor Determining Vessel Volumes Page 58 of 75 June 15. ms_office WorkSheet: Reference Article .Art Montemayor Determining Vessel Volumes Page 59 of 75 June 15. 2003 Rev: 0 FileName: 76469885.xls. ms_office WorkSheet: Reference Article .Art Montemayor Determining Vessel Volumes Page 60 of 75 June 15. 2003 Rev: 0 FileName: 76469885.xls. ms_office WorkSheet: Reference Article .Art Montemayor Determining Vessel Volumes Page 61 of 75 June 15.xls. 2003 Rev: 0 FileName: 76469885. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article .Art Montemayor Determining Vessel Volumes Page 62 of 75 June 15.xls. Art Montemayor Determining Vessel Volumes Page 63 of 75 June 15. 2003 Rev: 0 FileName: 76469885.xls.ms_office WorkSheet: Reference Article . Art Montemayor Determining Vessel Volumes Page 64 of 75 June 15. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article .xls. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article .xls.Art Montemayor Determining Vessel Volumes Page 65 of 75 June 15. xls. 2003 Rev: 0 FileName: 76469885.Art Montemayor Determining Vessel Volumes Page 66 of 75 June 15.ms_office WorkSheet: Reference Article . Art Montemayor Determining Vessel Volumes Page 67 of 75 June 15.xls.ms_office WorkSheet: Reference Article . 2003 Rev: 0 FileName: 76469885. 2003 Rev: 0 FileName: 76469885.xls.Art Montemayor Determining Vessel Volumes Page 68 of 75 June 15.ms_office WorkSheet: Reference Article . xls.Art Montemayor Determining Vessel Volumes Page 69 of 75 June 15. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article . xls.ms_office WorkSheet: Reference Article . 2003 Rev: 0 FileName: 76469885.Art Montemayor Determining Vessel Volumes Page 70 of 75 June 15. xls.ms_office WorkSheet: Reference Article . 2003 Rev: 0 FileName: 76469885.Art Montemayor Determining Vessel Volumes Page 71 of 75 June 15. ms_office WorkSheet: Reference Article . 2003 Rev: 0 FileName: 76469885.Art Montemayor Determining Vessel Volumes Page 72 of 75 June 15.xls. Art Montemayor Determining Vessel Volumes Page 73 of 75 June 15.ms_office WorkSheet: Reference Article .xls. 2003 Rev: 0 FileName: 76469885. xls.Art Montemayor Determining Vessel Volumes Page 74 of 75 June 15. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article . Art Montemayor Determining Vessel Volumes Page 75 of 75 June 15. 2003 Rev: 0 FileName: 76469885.ms_office WorkSheet: Reference Article .xls. Art Montemayor Determining Vessel Volumes June 15.xls WorkSheet: Reference Article . 2003 Rev: 0 Page 76 of 83 FileName: 76469885.