APPLIED PROCESS DESIGN FOR CHEMICAL AND PETROCHEMICAL PLANTS, Volume 1, 3rd Edition

C1)
0
C1)
A-19. A-19.
(Continued). Capacities of Cylinders and Spheres (Continued). Capacities of Cylinders and Spheres
---,---------------- allon 42 Gallon
Sphere
Sphore
Sphere
Sphere
Bar,uls
Diam. Cu. Ft. Gallons 42 G;.illon Snburu Sphere I Diam. Cu. Ft. GallorlS 42 Gallon Sphero Suburu Diam. Cu. Ft. Gallons 4 1� rers Surface Volume Diam. Cu. Ft. Gallons Barrois Surface Volume
Barrels
por
per
,n per per J>Cr Sur tucu Volume ,n per por per Surfacu Volufllu in per per p or in Fool of por in
ft\ol Foot or Foo( of Foot of in Foot Fool of foot ,lf Fuul of on Feet Foot or Foot of Foo t of in in Foot Foot of Fool of in
- --- --- --
'" Ft.
CylimJer CylimJcr Cyl11l<lcr Sq. Ft. Cu. Cyl1111Jur CylultJor Cyl1mJtir Sq. Ft. Cu. "' Ft. Cylin�or Cylinder Cyli ndur S�. Ft. Cu. Ft. Cylinder Cylinder Cylin�er Sq. Ft. Cu. Ft.
-- --- --- ·-- -- ---
30 706.86 5287.7 125.90 2827.4 14137 42 1385.4 10364 246.76 5541.8 38792 54 2290.2 17132 407 .91 9160.9 82448 66 3421.2 25592 609.34 13685 150533
30)4' 718.69 5376.2 128.00 2874.8 14494 42l{ 1402.0 10488 249.70 5607.9 39489 54)4' 2311.5 17291 411 .69 9245.9 83598 66)4 3447.2 25787 613.97 13789 152250
30Yz 730.62 5465.4 130.13 2!l22.5 14856 42)1 1418.6 l0612 252.67 5674.5 40194 54)/i 2332.8 17451 415 .49 9331.3 84759 6672 3473.2 25982 618.61 13893 153980
30% 742.64 5555.4 '32.27 2970.6 15224 42}1 1435.4 10737 255.65 5714.5 40908 54% 2354.3 17611 419 .32 9417.1 85931 6671 3499.4 26177 623.27 13998 155723
31 754.77 5646.1 134.43 3019.1 15599 43 1452.2 108631258.65 5808.8 41630 55 2375.8 17772 423 .15 9503.3 87114 67 3525.7 26374 627.95 14103 157479
31 )4' 766.99 5737.5 136.61 3068.0 15979 43),{ 1469. 1 10990 261 .66 5876.5 42360 55J,i 2397.5 17934 427 .01 9589.9 88307 67�i 3552.0 26571 632.64 14208 159249
31,Yz 779.31 5829.7 138.80 3117.2 16366 43H 1486.2 11117 ,264.70 5944.7 43099 55!1 2419.2 18097 430 .88 9676.9 89511 677':! 3578.5 26769 637.35 14314 161031
31% 791.73 5922.6 141.01 3166.9 16758 43% 1503.3 11245 '267.75 6013.2 43846 55:)1 2441.1 18260 434 .77 9764.3 90726 67% 3605.0 26967 642.08 14420 162827
32 804.25 6016.2 143.24 3217.0 17157 44 1520.5 11374 270.82 6082.1 44602 56 2463.0 18245 438 .68 9852.0 91952 68 3631.7 27167 646.83 14527 164636
32J{ 816.86 6110.6 145.49 3267.5 17563 44�{ 1537.9 11504 273.90 6151.4 45367 56}{ 2485.0 18589 442 .61 9940.2 93189 68)i 3658.4 27367 651.59 14634 166459
32Yz 829.58 6205.7 147.75 3318.3 17974 441":! 1555.3 11634 277.01 6221.1 46140 56Yz 2507.2 18755 446 .55 10029 94437 68Yz 3685.3 27568 656.38 14741 168295
32% 842.39 6301.5 150.04 3369.6 18392 44% 1572.8 11765 280.13 6291.2 46922 56% 2529.4 18921 450 .51 10118 95697 68�� 3712.2 27769 661.18 14849 170144
33 855.30 6398.1 152.34 3421.2 18817 45 1590.4 11897 283.27 6361. 7 47713 57 2551.8 19088 454 .49 10207 96967 69 3739.3 27972 665.99 14957 172007
33)4' 868.31 6495.4 154.65 3473.2 19247 45)'.i' 1608.2 12030 286.42 6432.6 48513 57)4' 2574.2 19256 458 .48 10297 98248 69)4 3766.4 28175 670.83 15066 173883
33),2 881.41 6593.4 156.99 3525.7 19685 45Vi 1626.0 12163 28().60 6503.9 49321 67)":! 2596.7 1!:l425 462 .50 10387 99541 69Y2 3793.7 28379 675.68 15175 175773
33;),� 894.62 6692.2 159.34 3578.5 20129 4571 1643.9 12297 292.79 6575.5 50139 57;4 2619.4 19594 466 .53 10477 100845 69% 3821.0 28583 680.55 15284 177677
34 907.92 6791. 7 161.71 3631.7 20580 46 1661.9 12432 296.00 6647.6 50965 58 2642.1 19764 470 .57 10568 102160 70 3848.5 28788 685.44 15394 179594
34),{ 921.32 6892.0 164.09 3685.3 21037 46'{ 1680.0 12567 299.22 6720.1 51800 58!4 2664.9 19935 474 .64 10660 103487 70!4 3876.0 28994 G90.3·t 15504 181525
34,Yz 934.82 6992.9 166.50 3739.3 21501 46Vi 1698.2 12704 302.47 6792.9 52645 58),1 2687.8 20106 478 .72 10751 104825 70)1 3903.6 29201 695.27 15615 183470
34% 948.42 7094.7 168.92 3793.7 21972 4GX 1716.5 12841 305.73 6866.1 53499 58% 2710.9 20279 482 .82 10843 106175 70% 3931.4 29409 700.21 15725 185429
35 962.11 7197.1 171.36 3848.5 22449 47 1734.9 12978 309.01 6939.8 54362 59 2734.0 20452 486 .94 10936 107536 71 3959.2 29617 705.16 15837 187402
35>,( 975.91 7300.3 173.82 3903.6 22934 47){ 1753.5 13117 312.30 7013.8 55234 597-i' 2757.2 20625 491 .08 11029 108909 71),;i' 3987. 1 29826 710.14 15948 189388
35Yz 989.80 7404.2 176.29 3959.2 23425 47)2 1772. 1 13256 315.62 7088.2 56115 59,Yz 2780.5 20800 495 .23 11122 110293 71Yz 4015.2 30035 715.13 16061 191389
35% 1003.8 7508.9 178.78 4015.2 23924 47:)1 1790.8 13396 318.95 7163.0 57006 59% 2803.9 20975 499 .40 11216 111690 71% 4043.3 30246 720.14 16173 193404
36 1017.9 7614.2 181.29 4071.5 24429 48 1809.G 13536 322.30 7238.2 57906 60 2827.4 21151 503 .59 11310 113097 72 4071.5 30457 725.17 16286 195432
36!,.;i' 1032.1 7720.4 183.82 4128.2 2 4942 48).f 1828.5 13678 325.66 7313.8 58815 60�{ 2851.0 21327 507 .79 11404 114517 72>{ 4099.8 30669 730.21 16399 197475
3GYz 1046.3 7827.2 186.36 4185.4 2 5461 48)'2 1847.5 13820 329.05 7389.8 59734 60Yz 2874.8 21505 512 .02 11499 115948 72Y2 4128.2 30881 735.27 16513 199532
36% 1060.7 7934.8 188.92 4242.9 2 5988 48% 1866.5 13963 332.45 7466.2 60663 60:\i 2898.6 21683 516 .26 11594 117392 72Yt 4156.8 31095 740.35 16627 201603
37 1075.2 8043.1 191.50 4300.8 2 6522 49 1885.7 14106 335.86 7543.0 61601 61 2922.5 21862 520 .51 11690 118847 73 4185.4 31309 745.45 16742 203689
37)4' 1089.8 8152.2 194.10 4359.2 27063 49'{ 1905.0 14251' 339.30 7620.1 62549 61 )4' 2946.5 22041 524 .79 11786 120314 73),i 4214.1 31524 750.56 16856 205789
37,Yz I 104.5 8262.0 196.71 4417.9 27612 49),z 1924.4 14396 342. 75 7697. 7 63506 61 J,� 2970.6 22221 529 .08 11882 121793 73Yi 4242.9 31739 755.70 16972 207903
37:)4 1119.2 8372.5 199.35 4477.0 2 8168 49:)1 1943.9 14541 346.23 7775.6 64473 Gt% 2994.8 22402 533 .39 11979 123285 73% 4271.8 31956 760.85 17087 210032
38 1134.1 8483.8 201.99 4536.5 2 8731 50 1963.5 14688 349.71 7854.0 65450 62 3019.1 22584 537 .72 12076 124788 74 4300.8 32173 766.01 17203 212175
38y.( 1149.1 8595.8 204.66 4596.3 2 9302 50){ 198.1.2 14835 353.22 7932.7 66437 62>{ 3043.5 22767 542 .06 12174 126304 74!4 4329.9 32390 771.20 17320 214332
38YiJ 1164.2 8708.5 207.35 4656.6 2 9880 SOY.\ 2003.0 14983 356.74 8011.8 67433 62Y2 3068.0 22950 546 .43 12272 127832 74Yz 4359.2 32609 776.40 17437 216505
38% 1179.3 8822.0 210.05 4717.3 30466 50% 2022.8 15132 360.28 8091.4 68439 62% 3092.6 23134 550 .81 12370 129372 74% 4388.5 32828 781.62 17554 218692
39 1194.6 8936.2 212.77 4778.4 3 1059 51 2042.8 15281 363.84 8171.3 69456 63 3117.2 23319 55 5.21 12469 130924 i 75 4417.9 33048 786.86 17671 220893
39)4' 1210.0 9051.1 215.50 4839.8 31660 51 �.t' 2062.9 15432 367.42 8251.6 70482 63)4' 3142.0 23504 559 .62 12568 132489 4447.4 33269 792.11 17789 223110
I 75!/i
39!,1 1225.4 9166.8 218.26 4901.7 32269 5H� 2083.1 15582 371.01 8332.3 71519 6372 3166.9 23690 56 4.05 12668 134066 75Y.\ 4477.0 33490 797.38 17908 225341
39% 1241.0 9283.2 221.03 49G3.9 3 2886 51;!4' 2103.3 15734 374.62 8413.4 72565 63% 3191.9 23877 56 8.50 12768 135656 I 75% 4506 7 33712 802.67 18027 227587
40 1256.6 9400.3 223.82 5026.5 33 510 52 2123.7 15887 378.25 8494.9 73622 64 3217.0 24065 57 2.97 12868 137258 I 76 4536.5 33935 807.98 18146 229847
40)4' 1272.4 9518.2 226.62 5089.6 3 4143 52t,i' 2144.2 16040 381.90 8576.7 74689 64)4' 3242.2 24253 57 7.46 12969 138873 , 76)4' 4566.4 34159 813.30 18265 232123
40,Yz 1288.2 9636.8 229.45 5153.0 3 4783 52!·2 2164.8 16193 385.56 8659.0 75766 64.l/2 3267.5 24442 58 1.96 13070 140500 4596.] 34383 818.64 18385 234414
40% 1304.2 9756.1 232.29 5216.8 3 5431 52% 2185.4 16348 389.21 8741.7 76854 64% 3292.8 24632 58 6.48 13171 142141 I 76J,2 4626.4 34608 824.00 18506 236719
76%
41 1320.3 9876.2 235.15 5281.0 3 6087 53 2206.2 16503 392.94 8824.7 77952 65 3318.3 24823 59 1.02 13273 143793 I 77 4656.6 34834 829.38 18627 239040
417-i' 1336.4 9997.0 238.02 5345.6 36751 53}.( 2227.0 16659 396.65 8908.2 79060 65)4' 3343.9 25014 5.57 13376 145459 77>{ 4686.9 35061 834.77 18748 241376
41 Yz 1352.7 10119. 240.92 5410.6 37423 5372 2248.0 16816 400.39 8992.0 80179 65Yz 3369.6 25206 59 .14 13478 147137 77)/i 4717.3 35288 840.19 18869 243727
600
41% 1369.0 10241. 243.83 5476.0 38104 53%' 2269.1 16974 404.14 9076.3 81308 246093
65% 3395.3 25399 60 4.73 13581 148828 77% 4747.R 35516 845.62 18991
I

C1)
0
C1)
A-19. A-19.
(Continued). Capacities of Cylinders and Spheres (Continued). Capacities of Cylinders and Spheres
---,---------------- allon 42 Gallon
Sphere
Sphore
Sphere
Sphere
Bar,uls
Diam. Cu. Ft. Gallons 42 G;.illon Snburu Sphere I Diam. Cu. Ft. GallorlS 42 Gallon Sphero Suburu Diam. Cu. Ft. Gallons 4 1� rers Surface Volume Diam. Cu. Ft. Gallons Barrois Surface Volume
Barrels
por
per
,n per per J>Cr Sur tucu Volume ,n per por per Surfacu Volufllu in per per p or in Fool of por in
ft\ol Foot or Foo( of Foot of in Foot Fool of foot ,lf Fuul of on Feet Foot or Foot of Foo t of in in Foot Foot of Fool of in
- --- --- --
'" Ft.
CylimJer CylimJcr Cyl11l<lcr Sq. Ft. Cu. Cyl1111Jur CylultJor Cyl1mJtir Sq. Ft. Cu. "' Ft. Cylin�or Cylinder Cyli ndur S�. Ft. Cu. Ft. Cylinder Cylinder Cylin�er Sq. Ft. Cu. Ft.
-- --- --- ·-- -- ---
30 706.86 5287.7 125.90 2827.4 14137 42 1385.4 10364 246.76 5541.8 38792 54 2290.2 17132 407 .91 9160.9 82448 66 3421.2 25592 609.34 13685 150533
30)4' 718.69 5376.2 128.00 2874.8 14494 42l{ 1402.0 10488 249.70 5607.9 39489 54)4' 2311.5 17291 411 .69 9245.9 83598 66)4 3447.2 25787 613.97 13789 152250
30Yz 730.62 5465.4 130.13 2!l22.5 14856 42)1 1418.6 l0612 252.67 5674.5 40194 54)/i 2332.8 17451 415 .49 9331.3 84759 6672 3473.2 25982 618.61 13893 153980
30% 742.64 5555.4 '32.27 2970.6 15224 42}1 1435.4 10737 255.65 5714.5 40908 54% 2354.3 17611 419 .32 9417.1 85931 6671 3499.4 26177 623.27 13998 155723
31 754.77 5646.1 134.43 3019.1 15599 43 1452.2 108631258.65 5808.8 41630 55 2375.8 17772 423 .15 9503.3 87114 67 3525.7 26374 627.95 14103 157479
31 )4' 766.99 5737.5 136.61 3068.0 15979 43),{ 1469. 1 10990 261 .66 5876.5 42360 55J,i 2397.5 17934 427 .01 9589.9 88307 67�i 3552.0 26571 632.64 14208 159249
31,Yz 779.31 5829.7 138.80 3117.2 16366 43H 1486.2 11117 ,264.70 5944.7 43099 55!1 2419.2 18097 430 .88 9676.9 89511 677':! 3578.5 26769 637.35 14314 161031
31% 791.73 5922.6 141.01 3166.9 16758 43% 1503.3 11245 '267.75 6013.2 43846 55:)1 2441.1 18260 434 .77 9764.3 90726 67% 3605.0 26967 642.08 14420 162827
32 804.25 6016.2 143.24 3217.0 17157 44 1520.5 11374 270.82 6082.1 44602 56 2463.0 18245 438 .68 9852.0 91952 68 3631.7 27167 646.83 14527 164636
32J{ 816.86 6110.6 145.49 3267.5 17563 44�{ 1537.9 11504 273.90 6151.4 45367 56}{ 2485.0 18589 442 .61 9940.2 93189 68)i 3658.4 27367 651.59 14634 166459
32Yz 829.58 6205.7 147.75 3318.3 17974 441":! 1555.3 11634 277.01 6221.1 46140 56Yz 2507.2 18755 446 .55 10029 94437 68Yz 3685.3 27568 656.38 14741 168295
32% 842.39 6301.5 150.04 3369.6 18392 44% 1572.8 11765 280.13 6291.2 46922 56% 2529.4 18921 450 .51 10118 95697 68�� 3712.2 27769 661.18 14849 170144
33 855.30 6398.1 152.34 3421.2 18817 45 1590.4 11897 283.27 6361. 7 47713 57 2551.8 19088 454 .49 10207 96967 69 3739.3 27972 665.99 14957 172007
33)4' 868.31 6495.4 154.65 3473.2 19247 45)'.i' 1608.2 12030 286.42 6432.6 48513 57)4' 2574.2 19256 458 .48 10297 98248 69)4 3766.4 28175 670.83 15066 173883
33),2 881.41 6593.4 156.99 3525.7 19685 45Vi 1626.0 12163 28().60 6503.9 49321 67)":! 2596.7 1!:l425 462 .50 10387 99541 69Y2 3793.7 28379 675.68 15175 175773
33;),� 894.62 6692.2 159.34 3578.5 20129 4571 1643.9 12297 292.79 6575.5 50139 57;4 2619.4 19594 466 .53 10477 100845 69% 3821.0 28583 680.55 15284 177677
34 907.92 6791. 7 161.71 3631.7 20580 46 1661.9 12432 296.00 6647.6 50965 58 2642.1 19764 470 .57 10568 102160 70 3848.5 28788 685.44 15394 179594
34),{ 921.32 6892.0 164.09 3685.3 21037 46'{ 1680.0 12567 299.22 6720.1 51800 58!4 2664.9 19935 474 .64 10660 103487 70!4 3876.0 28994 G90.3·t 15504 181525
34,Yz 934.82 6992.9 166.50 3739.3 21501 46Vi 1698.2 12704 302.47 6792.9 52645 58),1 2687.8 20106 478 .72 10751 104825 70)1 3903.6 29201 695.27 15615 183470
34% 948.42 7094.7 168.92 3793.7 21972 4GX 1716.5 12841 305.73 6866.1 53499 58% 2710.9 20279 482 .82 10843 106175 70% 3931.4 29409 700.21 15725 185429
35 962.11 7197.1 171.36 3848.5 22449 47 1734.9 12978 309.01 6939.8 54362 59 2734.0 20452 486 .94 10936 107536 71 3959.2 29617 705.16 15837 187402
35>,( 975.91 7300.3 173.82 3903.6 22934 47){ 1753.5 13117 312.30 7013.8 55234 597-i' 2757.2 20625 491 .08 11029 108909 71),;i' 3987. 1 29826 710.14 15948 189388
35Yz 989.80 7404.2 176.29 3959.2 23425 47)2 1772. 1 13256 315.62 7088.2 56115 59,Yz 2780.5 20800 495 .23 11122 110293 71Yz 4015.2 30035 715.13 16061 191389
35% 1003.8 7508.9 178.78 4015.2 23924 47:)1 1790.8 13396 318.95 7163.0 57006 59% 2803.9 20975 499 .40 11216 111690 71% 4043.3 30246 720.14 16173 193404
36 1017.9 7614.2 181.29 4071.5 24429 48 1809.G 13536 322.30 7238.2 57906 60 2827.4 21151 503 .59 11310 113097 72 4071.5 30457 725.17 16286 195432
36!,.;i' 1032.1 7720.4 183.82 4128.2 2 4942 48).f 1828.5 13678 325.66 7313.8 58815 60�{ 2851.0 21327 507 .79 11404 114517 72>{ 4099.8 30669 730.21 16399 197475
3GYz 1046.3 7827.2 186.36 4185.4 2 5461 48)'2 1847.5 13820 329.05 7389.8 59734 60Yz 2874.8 21505 512 .02 11499 115948 72Y2 4128.2 30881 735.27 16513 199532
36% 1060.7 7934.8 188.92 4242.9 2 5988 48% 1866.5 13963 332.45 7466.2 60663 60:\i 2898.6 21683 516 .26 11594 117392 72Yt 4156.8 31095 740.35 16627 201603
37 1075.2 8043.1 191.50 4300.8 2 6522 49 1885.7 14106 335.86 7543.0 61601 61 2922.5 21862 520 .51 11690 118847 73 4185.4 31309 745.45 16742 203689
37)4' 1089.8 8152.2 194.10 4359.2 27063 49'{ 1905.0 14251' 339.30 7620.1 62549 61 )4' 2946.5 22041 524 .79 11786 120314 73),i 4214.1 31524 750.56 16856 205789
37,Yz I 104.5 8262.0 196.71 4417.9 27612 49),z 1924.4 14396 342. 75 7697. 7 63506 61 J,� 2970.6 22221 529 .08 11882 121793 73Yi 4242.9 31739 755.70 16972 207903
37:)4 1119.2 8372.5 199.35 4477.0 2 8168 49:)1 1943.9 14541 346.23 7775.6 64473 Gt% 2994.8 22402 533 .39 11979 123285 73% 4271.8 31956 760.85 17087 210032
38 1134.1 8483.8 201.99 4536.5 2 8731 50 1963.5 14688 349.71 7854.0 65450 62 3019.1 22584 537 .72 12076 124788 74 4300.8 32173 766.01 17203 212175
38y.( 1149.1 8595.8 204.66 4596.3 2 9302 50){ 198.1.2 14835 353.22 7932.7 66437 62>{ 3043.5 22767 542 .06 12174 126304 74!4 4329.9 32390 771.20 17320 214332
38YiJ 1164.2 8708.5 207.35 4656.6 2 9880 SOY.\ 2003.0 14983 356.74 8011.8 67433 62Y2 3068.0 22950 546 .43 12272 127832 74Yz 4359.2 32609 776.40 17437 216505
38% 1179.3 8822.0 210.05 4717.3 30466 50% 2022.8 15132 360.28 8091.4 68439 62% 3092.6 23134 550 .81 12370 129372 74% 4388.5 32828 781.62 17554 218692
39 1194.6 8936.2 212.77 4778.4 3 1059 51 2042.8 15281 363.84 8171.3 69456 63 3117.2 23319 55 5.21 12469 130924 i 75 4417.9 33048 786.86 17671 220893
39)4' 1210.0 9051.1 215.50 4839.8 31660 51 �.t' 2062.9 15432 367.42 8251.6 70482 63)4' 3142.0 23504 559 .62 12568 132489 4447.4 33269 792.11 17789 223110
I 75!/i
39!,1 1225.4 9166.8 218.26 4901.7 32269 5H� 2083.1 15582 371.01 8332.3 71519 6372 3166.9 23690 56 4.05 12668 134066 75Y.\ 4477.0 33490 797.38 17908 225341
39% 1241.0 9283.2 221.03 49G3.9 3 2886 51;!4' 2103.3 15734 374.62 8413.4 72565 63% 3191.9 23877 56 8.50 12768 135656 I 75% 4506 7 33712 802.67 18027 227587
40 1256.6 9400.3 223.82 5026.5 33 510 52 2123.7 15887 378.25 8494.9 73622 64 3217.0 24065 57 2.97 12868 137258 I 76 4536.5 33935 807.98 18146 229847
40)4' 1272.4 9518.2 226.62 5089.6 3 4143 52t,i' 2144.2 16040 381.90 8576.7 74689 64)4' 3242.2 24253 57 7.46 12969 138873 , 76)4' 4566.4 34159 813.30 18265 232123
40,Yz 1288.2 9636.8 229.45 5153.0 3 4783 52!·2 2164.8 16193 385.56 8659.0 75766 64.l/2 3267.5 24442 58 1.96 13070 140500 4596.] 34383 818.64 18385 234414
40% 1304.2 9756.1 232.29 5216.8 3 5431 52% 2185.4 16348 389.21 8741.7 76854 64% 3292.8 24632 58 6.48 13171 142141 I 76J,2 4626.4 34608 824.00 18506 236719
76%
41 1320.3 9876.2 235.15 5281.0 3 6087 53 2206.2 16503 392.94 8824.7 77952 65 3318.3 24823 59 1.02 13273 143793 I 77 4656.6 34834 829.38 18627 239040
417-i' 1336.4 9997.0 238.02 5345.6 36751 53}.( 2227.0 16659 396.65 8908.2 79060 65)4' 3343.9 25014 5.57 13376 145459 77>{ 4686.9 35061 834.77 18748 241376
41 Yz 1352.7 10119. 240.92 5410.6 37423 5372 2248.0 16816 400.39 8992.0 80179 65Yz 3369.6 25206 59 .14 13478 147137 77)/i 4717.3 35288 840.19 18869 243727
600
41% 1369.0 10241. 243.83 5476.0 38104 53%' 2269.1 16974 404.14 9076.3 81308 246093
65% 3395.3 25399 60 4.73 13581 148828 77% 4747.R 35516 845.62 18991
I

A-19. A-19.
( Continued). Capacities of Cylinders and Spheres ( Continued). Capacities of Cylinders and Spheres
--·---···----·-· --·---------. ---------
4
��
4 11 4 01an1./ Onuons ,Ji;�:;�[�" l'I I Gauons ia ; :;"
Diam. Cu. Ft. Gallons ia ; :;n Sphere Sphoro Diam. Cu. Ft. Gallons ia�:�\�" Sphere 1--S����- Co. Fl. Sphere Sphere Diani. I Cu Fl. � � 1 Sphere Sphere
in per per pnr Surface Volumo in ner per por Surface Volume Hl _ per pr.r our Surface Volume I ,n por per por Surface Volume
Feet Fo?t of Fo?l or Foot 0 , in in Foot Foot of Foot of Foot of in in Feet Foot of Foot of foot of rn ,n Feet Foot of Foot or Fool of in ,n
Cyl,ndor Cylondor Cylindor Sq. Ft. Cu. Ft. I Cylinder Cy!indor Gylindor Sq. Ft. Cu. Ft. Cyhnuer Cyl,nclcr Cyl1r1dor Sq Fl Cu. Ft. � Cylinder Cyl,ndcr Cyliruler Sq. Ft. Cu. Ft.
---- ----- ---- ---- --- ---- -- --· ---- ----- -------- 102 - �;;:� �;� 2�:: ��·;:4 1?685155564·7· 1•
78 4778.4 35745 851.06119113 248475 90 6361.7 47589 1133.1 25447 381704 [ 1 114 I 10207 76354 .181 �-� ���2�- . ;75735
78),{ 4809.0 35974 856.53 19236 250872. 90),,.i 6397.1 47854 1139.4 25588 384893 102 1., 8211.4 61425 1462.5 32846 559743 '114'.il 10252 76689 1825.9 41007 780849
78Yz 4839.8 36204 862.01 19359 253284 90 Yz 6432.6 48119 1145. 7 25730 388101 102],� 8251.6 61726 1469.7 33006 563859, 114!".! 10297 77025 1833.9 41187 785986
78% 4870.7 36435 867.51 19483 255712 90% 6468.2 48385 1152.0 25873 391326 102};; 8291.9 62028 1476.8 33168 567994 114% 10342 7736211841.9 41367 791146
79 4901.7 36667 873.02 19607 258155 91 6503.9 48652 1158.4 26016 394569 103 8332.3 62330 1484.0 33329 572151 115 10387 77699 Hl50.0 41548 796328
79� 4932.7 36899 878.56 19731 260613 91),,.i 6539.7 48920 1164.8 26159 397830 1031.; 83.72.8 62633 1491.3 33491 576327 115'.i 10432 78038 1858.0 41728 801533
79Yz 4963.9 37133 884.11 19856 263087 91Yz 6575.5 49189 1171.2 26302 401109 103]:i 8413.4 62936 1498.5 33654 580523 115!:1 10477 78376 1866.1 41910 806760
79% 4995.2 37367 889.68 19981 265577 91 % 6611.5 49458 1177.6 26446 404405 101% 8454.1 63241 1505.7 33816 584740 115)1 10523 78716 1874.2 42091 812010
80 5026.5 37601 895.27 20106 268083 i 92 6647.6 49728 1184.0 26590 407720 104 8494.9 63546 1513.0 33979 588977 : 116 10568 79057 1882.3 42273 817283
80� 5058.0 37837 900.87 20232 270604 ' 92 l:( 6683.8 49998 1190.4 26735 411053 104 1., 8535.8 63852 1520.3 34143 593235 ! 116.1., 10614 79398 1890.4 42456 822579
80Yz 5089.6 38073 906.49 20358 273141 92Yz 6720.1 50270 1196.9 26880 414404 104\i 8576.7 64159 1527.6 34307 597513 .116!1 10660 79739 1898.6 42638 827897
8617.8
11
80% 5121.2 38310 912.13 20485 2756931 92% 6756.4 50542 1203.4 27026 417773 104% 64466 1534.9 34471 601812 I 116% 10705 80082 1906.7 42822 833238
81 5153.0 38547 917.79 20612 278262 93 6792.9 50814 1209.9 27172 421160 105 8659.0 64774 1542.2 34636 606131 117 10751 80425 1914.9 43005 838603
an1 5184.9 38785 923.46 20739 280846 93),,.i 6829.5 51088 1216.4 27318 424566 105 1.1 8700.3 65083 1549.6 34801 610471 117'.i 10797 807G9 1923.1 43189 843990
81 Yz 5216.8 39024 929.15 20867 283447 93Yz 6866.1 51362 1222.9 27465 427990 105h 8741.7 65392 1557.0 34967 614831. 117):1 10843 81114 1931.3 43374 849400
619213 1 1•
81% 5248.9 39264 934.86 20995 286063 93% 6902.9 51637 1229.5 27612 431432 1osr1 8783.2 65703 1564.3 35133 117;-:, 10890 81460 1939.5 43558 854833
82 5281.0 39505 940.59 21124 288696 94 6939.8 51913 1236.0 27759 434893 lOG 8824.7 66014 1571.8 35299 623615 118 10936 81806 1947.8 43744 860290
6280371
82),1 5313.3 39746 946.33 21253 291344 94),,.i 6976.7 52190 1242.6 27907 438372 106', 88664 66325 1579.2 35466 118].i 10982 82153 1956.0 43929 865769
82Yz 5345.6 39988 952.09 21382 294009 94Yz 7013.8 52467 1249.2 28055 441870 106!·i 8908.2 66638 1586.6 35613 632481 118\i 11029 82501 1964.3 44115 871272
82% 5378.1 40231 957.87 21512 296690 94% 7051.0 52745 1255.8 28204 445386 106% 8950.1 66951 1594.1 35800 636945 118% 11075 82849 1972.6 44301 876798
83 5410.6 40474 963.67 21642 299387 95 7088.2 53024 1262.5 28353 448920 107 8992.0 67265 1601.5 35968 641431 119 11122 83199 1980.9 44488 882347
83� 5443.3 40718 969.48 21773 302100 95),;' 7125.6 53303 1269.1 28502 452474 107!:, 9034.1 67580 1609.0 36136 645938 119':i 11169 83548 1989.2 44675 887920
83),,:i 5476.0 40963 975.32 21G04 304830 95),1 7163.0 53583 1275.8 28652 456046 107)-<z 9076.3 67895 1616.6 36305 650465 119Y2 11216 83899 1997.6 44863 893516
83% 55C8.8 41209 981.16 22035 307576 95% 7200.6 53864 1282.5 28802 459637 107% 9118.5 68211 1624.1 36474 655014 119% 11263 84251 2006.0 45051 899136
84 5541.8 41455 987.03 22167 310339 96 7238.2 54146 1289.2 28953 463247 108 9160.9 68528 1631.6 36644 659584 120 11310 84603 2014.3 45239 904779
910445
108):, 9203.3 68846 1639.2 36813 664175 120)., 11357
84956 2022.8 45428
84},4 5574.8 41702 992.92 22299 313118 96),4 7276.0 54428 1295.9 29104 466875
84Yz 5607.9 41950 998.82 22432 315914 96Yz 7313.8 54711 1302.6 29255 470523 108)2 9245.9 69164 1646.8 36984 668787 120Vi 11404 85.109 2031.2 45617 916136
921850
108% 9288.6 69483 1654.4 37154
673421
120% 11452
85664 2039.6 45806
84% 5641.2 42199 1004.7 22565 318726 96% 7351.8 54995 1309.4 29407 474189
85 5674.5 42448 1010.7 22698 321555 97 7389.8 55280 1316.2 29559 477874 109 9331.3 69801 1662.0 37325 678076, 121 11499 86019 2048.1 45996 927587
121!:i 11547 86374 2056.5 46186
1091,, 9374.2 70124
1669.6 37497
682752
933349
85� 5707.9 42698 1016.6 22832 324401 97)� 7428.0 55565 1323.0 29712 481579 1 687450 121 >l 11594 86731 2065.0 46377 939134
85Yz 5741.5 42949 1022.6 22966 327263 97Yz 7466.2 55851 1329.8 29865 485302 109. � 9417.1 70445 1677.3 37668 692169 121 ;-:, 11642 87088 2073.5 46568 944943
109% 9460.2 70767 1684.9 37841
85% 5775.1 43201 1028.6 23100 330142 97% 7504.5 56138 1336.6 30018 489045
86 5808.8 43453 1034.6 23235 333038 98 7543.0 56425 1343.5 30172 492807 110 1 9503.3 71090 1692.6 38013 696910 122 1 11690 87446 2082.1 46759 950776
701672
11738 87805 2090.6 46951
956633
122 :i
86� 5842.6 43706 1040.6 23371 335951 98!4 7581.5 56714 1350.3 30326 496588 110 .j 9546.6 71413 1700.J 38186 706457 122H 11786 88165 2099.2 47144 962514
1708.o :18360
110!
9589.9 71737
2
86Yz 5876.5 43960 1046.7 23506 338881 98 �1 7620.1 57003 1357.2 30481 500388 110% 9633.4 72062 1715,8 38533 711262 122% 11834 88525 2107.7 47336 968419
86% 5910.6 44214 1052.7 23642 341828 98% 7658.9 57292 1364.1 30635 504208
9676.9 72388 172.1.5 38708
111
87 5944.7 44469 1058.8 23779 344791 99 7697.7 57583 1371.0 30791 508047 111 .j 9720.5 72715 1731.3 38882 716090 123 11882 88886 2116.3 47529 974;348
980101
720939 123!1 11931
89247 21'24.9 47723
1
87!,,:i' 5978.9 44725 1064.9 23916 347772 99).:( 7736.6 57874 1377.9 30946 511906 11g 9764,3 73042 1739.1 39057 725810 123),i 11979 89610 2133.6 47916 986278
2
87Yz 6013.2 44982 1071.0 24053 350770 99Yz 7775.6 58166 1384.9 31103 515784 111% 9808.1 73370 1746.9 39232 730704 123% 12028 89973 2142.2 48111 992280
87% 6047.6 45239 1077.1 24190 353785 99% 7814.8 58458 1391.9 31259 519682
112 9852.0 73698 1754.7 39408 735619 124 12076 90337 2150.9 48305 998306
88 6082.1 45497 1083.3 24328 356818 100 7854.0 58752 1398.9 31416 523599 112!, 9896.1 74028 1762.6 39584 740556 124):, 12125 90701 2159.6 48500 1004356
88).i 6116.7 45756 1089.4 24467 359868 100\4 7893.3 59046 1405.9 31573 527536 112)';; 9940.2 74358 1770.4 39761 745515 124)-:i 12174 91067 2168.3 48695 1010431
88Yz 6151.4 46016 1095.6 24606 362935 100Yz 7932.7 59341 1412.9 31731 531492 112% 9984.4 74G89 1778,3 39938 750496 124% 12223 91433 2177.0 48891 1016530
88% 6186.2 46276 1101.8 24745 366019 100% 7972.2 59636 1419.9 31889 535468
113 10029 75020 1786.2 40115 755499 125 12272 91800 2185.7 49087 1022654
89 6221.1 46537 1108.0 24885 369121 101 8011.8 59933 1427.0 32047 539464 113 .j 10073 75353 1 794.1 40293 760525 125 ):, 12321 92167 2194.5 49284 1028802
89),,.i 6256.1 46799 1114.3 25025 372240 1101 ! 4 8051.6 60230 1434.0 32206 543480 113 :110118 75686 1802.0 40471 765572 12c,)1 12370 92536 2203.2 49481 1034975
89Yz 6291.2 47062 1120.5 25165 375377 l101Yzl8091.4 60528 1441.1 32365 547516 113 110162 76019 1810.0 40649 770642 125% 12420 92905 2212.0 49678 1041172
89% 6326.4 47325 1126.8 25306 378531 i101% 8131.3 60826 1448.2 32525 551572

A-19. A-19.
( Continued). Capacities of Cylinders and Spheres ( Continued). Capacities of Cylinders and Spheres
--·---···----·-· --·---------. ---------
4
��
4 11 4 01an1./ Onuons ,Ji;�:;�[�" l'I I Gauons ia ; :;"
Diam. Cu. Ft. Gallons ia ; :;n Sphere Sphoro Diam. Cu. Ft. Gallons ia�:�\�" Sphere 1--S����- Co. Fl. Sphere Sphere Diani. I Cu Fl. � � 1 Sphere Sphere
in per per pnr Surface Volumo in ner per por Surface Volume Hl _ per pr.r our Surface Volume I ,n por per por Surface Volume
Feet Fo?t of Fo?l or Foot 0 , in in Foot Foot of Foot of Foot of in in Feet Foot of Foot of foot of rn ,n Feet Foot of Foot or Fool of in ,n
Cyl,ndor Cylondor Cylindor Sq. Ft. Cu. Ft. I Cylinder Cy!indor Gylindor Sq. Ft. Cu. Ft. Cyhnuer Cyl,nclcr Cyl1r1dor Sq Fl Cu. Ft. � Cylinder Cyl,ndcr Cyliruler Sq. Ft. Cu. Ft.
---- ----- ---- ---- --- ---- -- --· ---- ----- -------- 102 - �;;:� �;� 2�:: ��·;:4 1?685155564·7· 1•
78 4778.4 35745 851.06119113 248475 90 6361.7 47589 1133.1 25447 381704 [ 1 114 I 10207 76354 .181 �-� ���2�- . ;75735
78),{ 4809.0 35974 856.53 19236 250872. 90),,.i 6397.1 47854 1139.4 25588 384893 102 1., 8211.4 61425 1462.5 32846 559743 '114'.il 10252 76689 1825.9 41007 780849
78Yz 4839.8 36204 862.01 19359 253284 90 Yz 6432.6 48119 1145. 7 25730 388101 102],� 8251.6 61726 1469.7 33006 563859, 114!".! 10297 77025 1833.9 41187 785986
78% 4870.7 36435 867.51 19483 255712 90% 6468.2 48385 1152.0 25873 391326 102};; 8291.9 62028 1476.8 33168 567994 114% 10342 7736211841.9 41367 791146
79 4901.7 36667 873.02 19607 258155 91 6503.9 48652 1158.4 26016 394569 103 8332.3 62330 1484.0 33329 572151 115 10387 77699 Hl50.0 41548 796328
79� 4932.7 36899 878.56 19731 260613 91),,.i 6539.7 48920 1164.8 26159 397830 1031.; 83.72.8 62633 1491.3 33491 576327 115'.i 10432 78038 1858.0 41728 801533
79Yz 4963.9 37133 884.11 19856 263087 91Yz 6575.5 49189 1171.2 26302 401109 103]:i 8413.4 62936 1498.5 33654 580523 115!:1 10477 78376 1866.1 41910 806760
79% 4995.2 37367 889.68 19981 265577 91 % 6611.5 49458 1177.6 26446 404405 101% 8454.1 63241 1505.7 33816 584740 115)1 10523 78716 1874.2 42091 812010
80 5026.5 37601 895.27 20106 268083 i 92 6647.6 49728 1184.0 26590 407720 104 8494.9 63546 1513.0 33979 588977 : 116 10568 79057 1882.3 42273 817283
80� 5058.0 37837 900.87 20232 270604 ' 92 l:( 6683.8 49998 1190.4 26735 411053 104 1., 8535.8 63852 1520.3 34143 593235 ! 116.1., 10614 79398 1890.4 42456 822579
80Yz 5089.6 38073 906.49 20358 273141 92Yz 6720.1 50270 1196.9 26880 414404 104\i 8576.7 64159 1527.6 34307 597513 .116!1 10660 79739 1898.6 42638 827897
8617.8
11
80% 5121.2 38310 912.13 20485 2756931 92% 6756.4 50542 1203.4 27026 417773 104% 64466 1534.9 34471 601812 I 116% 10705 80082 1906.7 42822 833238
81 5153.0 38547 917.79 20612 278262 93 6792.9 50814 1209.9 27172 421160 105 8659.0 64774 1542.2 34636 606131 117 10751 80425 1914.9 43005 838603
an1 5184.9 38785 923.46 20739 280846 93),,.i 6829.5 51088 1216.4 27318 424566 105 1.1 8700.3 65083 1549.6 34801 610471 117'.i 10797 807G9 1923.1 43189 843990
81 Yz 5216.8 39024 929.15 20867 283447 93Yz 6866.1 51362 1222.9 27465 427990 105h 8741.7 65392 1557.0 34967 614831. 117):1 10843 81114 1931.3 43374 849400
619213 1 1•
81% 5248.9 39264 934.86 20995 286063 93% 6902.9 51637 1229.5 27612 431432 1osr1 8783.2 65703 1564.3 35133 117;-:, 10890 81460 1939.5 43558 854833
82 5281.0 39505 940.59 21124 288696 94 6939.8 51913 1236.0 27759 434893 lOG 8824.7 66014 1571.8 35299 623615 118 10936 81806 1947.8 43744 860290
6280371
82),1 5313.3 39746 946.33 21253 291344 94),,.i 6976.7 52190 1242.6 27907 438372 106', 88664 66325 1579.2 35466 118].i 10982 82153 1956.0 43929 865769
82Yz 5345.6 39988 952.09 21382 294009 94Yz 7013.8 52467 1249.2 28055 441870 106!·i 8908.2 66638 1586.6 35613 632481 118\i 11029 82501 1964.3 44115 871272
82% 5378.1 40231 957.87 21512 296690 94% 7051.0 52745 1255.8 28204 445386 106% 8950.1 66951 1594.1 35800 636945 118% 11075 82849 1972.6 44301 876798
83 5410.6 40474 963.67 21642 299387 95 7088.2 53024 1262.5 28353 448920 107 8992.0 67265 1601.5 35968 641431 119 11122 83199 1980.9 44488 882347
83� 5443.3 40718 969.48 21773 302100 95),;' 7125.6 53303 1269.1 28502 452474 107!:, 9034.1 67580 1609.0 36136 645938 119':i 11169 83548 1989.2 44675 887920
83),,:i 5476.0 40963 975.32 21G04 304830 95),1 7163.0 53583 1275.8 28652 456046 107)-<z 9076.3 67895 1616.6 36305 650465 119Y2 11216 83899 1997.6 44863 893516
83% 55C8.8 41209 981.16 22035 307576 95% 7200.6 53864 1282.5 28802 459637 107% 9118.5 68211 1624.1 36474 655014 119% 11263 84251 2006.0 45051 899136
84 5541.8 41455 987.03 22167 310339 96 7238.2 54146 1289.2 28953 463247 108 9160.9 68528 1631.6 36644 659584 120 11310 84603 2014.3 45239 904779
910445
108):, 9203.3 68846 1639.2 36813 664175 120)., 11357
84956 2022.8 45428
84},4 5574.8 41702 992.92 22299 313118 96),4 7276.0 54428 1295.9 29104 466875
84Yz 5607.9 41950 998.82 22432 315914 96Yz 7313.8 54711 1302.6 29255 470523 108)2 9245.9 69164 1646.8 36984 668787 120Vi 11404 85.109 2031.2 45617 916136
921850
108% 9288.6 69483 1654.4 37154
673421
120% 11452
85664 2039.6 45806
84% 5641.2 42199 1004.7 22565 318726 96% 7351.8 54995 1309.4 29407 474189
85 5674.5 42448 1010.7 22698 321555 97 7389.8 55280 1316.2 29559 477874 109 9331.3 69801 1662.0 37325 678076, 121 11499 86019 2048.1 45996 927587
121!:i 11547 86374 2056.5 46186
1091,, 9374.2 70124
1669.6 37497
682752
933349
85� 5707.9 42698 1016.6 22832 324401 97)� 7428.0 55565 1323.0 29712 481579 1 687450 121 >l 11594 86731 2065.0 46377 939134
85Yz 5741.5 42949 1022.6 22966 327263 97Yz 7466.2 55851 1329.8 29865 485302 109. � 9417.1 70445 1677.3 37668 692169 121 ;-:, 11642 87088 2073.5 46568 944943
109% 9460.2 70767 1684.9 37841
85% 5775.1 43201 1028.6 23100 330142 97% 7504.5 56138 1336.6 30018 489045
86 5808.8 43453 1034.6 23235 333038 98 7543.0 56425 1343.5 30172 492807 110 1 9503.3 71090 1692.6 38013 696910 122 1 11690 87446 2082.1 46759 950776
701672
11738 87805 2090.6 46951
956633
122 :i
86� 5842.6 43706 1040.6 23371 335951 98!4 7581.5 56714 1350.3 30326 496588 110 .j 9546.6 71413 1700.J 38186 706457 122H 11786 88165 2099.2 47144 962514
1708.o :18360
110!
9589.9 71737
2
86Yz 5876.5 43960 1046.7 23506 338881 98 �1 7620.1 57003 1357.2 30481 500388 110% 9633.4 72062 1715,8 38533 711262 122% 11834 88525 2107.7 47336 968419
86% 5910.6 44214 1052.7 23642 341828 98% 7658.9 57292 1364.1 30635 504208
9676.9 72388 172.1.5 38708
111
87 5944.7 44469 1058.8 23779 344791 99 7697.7 57583 1371.0 30791 508047 111 .j 9720.5 72715 1731.3 38882 716090 123 11882 88886 2116.3 47529 974;348
980101
720939 123!1 11931
89247 21'24.9 47723
1
87!,,:i' 5978.9 44725 1064.9 23916 347772 99).:( 7736.6 57874 1377.9 30946 511906 11g 9764,3 73042 1739.1 39057 725810 123),i 11979 89610 2133.6 47916 986278
2
87Yz 6013.2 44982 1071.0 24053 350770 99Yz 7775.6 58166 1384.9 31103 515784 111% 9808.1 73370 1746.9 39232 730704 123% 12028 89973 2142.2 48111 992280
87% 6047.6 45239 1077.1 24190 353785 99% 7814.8 58458 1391.9 31259 519682
112 9852.0 73698 1754.7 39408 735619 124 12076 90337 2150.9 48305 998306
88 6082.1 45497 1083.3 24328 356818 100 7854.0 58752 1398.9 31416 523599 112!, 9896.1 74028 1762.6 39584 740556 124):, 12125 90701 2159.6 48500 1004356
88).i 6116.7 45756 1089.4 24467 359868 100\4 7893.3 59046 1405.9 31573 527536 112)';; 9940.2 74358 1770.4 39761 745515 124)-:i 12174 91067 2168.3 48695 1010431
88Yz 6151.4 46016 1095.6 24606 362935 100Yz 7932.7 59341 1412.9 31731 531492 112% 9984.4 74G89 1778,3 39938 750496 124% 12223 91433 2177.0 48891 1016530
88% 6186.2 46276 1101.8 24745 366019 100% 7972.2 59636 1419.9 31889 535468
113 10029 75020 1786.2 40115 755499 125 12272 91800 2185.7 49087 1022654
89 6221.1 46537 1108.0 24885 369121 101 8011.8 59933 1427.0 32047 539464 113 .j 10073 75353 1 794.1 40293 760525 125 ):, 12321 92167 2194.5 49284 1028802
89),,.i 6256.1 46799 1114.3 25025 372240 1101 ! 4 8051.6 60230 1434.0 32206 543480 113 :110118 75686 1802.0 40471 765572 12c,)1 12370 92536 2203.2 49481 1034975
89Yz 6291.2 47062 1120.5 25165 375377 l101Yzl8091.4 60528 1441.1 32365 547516 113 110162 76019 1810.0 40649 770642 125% 12420 92905 2212.0 49678 1041172
89% 6326.4 47325 1126.8 25306 378531 i101% 8131.3 60826 1448.2 32525 551572

608 Applied Process Design for Chemical and Petrochemical Plants

A-19.
( Concluded). Capacities of Cylinders and Spheres
..... -- -··-----------
Ft. �2 Gallon 42 Gallon
Diam. Cu. G,1llons Barrois Sphr.re Snhcre Diam, Cu. Ft. Ga!lons Barrels Splu=iro Sphere
in per per por Sur r.rce Volumo in por por por Surface Vulumc
Feet Foot nf Fool of Fnot of ,n in Feel Foot of Foot of Foot of in in
Cylintlcr Cylimler C,-Jmder Sq. Ft. Cu. Ft. Cytin�o, Cylinder Cylin�er Sq. Ft. Cu. Ft.
. ···--- --- ·-- --- -
126 12469 93274 2220.8 49876 1047394 138 14957 111887 2664.0 59828 1376055
12H4 12519 93645 2229.6 50074 1053641 138 J.1 15011 112293 2673.6 60045 1383547
126)/.;i 12568 94016 2238.5 50?.73 1059913 13871 15066 112699 2683.3 60263 1391067
126% 12618 94388 2247.3 50471 10662091 138% 15120 113107 2693.0 60481 1398613
127 12668 94761 ?.?.56.2 50671 1072531 139 15175 113514 2702.7 60699 1406187
10788771
127.).� 12718 95134 2265.1 50870 139 ! ,j 15229 113923 2712.5 60917 1413788
127Y2 12768 95508 2274.0 51071 1085248 139},i 15284 114333 2722.2 61136 1421416
127% 12818 95883 2282.9 51271 1091645. 139% 15339 114743 2732.0 61356 1429072
128 12868 96259 ?.291.9 51472 1098066 140 15394 115154 2741.8 61575 1436755
128!;' 12918 96635 2300.8 51673 1104513 140!,'i 15449 115565 2751.6 61795 1444466
128}2 12969 97013 2309.8 51875 1110985 140)/.;i 15504 115978 2761.4 62016 1452204
128% 13019 97390 2318.8 52077 1117481 140% 15559 116391 2771.2 62237 1459970
129 13070 9776') 2327.8 52279 1124004 141 15615 116805 2781.1 62458 1467763
129!-i 13121 98148 2336.9 52482 11 30551 ! 14 1 ):i' 15670 117219 2790.9 62680 1475584
129}1 13171 98528 2345.9 52685 11371241141 J:1 15725 117634 2800.8 62902 1483433
129% 13222 98909 2355.0 52889 1143723 141 % 15781 118050 2810.7 63124 1491310
130 13273 99291 2364.1 53093 1150347 142 15837 118467 2820.6 63347 1499214
130!., 13324 99673 2373.2 53297 1156996 142Ji 15893 118885 2830.6 63570 1507146
130),2 13376 100056 2382.3 53502 1163671 142)1 15948 119303 2840.5 63794 1515107
130% 13427 100440 2391.4 53707 1170371 142% 16005 119722 2850.5 64018 1523095
131 13478 100824 2400.6 53913 1177098 143 16061 120142 2860.5 64242 1531111
131 ),1 13530 101209 2409.7 54119 1183850 143!,i 16117 120562 2870.5 64467 1539156
131 J/.;i 13581 101595 2418.9 54325 1190627 143):1 16173 120983 2880.6 64692 1547228
131% 13633 101982 2428.1 54532 1197431 143% 16230 121405 2890.6 64918 1555329
132 13685 102369 2437.4 54739 1204260 144 16286 121828- 2900.7 65144 1563458
132)i 13737 102757 2446.6 54947 1211116 144!.i 16343 122251 2910.7 65370 1571615
132)'1 13789 103146 2455.9 55155 1217997 144)'1 16399 122675 2920.8 65597 1579800
132% 13841 103536 2465.1 55363 1224904 144% 16456 123100 2931.0 65824 1588014
133 13893 103926 2474.4 55572 1231838 145 16513 123526 2941.1 66052 1596256
133)i 13945 104317 2483.7 55781 16570 123952 2951.2 66280 1604527
"'"" ' ., . ( 16627 124379 2961.4 66508
133)\i 13998 104709 2493.1 55990 1245783 145)\i 16128?.6
133% 14050 105102 2502.4 56200 1252795 I 145;)1 16684 124807 2971.6 66737 1621154
134 14103 105495 2511.8 56410 1259833 146 16742 125235 2981.8 66966 1629511
134).i 14155 105889 2521.2 56621 12668981 146):i 16799 125665 2992.0 67196 1637896
134)1 14208 106284 2530.6 56832 1273988 146 ,l � 16856 126095 3002.3 67426 1646310
134% 14261 106679 2540.0 57044 1281106 146% 16914 126525 3012.5 67656 1654752
135 14314 107075 2549.4 57256 1288249 147 16972 126957 3022.8 67887 1663224
135!J 14367 107472 2558.9 57468 1295420: 14 n:i 17029 127389 3033.1 68118 1671724
135)1 14420 107870 2568.3 57680 1302616 147)2 17087 127822 3043.4 68349 1680253
135% 14473 108268 2577.8 57893 13098401147% 17145 128256 3053.7 68581 1688811
136 14527 108667 2587.3 58107 1317090 148 17203 128690 3064.0 68813 1697398
136) i 14580 109067 2596.8 58321 1324366 1481i 17262 129125 3074.4 69046 1706015
136!,'2 14634 109468 2606.4 58535 1331 67011148 t 1 17320 129561 3084.8 69279 1714660
136% 14687 109869 2615.9 58750 1339000 148% 17378 129998 3095.2 69513 1723334
137 14741 110271 2625.5 58965 1346357, 149 17437 130435 3105.6 69746 1732038
13n� 14795 110674 2635.1 59180 1353741 149), 17495 130873 3116.0 69981 1740771
137 !-1 141)49 111078 2644.7 59396 1361152 149}'1 17554 131312 3126.5 70215 1749533
137% 14903 111482 2654.3 59612 1368590 149% 17613 131751 3136.9 70450 1758325
150 17671 132192 3147.4 70686 1767146

Appendix 609
A-20.
Tank Capacities, Horizontal Cylindrical-
Contents of Tanks with Flat Ends
When Filled to Various Depths

hin mctrr l iepth of liquid, in inches = A
of fortk f111/ 1--------------------------------------------------t
3•
9• 12·
6"
i11rhr� lnnk --�---·
12" .S.R" l.i!i 2.�4
1x· 11.2'2 l.4!i :l.�r, r..r,1
2·1" 2:u,0 1.70 4.GO 8.0S I l.7!i 15 • 18 • 21"
-- -- ----- ------
-·-
3()" :rn.72 l.!ll 5.21 !l.27 l:J.72 IR.1G
36" !i2.K� 2.12 i'i.7!1 111.:J,1 1:,.4:J 20.R!i 21;.41
42" 7 t.!17 2.2s 6.:11 11.:i 1 1 ri.!17 n.01 211.47 :1: •. nn 24" 21 • 30 •
---- -- --- - --· ---- ·---- -- -- >----- t----- Tu ascertain the contents or a tank over
4R" !1·1.1'1 2.1', s.ts 12.2(1 18.:J� 2',.J(I :12.211 :rn.:,4 47.(:0 one-half full: Let A - depth of unfilled
51" 1 J.�.n., 2.liO 7.22 l:1.(1,1 m.ss 21i.!li :14.72 42.80 .11.1>� :,!l.-1!1 portion. Find from thr tahle the quantity
60" l·lliY!I 2.i:i 7.li·I J:l.k2 211.!ll 2R.72 :)7.111\ 4!i.82 :,·1.�i li4.II i:l.44 33• 36" 39• corresponding to a ,lepth A. Subtract this
--- ---- ---+------l---- ---,--1--- --·-r- --+--·i---l----+--1 quantity from the contents of a full tank.
-
66" Iii.Tl 2.H!l 8.04 1,\,:,1; 22.117 :m.:li :111.2s 4R.,;,-, :,s.:m r,R.41 71\.!i!l 8R.Rli
72" 211.:,2 :J.1'2 R.42 J:,.21i 2:1.Ji :ll.92 41.:11; :,1.12 fd.71 72.4', 83.41 9•1.54 !O,,,;r,
78" 24�.2·1 :J.J!i �.iR J',.'>1 2-L2i :i:1.41 4:J.34 :;:l.RI> 61.Ri if..27 87.97 99.90 111.97 124.l:l 42• 45" 48"
- -- - -- --+---+----+--- -- �- ,, __ , __ , __ _,__ __ , _
84" 2xi.!H> :1.�1; n.12 l'i.:,i 2.;.2.1 :1-1.s,, ,J',.2.1 ,,r •. 2!1 n;.s, 1n.n1 n2.10 !04.!>8 1;1.s:; 110.87 14:J.n'>
90· :J:111.4!1 :u:1 1u1; 11.20 21;,211 :1r,.21 47.W, ,.�.,;1 10.1:, s1.:rn %.fl 111'1..�1 12:J.4.i 1:n.28 1:,1.2:1 u;,;.2,;
96" 1ili.1:2 :1.:;o n.i!I 17.RO 27. t:i :11.:,2 18.R I J;ll.�4 n.12 81i. ;:1 I 011.:in 114.44 I 28.7n J 4.l.40 \ .',8.17 171.0f, l.�R.111 51 • 54 • 57 • 60 •
·- - - ·------!--,--+--,--- -- -··-- ------- ....---- --- -- -- - -- ---- -- --- --
--
--!-----!
I()�• 124..',I) :1.1;1 10.10 IR.17 28.01 :in.no .',11.4!1 fi�.!ln 7fi. lR 8n.94 104.20 I IR.89 11.1.n2 149.2:, lfi4.81 !RO.:,.l 1%.:!7 212.2:i .
101," 1rn.111 :u1 10.:rn iR.!14 2R.!111 10.11:1 ,,2.14 1i,>.11!:117H.74 n:i.04 101.81 121.11 1:18.87 1,,4.80 1n10 1s1.11 204.:n 221.14 2:18.0!i .
114" !j:J0.2!i :J.78 lll.H 1!1.4!1 2!1.75 11.n :,:J.7:\ fi7.lll 81.21 Ofi.05 111.4:l 127.:n 14:1.r,.1 IG0.1.1 177.31 194.fill 212.05 22!1.6.1 247.:l7 2f,:i.l1
120" 5H7.:,4 :1.!>L 10.98 20.02 30.57 42.19 .',:i.21\ GQ.116 83.US 08.0!i 114.87 131.:12 148.25 IG5.58 183.27 201.24 21n.46 237.87 256.43 27:i.08 203.77
Contents in U.S. gallons per 1 foot of length.
By permission, The Permutit Co., Inc., Data Book, 1953.
A-21.
Tank Capacities, Horizontal Cylindrical-
Contents of Standard Dished Heads
When Filled to Various Depths
/1"'111,Ar lJepth of liquid, in inches - A
of h,·,lfl fr,1/ �--------------------------------------------, II
,_
inrhr.� Ar,ui 3• - 5• I i i 9• 12• Radius= Diameter
12" 0.4'.I 0.0:i 0.20,. . tr --=- � 1,
18'' 1.1r. 11.117 0.:12 O.f>8 J /ef "-�
24" 1.22 � 1 � o_:_4_1, o.95 1.r,1 _1!_� __ I_!_· __ __:!_'.' j __ ff
r,
-- ��
__
30" fi .. 111 0.10 0.4!1 l.18 2.10 J. ts
:lfi" I0.8H II.II 0.51) un 2.,l4 3.'12 :,.4·1 !����
4:!'' 17.28 0.12 0.ft3 1.r>CJ 2.!14 4.fi4 fi.:i7 8.G4 24" 27" 30"
-- ---· - ·--- ·-·· -To ascertain the contents of a head over
Ml" 2!i.i�l n.1:1 o.es l.7!i :u1 ;;_2n 7.G2 JO.IQ 12.8'1 one-half full: Let A - depth of unfilled
54. 3G.7'2 11.14 tl.74 1.no 1.lH !i.!ll 8.W 11.fi:, 14.05 IR.1fi port.ion. Vind from the table the quantity
60" 511.17 n.: 4 ll.>!2 2.117 :l.nR G.4'1 !1.54 13.03 1r,.87 20.nr. 2:,.1s 33' 36 • 39" corrrspnnding to a depth h, Subtract this
quantily from the contents or a full head.
66" 67.01 n.1!"1 O.R3 2. l!l 4.2:i f..!l� lfl.1fi 14.10 IS.f,8 2:1.1:1 2R.42 :l1.:.2
72 • R7.fl.l IJ.lfi 0.88 2.:12 4.:-,2 ;.4; 11.;r. 1r.As 20.18 2.·,.H :n.-1r. :i;.41 n.:;2
78" 110.ft•i 0. ii 0.�.1 2A4 4.in 7.!17 11.n4 J(i.li.', 22.02 27.n7 34.1!1 41.IG 4S.ZII .,,,.:i1 42" 45• 48"
-1------1--�-·-··---I--·- ---- --- -- ---t----·--
;·J �� !i!} ) � 1.;-4 ���I=��!
81" 118.22 11.!S 0.98 2.;,9 5.0i 8.41 12.r,0 li.7R nr.n :10.11 37.rn 44.7', ,,2.r,7 Bn.P..1 r,9_11
90" 170.111 11.18 l.0(1 2.fi8 :i.:i:J 8.�I 11 .' J.1 rs .. ,r. 2•,.12 :12.1H :J!l.nn 4s_n :,n.11!1 fifi.14 1s.,,2 ss.oo .. �� - �
96'' 2111;_:12 0.20 1.07 2.8:1 ti.!")\\ !l.:Jli 14.11 1�.n112r..r,1114_1; 42.'>2 s1.r,.1 n1.1:1 11.22 81.tiG n:14 103.16 51" 54"_! 57• so·
----- �-- ---- --- -- ·--- -·- -------- --- --------·;� --;;;;� -;!J-.��
102" 247..18 o.�� l.H 1.111 .1.8!1 U.87 11m 21.111 28.l J :lo. I� 4:i.l!l :11.n1 G.'i.:31
108 • 2!J'l.i7 11.211 1.13 :1.1,:1 U.04 10.21 i:>.:,u 21.!i:J 2(147 :1s.o:i 47.,;6 :i7.H7 1;�1.14 81.n., 9.1.51 !Of>.47 l W.7li 113.2fi 146.881 .....
114" �\,1!",.:J I 0.21 I.I fi :1.12 ().25 10.:i;, lli.l)(j 22.811 ao.t» :J!J.7:1 4�.RJ 60.88 7�.85 8:,.01 nn5 111.t11 127.!ifi 142,,11 157.51 112.;s
120" 402.2'/ 0.21 I.IQ 3.23 6.-17 !0.9J lf,.LlR 2:l.70 �l.% 41.4:1 !i2.114 6:J.i3 7r,.40 89.9.1 104.32 J 19.39 135.04 151.15 157.621181.32 201.13
Contents in U.S. gallons for one head only. This table
is only approximate, but close enough for practical use.
By permission, The Permutit Co., Inc., Data Book, 1953.

610 A-22.
Miscellaneous Formulas
( Courtesy of Chicago Bridge and Iron Co.)
1. Area of Roofs. 7. Heads for Horizontal Cylindrical Tanks:
Umbrella Roofs: Hemi-ellipsoidal Heads have an ellipsoidal cross section, usually
D = diameter of tank in feet. with minor axis equal to one half the major axis-that is, depth
= � D, or more.
Surface area in } { = 0.842 D 2 ( when radius = diameter)
square feet = 0.882 D" (when radius= 0.8 diameter) Dished or Basket Heads consist of a spherical segment nor-
mally dished to a radius equal to the inside diameter of the
Conical Roofs: tank cylinder (or within a range of 6 inches plus or minus)
Surface area in} { = 0.787 o• (when pitch is% in 12) and connected to the straight cylindrical flange by a "knuckle"
square feet = 0.792 o• (when pitch is lY:i in 12) whose inside radius is usually not less than 6 per cent of the
inside diameter of the cylinder nor less than 3 times the thick-
2. Average weights. ness of the head plate. Basket heads closely approximate hemi-
ellipsoidal heads.
Steel -490 pounds per cubic foot-specific gravity 7.85
Wrought iron -485 pounds per cubic foot-specific gravity 7.77 Bumped Heads consist of a spherical segment joining the
tank cylinder directly without the transition "knuckle." The
Cast iron --450 pounds per cubic foot-specific gravity 7.21 radius = D, or less. This type of head is used only for pressures
l cubic foot air or gas at 32° F., 760 m.m. barometer = mole- of 10 pounds per square inch or less, excepting where a com-
cular weight x 0.0027855 pounds. pression ring is placed at the junction of head and shell.
Sur/ace Area of Heads:
3. Expansion in steel pipe = 0.78 inch per 100 lineal
feet per 100 degrees Fahr. change in temperature = (7a) Hemi-ellipsoidal Heads:
0
0.412 inch per mile per degree Fahr. temperature S =,.. R [l + K (2-K) J
2
change. S = surface area in square feet
R = radius of cylinder in feet
4. Linear coefficients of expansion per degree increase K = ratio of the depth of the head (not including the
in temperature: straight flange) to the radius of the cylinder
Per Degree Per Degree The above formula is not exact but is within limits of
practical accuracy.
Fahrenheit Centigrade
STRUCTURAL STEEL-A-7 (7b) Dished or Basket Heads:
70° to 200° F 0.0000067 Formula (7a) gives surface area within practical limits.
21.1 ° lo 93° C . 0.0000121 (7c) Bumped Heads:
STAINLESS STEEL· TYPE 304 S = ,.. R' (1 + K")
32° to 932° F 0.0000102 S, R, and K as in formula (7a)
0° lo 500° C. . 0.0000184
ALUMINUM Volume of Heads:
-76° to 68° F 0.0000120
-60° to 20° C. . 0.0000216 ( 7 d) Hemi-ellipsoidal Heads:
V =%,..KR"
5. To determine the net thickness of shells for horizontal R = radius of cylinder in feet
cylindrical pressure tanks: K = ratio of the depth of the head ( not including the
straight flange) to the radius of the cylinder
T= 6PD
s (7e) Dished or Basket Heads:
P = working pressure in pounds per square inch Formula (7d) gives volume within practical limits.
D = diameter of cylinder in feet (70 Bumped Heads:
V = Y:l ,.. K R' (1 + Ifs K 2)
S = allowable unit working stress in pounds per square inch V, Kand R as in formula (7d)
T = Net thickness in inches Note: K in above formulas may be determined as follows:
Resulting net thickness must be corrected to gross or actual Herni-ellipsoidal heads-K is known
thickness by dividing by joint efficiency.
Dished Heads-K = M- \I (M-1) (M + l - 2m)
Bumped Heads- K = [M- V M"-1]
6. To determine the net thickness of heads for cylindrical
pressure tanks: MR = principal radius of head in feet
mR = radius of knuckle in feet
(6a) Ellipsoidal or Bumped Heads: R = radius of cylinder in feet
T= 6PD M= MR m=mR
s R R
T, P and D as in formula 5 For bumped heads m = o
(6b) Dished or Basket Heads:
T = 10.6P(MR) 8. Total volume or length of shell in cylindrical tank
s with ellipsiodal or hemispherical heads:
T, S and P as in formula 5 V = Total volume
MR = principal radius of head in feet L = Length of cylindrical c
Resulting net thickness of heads is both net and gross thick- shell I I )IT
O
_
ness if one piece seamless heads are used, otherwise net thick- KD = Depth of head .....___- -
I
ness must be corrected to gross thickness as above. v = ,.. D' KD)icol �
Formulas 5 and 6 must often be modified to comply with -4- (L + 1\1:i
various engineering codes, and state and municipal regulations. .,,.oz
Calculated gross plate thicknesses are sometimes arbitrarily L= (V7-) -1\l;iKD
increased to provide an additional allowance for corrosion. 4

Appendix 611
A-23.
A-22. Decimal Equivalents in Inches,
(Continued). MisceUaneous Formulas Feet and Millimeters
9. Volume or contents of partially filled horizontal cylin- In. Equiv. for Decimals Millimeter Equiv. In. Equiv. for
drical tanks: Decimal of In. for Decimal of In. Decimal of Ft.
=-===========-
= ::.
(9a) Tank cylinder or shell. (straight �'11 Y64
portion only; <,. e- 1l.i2 .0156 0.397 o/i6
Q = RL[( � 8 � °)-sinecose J ' _ ; c �� .0313 0.794 %
2
%
.0469
l.191
%,
gi1
Q = partially filled volume or 1!is .0625 1.588 l�fo
1.984
.0781
contents in cubic feet
R = radius of cylinder in feel %2 .0938 2.381 lYs
%1
2.778
L = length of straight portion of cylinder in feet % .1094 3.175 l'l'J.6
.1250
%., .1406 3.572 111.!
1 u,,fo
The straight portion or flange of the heads must be considered %2 .1563 3.969
a part of the cylinder. The length of flange depends upon the 1%
diameter of tank and thickness of head but ranges usually be· llft-,1 .1719 4.366 I 211\o
tween 2 and 4 inches. o/\6 .1875 4.763 2 1 4
lo/61 .2031 5.159 2'l)6
a = !::,. R = depth of liquid in feet �<2 .2188 5.556
6. = R == a rano 1 10.i .2344 5.953 2%
.
a
o/io
2 1
R-a Yi .2500 6.350
Cos e = l -6., or -R 1%1 .2656 6.747 3
3o/i6
e = degrees %2 .2813 7.144 3%
1%1 .2969 7.541 3il/i6
(9b) Herni-ellipsoidal Heads: o/is .3125 7.938 3%
Q=%V6."0-%6.l
�
Q = partially filled volume or 2�"' .3281 8.334 3 1 6
111:i2
.3438
contents in cubic' feet 2o/t;t 8.7.'II 4 1 ,fi
V = total volume of one head % .3594 9.128 4o/i6
41h
9.525
.3750
per formula (7d) 2g1M .3906 9.922 4111i6
6. = 1f == a ratio 1%2 .4063 10.319 47/s
2'V54 .4219 10.716
a = !::,. R = depth of liquid in feet 'vio .4375 11.113 51A6
514
R = radius of cylinder in feet 2%4 .4531 1 l.509 Sy\.,
1%2 .4688 11.906 5%
(9c) Dished or Basket Heads:
Formula (9b) gives partially filled volume within 3%1 .4844 12.303 5 1 �'io
practical limits, and formula (7d) gives V within 112 .5000 12.700 6
practical limits. 33/t;t .5156 13.097 6o/i.6
( 9d) Bumped Heads: 1*2 .5313 13.494 6%
Formula (9b) gives partially filled volume within 35/&1 .5469 13.891 69/i.6
practical" limits, and formula (7f) gives V. o/:is 14.288 6-%
Note: To obtain the volume or quantity of liquid in partially 3-VG! .5625 14.684 6 1 �16
.5781
filled tanks, add the volume per formula (9a) for the cylinder lo/32 .5938 15.081
or straight portion to twice (for 2 heads) the volume per 3%-1 .6094 15.478 71Ai
7'!,'16
formula (9b), (9c) or (9d) for the type of head concerned. % .6250 15.875 7%
41AJ1 .6406 16.272 711116
IO. Volume or contents of partially .filled hemi-ellipsoidal 2'732 .6563 16.669 17h
4%,
heads with major axis vertical: 1:yfo .6719 17.066 81 1fo
17.463
.6875
814
Q = Partially filled vol- 4%1 .7031 17.859 B1A6
ume or contents in 2ijl32
cubic feet 4%1 .7188 18.256 8%
.7344
18.653
V = Total volume of one % .7500 19.050 81o/16
9
head per formula 4o/c,1 .7656 19.447 93A6
(7d) �L�Jm 2%2 .7813 19.844 9%
R = Radius of cylinder
in feet 5�(,4 .7969 20.241 90A.6
R I: lo/]6 .8125 20.638 9%
(lOa) Upper Head: ------l <l � I 04 .8281 21.034 9 1 i}fo
Q = 112 V .6(1-%1::,.') % .8438 21.431 101,,s
5.)i1
a .8594 21.828 10-'Yio
!::,. = KR = a ratio 'Vs .8750 22.225 101h
a = 6. KR = depth "°Vca .8906 22.622 10 1 1h6
of liquid in feet 21)32 .9063 23.019 107/s
"%, .9219 23.416 111116
(10b) Lower Head: l(j,fo .9375 23.813 111Ji
Q = Ph V .6.'(l-Y:J6.) 6Vt,1 .9531 24.209 lH'l.6
!::,. = KR = a ratio 3Y:J2 .9688 24.606 11%
.
a
25.003
�
.9844
63,,(;l
12
a = 6. KR = depth 1 1.0000 25.400 11 1 6
of liquid in feet

A-24. A-24.

(By permission of Buffalo Tank Dir., Bethlehem Steel Corp.) ( Continued).

PROPERTIES OF THE CIRCLE AREA OF PLANE FICURES
Triangle: Base x Y2 perpendicular height.
,Fses-a) (s-h) \s-11),
Circumference c 6.28318 r - 3.14159 d s = Y2 sum of the three sides a, b and c.
Diameter c 0.31831 circumference
Area - 3.141 59 r• Trapezium: Sum of nron of the two triangles.
Trapezoid: },� sum of parallel sides x perpendicular height.
rr A
0
Arc a - 1800 - 0.017453 r A• Parallelogram: Huse x perpendicular hciaht.
1800 Regular Polygon: )'Ii 811111 of sides x inside radius.
Angle A 0 c .-r a - 57.29578 � Clrcle: 1r r• = 0.78!i·10 x din.' = 0.071)58 x circumferences
r
4 bl+ c• O
Radius r O
=-- 8 -b- Sector of Circle: � r'A = O.OU872lilir A = arc x Yi radius.
7
aeo
Chord c .. 2 ./ 2 br- bl .. 2 r aln : ( - 0)
_,---- c ,. Segment of Circle:�· � �� - sin A
Rise b • r - 'h .., 4 r1 - c• - 2 tan T 2 180
{- Circle of same area as square: d ia meter = sido x 1.128:\s
•2rainl - r+y- ./ r• - x• Square of same area as circle: side = dinrneter x 0.88fi2:�
y • b - r + .;--.,--:::::,; Elllpse: Long dinrnctcr x short din met.er x 0.78.540
x - ./ r• - (r + y - b)• Parabola: Dase x % perpendicular height.
Diameter of circle of equal periphery as squue • 1.27324 aide of equare
Side of square of equal periphery as circle - 0.78�0 diameter of circle
Diameter of circle circumscribed about square - 1.41421 side of square
Side of square inscribed in circle - 0.70711 diameter of circle -- Irregular plane surface
..
A - B
CIRCULAR SECTOR .., .. '7 c: +
c:
e
N
r =- radiu1 of circle y .. angle ncp In degree, .c ..c: .c "' .c ..c: ..c: ..c:
Area of Sector ncpo - 'h !length of arc nop X r)
a b
• Area of Circle X �
.. 0.0087266 X r• X y � --
C, - 1 I D
I I
�--- --- ---- - ----nd--------------...l
CIRCULAR SEGMENT
r = radius of circle x = chord b .a rise
Area of Segment nop=Area of Sector ncpo-Area of triangle ncp Divide 11,11y plan« i<11rfacc A, B, C. D, al<>11J!: a line rt -b into ILII cveu 1111111ber, n, of purnllo l
und aulhr-iently smnll strips, d, whos,• ordi11atcs are h,, h,, h,, h,, h, .... hn- 1, h», h 0+ 11 and
(length of arc nop X r) - x (r - b) nonsidering contours between t.hre« ordinates as pnruholie curves, then for sect ion AUCD,
2 1
Area of Segment nsp= Area of Circle - Aru of Segment nop Arca ={-[1i + hn+1+4(h,+ h, -l-h •... +h») +2(h 3 +h, ·+-h, ... +h11-,)]
or, approximately, Arna = Sum of ordinates x width, d.



VALUES FOR FUNCTIONS OF 7r
,,. = 3.14159265359, log .. 0.4971499 VOLUME OF A WEDCE
,.a - 9.8696044, log .. 0.9942998 } = 0.3183099, log = 1.5028501 � {· �0.5641896, log-1.7514251 This formula is useful in ,,I,laini11g the eon ten ts of
,... - .. - speciul, wedge-shaped, tank bottoms,
x • - 31.0062767, log � 1.4914497 _!_ - 0.1013212, log = 1.0057002 180 .. 0.0174533, log-2.2418774
..
-
180
.J,i. 1.7724S39, log - 0.2485749 � - 0.0322515, log .. 2.5085503 -;;:- • H.2957795, log-1.758122& Volume=��(]+ m + n)
(j

A-24. A-24.

(By permission of Buffalo Tank Dir., Bethlehem Steel Corp.) ( Continued).

PROPERTIES OF THE CIRCLE AREA OF PLANE FICURES
Triangle: Base x Y2 perpendicular height.
,Fses-a) (s-h) \s-11),
Circumference c 6.28318 r - 3.14159 d s = Y2 sum of the three sides a, b and c.
Diameter c 0.31831 circumference
Area - 3.141 59 r• Trapezium: Sum of nron of the two triangles.
Trapezoid: },� sum of parallel sides x perpendicular height.
rr A
0
Arc a - 1800 - 0.017453 r A• Parallelogram: Huse x perpendicular hciaht.
1800 Regular Polygon: )'Ii 811111 of sides x inside radius.
Angle A 0 c .-r a - 57.29578 � Clrcle: 1r r• = 0.78!i·10 x din.' = 0.071)58 x circumferences
r
4 bl+ c• O
Radius r O
=-- 8 -b- Sector of Circle: � r'A = O.OU872lilir A = arc x Yi radius.
7
aeo
Chord c .. 2 ./ 2 br- bl .. 2 r aln : ( - 0)
_,---- c ,. Segment of Circle:�· � �� - sin A
Rise b • r - 'h .., 4 r1 - c• - 2 tan T 2 180
{- Circle of same area as square: d ia meter = sido x 1.128:\s
•2rainl - r+y- ./ r• - x• Square of same area as circle: side = dinrneter x 0.88fi2:�
y • b - r + .;--.,--:::::,; Elllpse: Long dinrnctcr x short din met.er x 0.78.540
x - ./ r• - (r + y - b)• Parabola: Dase x % perpendicular height.
Diameter of circle of equal periphery as squue • 1.27324 aide of equare
Side of square of equal periphery as circle - 0.78�0 diameter of circle
Diameter of circle circumscribed about square - 1.41421 side of square
Side of square inscribed in circle - 0.70711 diameter of circle -- Irregular plane surface
..
A - B
CIRCULAR SECTOR .., .. '7 c: +
c:
e
N
r =- radiu1 of circle y .. angle ncp In degree, .c ..c: .c "' .c ..c: ..c: ..c:
Area of Sector ncpo - 'h !length of arc nop X r)
a b
• Area of Circle X �
.. 0.0087266 X r• X y � --
C, - 1 I D
I I
�--- --- ---- - ----nd--------------...l
CIRCULAR SEGMENT
r = radius of circle x = chord b .a rise
Area of Segment nop=Area of Sector ncpo-Area of triangle ncp Divide 11,11y plan« i<11rfacc A, B, C. D, al<>11J!: a line rt -b into ILII cveu 1111111ber, n, of purnllo l
und aulhr-iently smnll strips, d, whos,• ordi11atcs are h,, h,, h,, h,, h, .... hn- 1, h», h 0+ 11 and
(length of arc nop X r) - x (r - b) nonsidering contours between t.hre« ordinates as pnruholie curves, then for sect ion AUCD,
2 1
Area of Segment nsp= Area of Circle - Aru of Segment nop Arca ={-[1i + hn+1+4(h,+ h, -l-h •... +h») +2(h 3 +h, ·+-h, ... +h11-,)]
or, approximately, Arna = Sum of ordinates x width, d.



VALUES FOR FUNCTIONS OF 7r
,,. = 3.14159265359, log .. 0.4971499 VOLUME OF A WEDCE
,.a - 9.8696044, log .. 0.9942998 } = 0.3183099, log = 1.5028501 � {· �0.5641896, log-1.7514251 This formula is useful in ,,I,laini11g the eon ten ts of
,... - .. - speciul, wedge-shaped, tank bottoms,
x • - 31.0062767, log � 1.4914497 _!_ - 0.1013212, log = 1.0057002 180 .. 0.0174533, log-2.2418774
..
-
180
.J,i. 1.7724S39, log - 0.2485749 � - 0.0322515, log .. 2.5085503 -;;:- • H.2957795, log-1.758122& Volume=��(]+ m + n)
(j

A-24. A-24.

( Continued). ( Continued).
TRICONOMETRIC FORMULAS PROPERTIES OF SECTIONS



Radlu1 AF - 1
TRIGONOMETRIC • 1in• A+ co1• A » 1in A coaec A SQUARE
FUNCTIONS • co• A sec A - tan A cot A Axis of n,omenh through center A di
1
Sine A • COi A• _,_ -co• A tan Ae ..J1-co1 A• BC d
cot A col8eA "t 0 - 2
c
- 1 -
Cosine A - eln A. • aln A cot A• V1-ain 1 A • AC ----- __ _l
aecA
tanA
Tangent A • sin A = - 1 - • aln A aeo A • FD
co1 A cot A s d•
COi A 1 6
Cotangent A • sin A unA • coa A eesee A • HG
=
d-- d
tan A 1 r ..J12 • .288675 d
Secant A - ain A - cos A • AD
cot A 1 --------------------··
Coaecant A • coaA • ain A • AG
.. -----�--��------- -.,=�=m�==��- SQUARE
RIGHT ANGLED Axia of moment, on baH A di
TRIANGLES a1 1:11 c• -bl c d
b• - c.• -a• d•
cl • a• +bl l .. -4---t-- .1 T
>
- -��-�-·--- -- ---�-=----- 8 T "O
di
"O
d
::,
Known Required r ..J"i - ,177360 d CD
A B • b c Aro a d Q.
;c
b ab
•• b tan A• f tan B = - ..J a•+ bl 2
a
a, c aln A• � coa B • � vc•-=-:i•· a ..Jc•- a•
0 2 SQUARE
a a• cot A
A, a 90°-A a cot A iinA --2- Axis of momenta on diagonal
b b• tan A • ,707107 d
A,b 90°-A b tan A coaA -- 2 -
c 1 sin 2 A d•
A,c 90° -A c sin A c coa A 4 12
di
S • &,/2 • ,117851 d•
a• • b• + c• - 2 be coa A
a+b+c d
• - --2-- bl - a• + c• - 2 ac cos B r v12 • .288675 d
c• • a• + bl - 2 ab coa C

Required RECTANGLE
Known A bd
A B c b 0 Area Axia of moment, through center
1 1 e d
a, b, c co,!.A • coa 2 B � coa c • "' • <•-•> (a-b) (a-o) 2
2
2
c
ci·-_,.-, � .<•-bi � · (a-c) _______ j_ bd•
� bo ac ab 12
a sin B a1in C bdl
a, A, B 180°-<A+B> -iTnA ,inA 8 T
b sin C
d
a, b, A sin B• ball!!- ---.ma r vl2 • ,2Ht75 d
a
CJ)
a 1in C ab sin C I>- ....
a, b,C tan A• l>-a coa C ..J a•+b•-2ab co• C -2-- I,)

A-24. A-24.

( Continued). ( Continued).
TRICONOMETRIC FORMULAS PROPERTIES OF SECTIONS



Radlu1 AF - 1
TRIGONOMETRIC • 1in• A+ co1• A » 1in A coaec A SQUARE
FUNCTIONS • co• A sec A - tan A cot A Axis of n,omenh through center A di
1
Sine A • COi A• _,_ -co• A tan Ae ..J1-co1 A• BC d
cot A col8eA "t 0 - 2
c
- 1 -
Cosine A - eln A. • aln A cot A• V1-ain 1 A • AC ----- __ _l
aecA
tanA
Tangent A • sin A = - 1 - • aln A aeo A • FD
co1 A cot A s d•
COi A 1 6
Cotangent A • sin A unA • coa A eesee A • HG
=
d-- d
tan A 1 r ..J12 • .288675 d
Secant A - ain A - cos A • AD
cot A 1 --------------------··
Coaecant A • coaA • ain A • AG
.. -----�--��------- -.,=�=m�==��- SQUARE
RIGHT ANGLED Axia of moment, on baH A di
TRIANGLES a1 1:11 c• -bl c d
b• - c.• -a• d•
cl • a• +bl l .. -4---t-- .1 T
>
- -��-�-·--- -- ---�-=----- 8 T "O
di
"O
d
::,
Known Required r ..J"i - ,177360 d CD
A B • b c Aro a d Q.
;c
b ab
•• b tan A• f tan B = - ..J a•+ bl 2
a
a, c aln A• � coa B • � vc•-=-:i•· a ..Jc•- a•
0 2 SQUARE
a a• cot A
A, a 90°-A a cot A iinA --2- Axis of momenta on diagonal
b b• tan A • ,707107 d
A,b 90°-A b tan A coaA -- 2 -
c 1 sin 2 A d•
A,c 90° -A c sin A c coa A 4 12
di
S • &,/2 • ,117851 d•
a• • b• + c• - 2 be coa A
a+b+c d
• - --2-- bl - a• + c• - 2 ac cos B r v12 • .288675 d
c• • a• + bl - 2 ab coa C

Required RECTANGLE
Known A bd
A B c b 0 Area Axia of moment, through center
1 1 e d
a, b, c co,!.A • coa 2 B � coa c • "' • <•-•> (a-b) (a-o) 2
2
2
c
ci·-_,.-, � .<•-bi � · (a-c) _______ j_ bd•
� bo ac ab 12
a sin B a1in C bdl
a, A, B 180°-<A+B> -iTnA ,inA 8 T
b sin C
d
a, b, A sin B• ball!!- ---.ma r vl2 • ,2Ht75 d
a
CJ)
a 1in C ab sin C I>- ....
a, b,C tan A• l>-a coa C ..J a•+b•-2ab co• C -2-- I,)

A-24. A-24. ...
O>
( Continued). ( Continued). ""'


PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS



RECTANGLE EQUAL RECTANGLES
Axis of moments through A
Axis of moments on base A bd center of gravity b (d - di)
d
I c d c 2
b (d' - d,•)
bd•
l __ .1 s - - 3- s b (d' - d,•) 'O
c
d
12
>
bd 2
6d
- - 3-
,/J - {di-=-if;s '2.
a,·
d
b- .577350 d 12(d - di) a.
.,
"'O
s
0
UNEQUAL RECTANGLES ,,,
RECTANGLE ,,,
A bd Axis of moments through
Axis of moments on diagonal center of gravity A bt + b,t, CJ
bd 1_� ,,,
CD
c 1 r---b-;1 'h bt• + b,t, (d - 'ht,)
vb•+d2 .,.---- -'--r c A ii"
' ----- ·---;:- I
I
b'd' j ·1·--- y I c bt> b,t,• :::,
.,
+ b,t,y,•
6 (bl + di) d d,------i-+- 12 + bty• + -,-2- o'
b 1 d 1 o
s Llt,;-·::F:9 -- s c s, zr
sv b' +d·1 -- -_-J __r� c, CD
._,_,
bd I ., f; 3
,1·;, (bl + di) --bl- � .... �
Ill
:::,
a.
RECTANGLE TRIANGLE
bd "'O
Axis of moments any line Axis of moments through A - 2 !2.
.,
through center of gravity A bd center of gravity
0
b sin a + d cos a 2d 0
c c - 3 �
2 CD
bd (b• sin•a + d 2 cos 2 a) bd' 3
12 - 36 �
2
s bd (b' sin•• + d 2 cos a) s bd2 "'O
6 (b sin a + d cos a) - 24 iii
d
iii
bJ. sinza + di cosza v,s- - :::,
� 12 .235702 d
HOLLOW RECTANGLE TRIANGLE
Axis of moments through center A bd - b1d1 Axis of moments on base A -2-
bd
�[=BIT c - 2 12 c 12
d
d
i
�
--1
bd' - b,d,•
bdl
J_�: --
a
bd' - b,d,•
bd•
s
I
6d
,/ 6- -
d
� -bd' ;;:·d··· s - 12
b .408248 d

A-24. A-24. ...
O>
( Continued). ( Continued). ""'


PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS



RECTANGLE EQUAL RECTANGLES
Axis of moments through A
Axis of moments on base A bd center of gravity b (d - di)
d
I c d c 2
b (d' - d,•)
bd•
l __ .1 s - - 3- s b (d' - d,•) 'O
c
d
12
>
bd 2
6d
- - 3-
,/J - {di-=-if;s '2.
a,·
d
b- .577350 d 12(d - di) a.
.,
"'O
s
0
UNEQUAL RECTANGLES ,,,
RECTANGLE ,,,
A bd Axis of moments through
Axis of moments on diagonal center of gravity A bt + b,t, CJ
bd 1_� ,,,
CD
c 1 r---b-;1 'h bt• + b,t, (d - 'ht,)
vb•+d2 .,.---- -'--r c A ii"
' ----- ·---;:- I
I
b'd' j ·1·--- y I c bt> b,t,• :::,
.,
+ b,t,y,•
6 (bl + di) d d,------i-+- 12 + bty• + -,-2- o'
b 1 d 1 o
s Llt,;-·::F:9 -- s c s, zr
sv b' +d·1 -- -_-J __r� c, CD
._,_,
bd I ., f; 3
,1·;, (bl + di) --bl- � .... �
Ill
:::,
a.
RECTANGLE TRIANGLE
bd "'O
Axis of moments any line Axis of moments through A - 2 !2.
.,
through center of gravity A bd center of gravity
0
b sin a + d cos a 2d 0
c c - 3 �
2 CD
bd (b• sin•a + d 2 cos 2 a) bd' 3
12 - 36 �
2
s bd (b' sin•• + d 2 cos a) s bd2 "'O
6 (b sin a + d cos a) - 24 iii
d
iii
bJ. sinza + di cosza v,s- - :::,
� 12 .235702 d
HOLLOW RECTANGLE TRIANGLE
Axis of moments through center A bd - b1d1 Axis of moments on base A -2-
bd
�[=BIT c - 2 12 c 12
d
d
i
�
--1
bd' - b,d,•
bdl
J_�: --
a
bd' - b,d,•
bd•
s
I
6d
,/ 6- -
d
� -bd' ;;:·d··· s - 12
b .408248 d

A-24. A-24.
( Continued). (Continued).


PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS


TRAPEZOID
Axis of momenb through PARABOLA
center of gravity 4
d(b+b,)
A - --2- 2 A m 3 ab
2
-r e d(2b + b1) T7, m - sa
3(b + b,)
a
c d• (b• + 4 bb1 + b1•) •t- 16
--+--- -T1
_j__ 36 (b + b,) -'----.- 1 •• - 175 a•b
4
s d• (bl + 4 bb, + b,•) 3..:l'... --+ -'L •• - ,s":ib•
12 (2b + b,) l<-b-
! 2 la 32 lb
r 6(b b,) ..J 2 (b• +4 bbt + bt•) - 105 a
----·--------- -·
2
HALF PARABOLA A - 3 ab
CIRCLE
r··n-
T."dl - 2 4 - ?.
Axis of moments A a _4 .. a -..:R2 .785398 di • 3,141593R• m sa
through center - 3
d
c T - R I n -8-b
c -r.d• 1:R• - a 11 8 •b
.1 - 64 - -4- � ,049087 d• ,785398 R• , . ·--r• ,. - 175 a
�-�- ab•
,:R>
s - 32 - -4- - .098175 d• .. .785398 R• 3 ..'.L - -+---.....---+- _ _j_ 3 - 480
"'d•
16 lb
d R •• - 105 a
4 - T -b--
4 �ab•
•• - 15
HOLLOW CIRCLE COMPLEMENT OF HALF
PARABOLA 1
Axis of moments A - - .785398 (d•-d,•) A 3 ab
through center
d -
G 7
2 m Toa
,(d -d, 4) - .049087 (d•-d,•)
4
64 n .!. b
4
4
s ,(d -d,•) .098175 d•-d.• 37 •b
32d d la - 2100 a
..J-d•+d,• 1
- ··--4-- la ab•
--b-- - 80
------
HALF CIRCLE PARABOLIC FILLET IN t
Axia of moments through 1.570796 R• RIGHT ANGLE &I 2...J·£
2
center of gravity c R (1-�) .575587 R -. r-m t
--§I R• ---- .109757 R• A -;;z:
b
3�
8 )
(
r
8
9�
�ti
6
24 (3.,-4)
4 t
......
--d-- s R• (9T.•-64) ,190687 R• m - n T m
R ,J-9-;,� ,264336 R 11 t• 01
6,-; '• la Hoo

A-24. A-24.
( Continued). (Continued).


PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS


TRAPEZOID
Axis of momenb through PARABOLA
center of gravity 4
d(b+b,)
A - --2- 2 A m 3 ab
2
-r e d(2b + b1) T7, m - sa
3(b + b,)
a
c d• (b• + 4 bb1 + b1•) •t- 16
--+--- -T1
_j__ 36 (b + b,) -'----.- 1 •• - 175 a•b
4
s d• (bl + 4 bb, + b,•) 3..:l'... --+ -'L •• - ,s":ib•
12 (2b + b,) l<-b-
! 2 la 32 lb
r 6(b b,) ..J 2 (b• +4 bbt + bt•) - 105 a
----·--------- -·
2
HALF PARABOLA A - 3 ab
CIRCLE
r··n-
T."dl - 2 4 - ?.
Axis of moments A a _4 .. a -..:R2 .785398 di • 3,141593R• m sa
through center - 3
d
c T - R I n -8-b
c -r.d• 1:R• - a 11 8 •b
.1 - 64 - -4- � ,049087 d• ,785398 R• , . ·--r• ,. - 175 a
�-�- ab•
,:R>
s - 32 - -4- - .098175 d• .. .785398 R• 3 ..'.L - -+---.....---+- _ _j_ 3 - 480
"'d•
16 lb
d R •• - 105 a
4 - T -b--
4 �ab•
•• - 15
HOLLOW CIRCLE COMPLEMENT OF HALF
PARABOLA 1
Axis of moments A - - .785398 (d•-d,•) A 3 ab
through center
d -
G 7
2 m Toa
,(d -d, 4) - .049087 (d•-d,•)
4
64 n .!. b
4
4
s ,(d -d,•) .098175 d•-d.• 37 •b
32d d la - 2100 a
..J-d•+d,• 1
- ··--4-- la ab•
--b-- - 80
------
HALF CIRCLE PARABOLIC FILLET IN t
Axia of moments through 1.570796 R• RIGHT ANGLE &I 2...J·£
2
center of gravity c R (1-�) .575587 R -. r-m t
--§I R• ---- .109757 R• A -;;z:
b
3�
8 )
(
r
8
9�
�ti
6
24 (3.,-4)
4 t
......
--d-- s R• (9T.•-64) ,190687 R• m - n T m
R ,J-9-;,� ,264336 R 11 t• 01
6,-; '• la Hoo

A-24. A-24. .....
0)
(Continued). (Concluded). 0)

PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS


n Nu m her of sides
REGULAR POLYGON 180°
*
Tffi A 2 uh
HALF ELLIPSE
AKis of moments
n
through center
1
2
4a
-3;
m
(
>
8
9<
�
1
�ab•
.J..3
la
3 11-- ---!--- --;;,• 11 - a•b � - _!__) "O
---
cii'
8
�-bj 1 a.
"tJ
2 Ii - 8 r.a•b A(6R• - a•) _ � A(l2R,• + a•) ...
--·24
--48-�-
0
r1 = ra = � 6R•;;�-a•. s
u,
u,
----------·- -- 0
CD
u,
ANGLE 2K
1 tan 20 .-;=-r;-
:::,
• QUARTER ELLIPSE A 4 r.ab Axis of moments through '°
0
center of gravity b' +ct d• + at ...
2 4 4a A t(b + C) X - (b + C) y - 2(b + C)
2
� ·n ,I m 1-; I. ---b- � K Product of Inertia about X-X &. Y-Y o
J
T n 4b 1-- r r · - a J I \ • - + 4fi,-+cf CD
abcdt
3
3r.
\
o'
•
a•bc � -...i..)
3-"---- -b�-r·Ja 11 ab' -- 9r. . y I I Ix 1° (t(d-yJ'+byl-a(y-tJ•) !!?.
16
a,
I-·· ---t--- --,.-I
I
:::,
n,
•
a.
(
4 )
I,
r. - -·--
� -(t(b-x)•+dx•-c(x-t)•)
9r.
16
Iv
...
!!.
1, .L �alb 'r �; --e;_J J 11 • Ix sin•o + Iv cos•o + K sin26 "tJ
,. 1 • lw • Ix cog19 + Iv ain•e- K sin28 0
4 16 0
16 r.ab J
CD
-�·r-\ 3
K Is negative when heel of angle, with respect
y 1- to c. g., 11 In 1et or 3rd quadrant, positive ff
when In 2nd or 4th quadrant. !!?.
Z·Z is axis of minimum I
• ELLIPTIC COMPLEMENT ·----------------- "tJ
iii
:::,
2 BEAMS AND CHANNELS ii,
Transverse force obllq ue
through center of gravity
� I
-- � I
b
I � 1 14 • lxcosz4i+lvainZ�
_:,: ----- ----- __ y__
(
M t. •in.to + ,: eose )
--b--· 3 .
-,./
where M is bending moment due to force F.
Extreme flber assumed same as for case
<to•O. If not, locate extreme fiber and find
f by usual method.
4 4
• To obtain properties of half circle, quarter circle and circular complement substitute a � b • R.

A-24. A-24. .....
0)
(Continued). (Concluded). 0)

PROPERTIES OF SECTIONS PROPERTIES OF SECTIONS


n Nu m her of sides
REGULAR POLYGON 180°
*
Tffi A 2 uh
HALF ELLIPSE
AKis of moments
n
through center
1
2
4a
-3;
m
(
>
8
9<
�
1
�ab•
.J..3
la
3 11-- ---!--- --;;,• 11 - a•b � - _!__) "O
---
cii'
8
�-bj 1 a.
"tJ
2 Ii - 8 r.a•b A(6R• - a•) _ � A(l2R,• + a•) ...
--·24
--48-�-
0
r1 = ra = � 6R•;;�-a•. s
u,
u,
----------·- -- 0
CD
u,
ANGLE 2K
1 tan 20 .-;=-r;-
:::,
• QUARTER ELLIPSE A 4 r.ab Axis of moments through '°
0
center of gravity b' +ct d• + at ...
2 4 4a A t(b + C) X - (b + C) y - 2(b + C)
2
� ·n ,I m 1-; I. ---b- � K Product of Inertia about X-X &. Y-Y o
J
T n 4b 1-- r r · - a J I \ • - + 4fi,-+cf CD
abcdt
3
3r.
\
o'
•
a•bc � -...i..)
3-"---- -b�-r·Ja 11 ab' -- 9r. . y I I Ix 1° (t(d-yJ'+byl-a(y-tJ•) !!?.
16
a,
I-·· ---t--- --,.-I
I
:::,
n,
•
a.
(
4 )
I,
r. - -·--
� -(t(b-x)•+dx•-c(x-t)•)
9r.
16
Iv
...
!!.
1, .L �alb 'r �; --e;_J J 11 • Ix sin•o + Iv cos•o + K sin26 "tJ
,. 1 • lw • Ix cog19 + Iv ain•e- K sin28 0
4 16 0
16 r.ab J
CD
-�·r-\ 3
K Is negative when heel of angle, with respect
y 1- to c. g., 11 In 1et or 3rd quadrant, positive ff
when In 2nd or 4th quadrant. !!?.
Z·Z is axis of minimum I
• ELLIPTIC COMPLEMENT ·----------------- "tJ
iii
:::,
2 BEAMS AND CHANNELS ii,
Transverse force obllq ue
through center of gravity
� I
-- � I
b
I � 1 14 • lxcosz4i+lvainZ�
_:,: ----- ----- __ y__
(
M t. •in.to + ,: eose )
--b--· 3 .
-,./
where M is bending moment due to force F.
Extreme flber assumed same as for case
<to•O. If not, locate extreme fiber and find
f by usual method.
4 4
• To obtain properties of half circle, quarter circle and circular complement substitute a � b • R.

Appendix 617

A-25.
Wind Chill Equivalent Temperatures on
Exposed Flesh at Varying Velocity

WIND VELOCITY (MILES PER HOUR)
45 35 25 20 15 10 5 3 2 0
90 89.5 89 88.5 88 88.75 87.5 87 86 84.5 83
82 81 80.5 80 79.5 78 76 74 72.5 70 60
72 71 69.5 68 67 65 60 57 53.5 47.5 23
63 61 59 57 55 52 44.5 39 34.5 20 -11
...... 51 49 47 45 42.5 38 28 18.5 11 0 -27
Q) 41 39 36 34 30.5 25 11 0 -9 -23.5 -38
E
"' a, 30 28 25 23 18 11 -5 -16.5 -40 Below -40 Below -40
c. 20 18 14 11 6 -2 -19 -40 Below -40 do do
E
Q) 10 7.5 3 0 -6 -15 -35 Below -40 do do do
I-
0 -2.5 -8 -12 -18 --29 Below -40 do do do do
-11 -14 --18 -23 -30 Below -40 do do do do do
-21 -24 --30 -35 Below -40 do do do do do do
-32 -35 --40 -40 do do do
instructions for use of the table:
(1) First obtain the temperature and wind velocity forecast data.
(2) Locate the number at the top corresponding to the expected wind speed (or the number closest to this).
(3) Read down this column until the number corresponding to the expected temperature (or the number closest to this) is reached.
(4) From this point follow across to the right on the same line until the last number is reached under the column marked zero (0) wind speed.
(5) This is the equivalent temperature reading. Example: weather information gives the expected temperature (at a given time, such as midnight) to be
35°F, and the expected wind speed (at the same time, midnight) to be 20 miles per hour (mph). Locate the 20 mph column at the top, follow down this
column to the number nearest to 35°F. The nearest number is 34°F. From this point, move all the way to the right on the same line and find the last
number, which is - 38°F. This means that with a temperature of 35°F, and a windspeed of 20 mph the rate of cooling of all exposed flesh is the same as
- 38°F, with no wind.
Reproduced by permission of the Department of the Army.
do means ditto.


A-26.
Impurities in Water

U. S. Systems of Expressing Impurities
I grain per gallon I grain calcium carbonate (CaCO,) per U. S. gallon of water
I part per million I part calcium carbonate (CaCO,) per 1,000,000 pans of water
I part per hundred thousand I part calcium carbonate (CaCO,) per 100,000 parts of water
Foreign Systems of Expressing Impurities
I English degree (or "Clark) I grain calcium carbonate (CaCO,) per British Imperial gal. of water
I French degree . I part calcium carbonate (CaCO,) per 100,000 parts of water
I German degree I part calcium oxide (CaO) per roo.ooo parts of water
Conversions

l'arL"' CaCo, Jo:nKlish Jo"r,•nch Gnman Milli-equivelente
per Liter or
Grain� CAro1
CONVEllSION TAIILF: l'tHl:-4 ('a(:01 Jirr llundrrd pn (J.S. Gallon Dr>Krr<"s Df'l{tPl'R Dr�rees F,quivaJ,.nt..a
Thousand
or
(Jo:xpn·�"l,.fi 1n :I �ii,:-nifif'ant FiKUrt•!'I) rwr �fillion (l'l!'l./100,flOO) (�p5!") O Clark 0 1' rf'nrh ac.,,rman pt-r Million
[ppm)
0
1 l'art JH'i" Million I. .1 .07 .I .O!i60 .020
1 Part. JJN Hundred Thousand JO.O I. .7 I. .�60 .20
I �rain pN U. S. Gallon 17.1 I. 71 I. J.2 t.71 .958 .343
1 Enzl i rh or Clark Degree 14.3 1.(3 .RU I. I.43 .ROO .286
1 Frr-nr-h Or,.:rN'! 10. I. .ssn .7 !. .5�0 .20
l Grrman n,'l,!rN� 17.9 I. 79 I.04 1.24 l. 79 I. _357
"' so. 6. 2.92 3.60 2.80 J.
1 l-:quivalrnt pr-r Millinn
By permission, The Perrnutit Co., Inc., Data Book, 1953.

618 Applied Process Design for Chemical and Petrochemical Plants


A-27.
Water Analysis Conversions for
Units Employed: Equivalents

J·ans per
WATER ANALYSIS IJNITS J>H.rl�" per MilligrarnR Grams llundr••d Gr11in!t Gralna per Kilof{rainfl per
CONVf:l\slON TAIILf; Million pN Li!N tu-r Lit er Thousand U.S. Gallon Hritiah Imp. Cubic Foot
( �"<prf'"l!'lr.:..l ta 3 �i9;nilirant Figurr!') (f,pml (m�m/1,) (grm!t L) (Pts./100,000) (•rs/U.S. gal) Gallon (Kgr/C'U. fl.)

I Part per Million i. 1. .001 .i .O!iR3 .07 .0004
1 Milli,:ram pr-r Liter 1. 1. .001 .1 .0583 .07 .0004
I Gram Jwr Liter 1000. 1000. 1. 100. !;JL3 70. .436
1 Part. pr-r J Iundred 'I'housend 10. 10. .OJ J. .583 • 7 .00436
I Grain ,,rr u.s. Gall•m 17.1 17.1 .017 1.71 1. 1.2 .1107�
I Grain prr Brili!'!h lmp. Gallon 1,.a 14.a .01·1 1.43 .K33 1. .0062
1 Kilr>Krain 1wr Cuhic F'nnt �:!lH. 2'l!hl. 2.291 229.4 134. 161. 1.
NoTE: In practice, water a nal ysis samples arc measured by volume. not by weight and corrections for variations ln·specific gravity are practically never
made. Therefore, parts per million ar e ;1�,umrcl to be the sarne as milligrams per luer anti hence the above relationships arc, for practical purposes, true.
By permission, The Permutit Co., Inc., Data Book, !953.





A-28.
Parts Per Million to Grains Per U. S. Gallon

A. To convert parts per million of B. To convert grains per U.S. gal-
hardness to grains per U.S. gal- lons to parts per million of hard-
lon, divide by the factor 17.r. ness, multiply by the factor 17.1.
Example: 2. 24.3 grains/U. S. gallon X 17.1 416 parts/million
1. 242 fl_�t.�/millior.
17.r q.1 grains/U. S. gallon
EqujvaJenls
Water analyses may also be expressed as:
No. of ppm of substance present
(1) Equivalents per million (epm)
Equivalent weight of substance
(2) Milli equivalents per liter (meq/1) .. Equivalents per million
(3) Parts per million expressed as CaCO,. No. of ppm CaCO. equivalent to No. of ppm of substance
present
No. of ppm of substance present X 50
(4) Fiftieths of equivalents per million (epm/xo)
Equivalent weight of substance
Nons: Numerically (1) and (2) arc equal. SC'c1i11n )C:<111 contains equivalent wciuhts of :1 numbc r of .o;11h..i:1nC'C'�.
Numerically (3) and (4) arc equal. Section :,cx111 contnins Iactors for converting various suhvtunces to CaC0 1 •
Section x x u t contains factors for various chemical conversions.
By permission, The Permutit Co., Inc., Data Book, 1953.

Appendix 619


A-29.
Formulas, Molecular and Equivalent Weights, and Conversion
Factors to CaC0 3 of Substances Frequently Appearing /l!ultipl11ing Factor
in the Chemistry of Water Softening ('onAir/criMg ,norte'lrar 1L"f,
of CaC01 a11 I fJO.
csco,
Sub11tnnc� �qviPUl#nl
lt,loluular Eq11ito(r.nl to CaCO, to
S11halunl"e For111ulrt u•tight u·rir;ht �quiral,n: euh,t,111 r �
--
Aluminum Al 27.0 9.0 6.illl O.IR
Aluminum C.hlnrid"'. AIClt 131. H.4 1.13 O.R9
Aluminum Chloride. AIC1,.RHtO. 241. R0.5 0.62 J.61
Aluminum Sulfer e Al.fSO.)l· JRlltO 6f;l'i . .t II I.I 0.45 2.22
Aluminum SuH11t.n Al.fSO,ll (•nhydrou11) . 342.1 67.0 O.RR 1.14
Aluminum Jlydr&l8. Al(OII), . 78.0 26.0 l.9t 0.62
-··-
Alumin11 Al,O, 101.9 17.0 2.94 O.S4
Sodium Aturninatc . N11.1Al11,, 163.9 27.1 l.83 0.65
Amrnnniurn Alurr. AltfSO,l 1 (NH,>,S0,·24Ht0 906.6 151.1 0.33 S-02
.Pota�i urn A I um . Al1(SO,l1K,SO,· 20110 94R.R 156. t 0.32 3.12
Arnmc)nia . NH, 17.0 17.0 2.94 0.34
Ammoniurr. (l,.m) Niie 18.0 IR.O 2.78 0.36
Amn1nnium C:hl(>rid,• . Nll1CI. 63.5 63.5 0.94 J.07
Ammonium Hyd roxide NJI,c>ll 35.l 35.1 1.43 0.70
Amrncmlum Su1C11tc (Nll1)rSO, 132. 66,1 0.76 1.s2
Har-iurn II• 137.4 6R.7 0.73 !.S7
Barium Carhnnate flllC01. 197.4 9R. 7 0.61 !.97
Buit.m C.hlorldr . fleC:lt·21J,O 24-1.3 122.2 {l.4i 2.H
Baricrn Hydroxide 1111.(0ll}t l 71. R5.7 0.69 1- 71
flariuni Chdrte nso. J !'.13. 76.7 0.65 U3
Barium Sulrat,! BaS(), 233.4 IJG. 7 C.43 2.33
r.11.1 ... ium. (;a 40.! 20.0 2.60 0.40
Calt-hJrn nit'arhnnale C11.(HC::O,h. 162. l 81.1 0.62 J.62
C.:ald:.tm C:RrhonP.te CaC01. JOO.OB 60.1 I.DO 1.00
<:al<"iurn Chlorfde . CoCli lll.O 65.5 0.90 1.11
t"alcium llydrMc. Ca(OIJ1, 74.1 37.1 1.35 0.74
Cal<"ium llypochlorltft. C•(CIUJt. lUI 35.R 0.70 1.•a
Cakium Oxide . Cao. b<i.J 2R.O J. 79 0.66
Cal<"ium �ulfarn CaSO, (anhydroU11) 136.1 68.1 0.74 1-36
Calriurn Sulfate CL.�0,·211,0 (iYPBUm) 172.2 86.1 0.68 1.12
C:alr!um Nitrate Ca(NO,), 164.J 82.1 0.61 1.64
f-- � :aleiurn Phosphate Ca,rJ'01)1 310.3 61.7 0.97 1.D3
' Carbnn C. 12.0 S.00 16.67 0.06
Cl,lnrin•• (Ion) Cl. 36.6 S6.6 0.11
C•111pl"r (Copri<"J Cu 6�.6 Sl.8 1.67 0.64
C.:<lpµrr Su)(ate (Cupric). CuS01 !GO. RO.O 0.63 J.60
Ct>ppN SuJ(ale (Cupric). CuSOc·SII.() 260. 125. 0.40 2-60
Irnn ( Frrrou11) J-'P.''. 65.8 27.9 1. 79 0.66
lrc•n ( F1Hri1') F�"'. 55.8 18.6 2.69 0.37
Ferrous Catbonete i'"P.f;01. 116. 57.9 0.86 1.16
Ferrnua HydroJ1.ide . Fe (OH>, R9.9 44.9 l.ll 0.90
F,•rrou!J (hidn FeO 71.A 35.9 J.39 0.72
Forrnua Sulfate F"SO, (anhydrous) 151.9 76.0 0.66 1-52
Ferrous SuHate Fe�O,· 7H,O 27H.O 139.0 0.36 2. 7K
Ferrous Sulfate. 1-'eSO, (a11hydrm1.'I) 151.9 151.9 oxidation
F,,rric Chloride i''PCl1 162. 5'-1 0.93 J.08
Forric Chloeide . F,�Ct,· 611,0 270. 90.1 0.56 1.80
Frrric Hyd roaido . Fe tOII), 107. 35.6 Ul o. 71
Ferr!c Oxldn },'p1(), 160. 26.6 I.BB 0.63
Fnric SuHal!! (}··Nri11ul) i' 1!t (S0,) 1 399.9 66. 7 0.76 1-33
0
Fert(JU9 or Fr-rrlc Fe or Fe. 65.8 65.8 o:tidation
Ferroue Sulf•Le. r-so.. 151.9 151.9 o:tidation
Fluorine. : : F. 19.0 19.0 2.� 0.3R
Hydr-ogen (Ion) H 1.01 1.01 60.0 0.02
Iudine 127. 127. 0.40 2.64
fA>ad : Pb 207. 104. 0.48 2,08
Magn"111urr. Mi 24.3 12.2 4.10 0.24
40.3
MagnCRium Oxid•! MgO 146.3 20.2 2.4B 0.40
MaKn"11ium Bieerbonete .
-------- Mi (H<:0,1t 84.3 73.2 0.68 J.46
42.2
1.19
MgCO,
O.R4
:\h,:riM1ium Cuh()nate
- Mg Ch 95.2 47.6 1.06 0.95
Mal(nPsium Chloride
�bgnPJ11iurr. J lydra!P. Mi(OHh 5R.3 29.2 1.71 0.68
Ma1,iC11es!um Ni teate . �hc<N(J.lJ ICR.3 74.2 0.67 l-48
Maa,:nPsium Phn�11hat.2 M21!PO,)t. 262.9 U.8 1.14 O.AB
:.20
� la._:ncsium .Sulfalr MgSO, 120.4 60.2 0.R3 0.55
I M an�anf"flP ( M anicank) Mo"' 12!',.R 62.9 2.73 0.37
64.9
27.!')
M11''
1.H2
M an,anr,e IM an,annua)
IA.3
!>4.9
O.RO
J.26
MnCh
M11t11{Anf· � 1> l:hloridP.
I Man�u,wi:e llioxidt>. �{nO,. l 5R. 21.7 2.30 0.4:i
H6.9
·�-0
0.89
Mrd()llh
44.,
1.13
Man�.,,.·,e llyd.ate
0.6�
l.90
MntO,.
26.3
Man1<anic (hidP
o. 71
70.9
MnU
1.41
35.5
ManKanous Oxlde
By permission, The Permutit Co., Inc., Data Book, 1953. ( continued on next page)

620 Applied Process Design for Chemical and Petrochemical Plants


A-29.
(Concluded). Formulas, Molecular and Equi,alent Weights, and
Conversion Factors to CaC0 3 of Substances Frequently Al11Wpt11i11g Puctor
Appearing in the Chemistry of Water Softening Ccm�idcrl11� moluular wt,
P/ C'uro, nit I 00.
ca.co ..
Sub:d11nre rquirlu.lr11t
,\Juluulu, e',/HirnftHl '" n,,·o. lo
Svb,ranu 1-'uruu,la trf'i11Jtt 1,1·,i11/tal t'!/llil'olf�nl •ll'•�tuHrC
Nilr&lc ( tun) NO, 62.0 62.0 O.Hl 1.24
1.2G
0.79
6:1.0
Nitric Aeid IINO, . 6:1.0 4.67 10.H 0.093
NiLrngen (Vall!nce 3) N'" 14.0 17.9 n.oss
NilrC>¥�n (Vah:nt:P r1) N'"" \4.0 :!.HO
:, 16.0 H.00 s.as 0.16
l'ho�phvru.:t (Vah:ricc :JI I'"'. 31.0 J0.3 ·1.76 0.21
6.20
l'hr�ph1,rua (Vah•m•e fi) . !""". 31.0 39 1 K.33 0.1:!
1.26
0.7H
l 'oUL.!i�i.um . K 3\J.l
I'orasstum Carbonate . K1f:01 l:lli. 69.1 o.n t.3K
Poresaium Chloride . KCI 74.6 7l.6 0.67 1.0
1.12
Potassium Hydroxide . KOU 56, I 66.1 0.8K 2.K7
0.3r;
Sil ver Chloride. A•Ci . 1-1:1.:1 143.3 0.29 a.so
Stlvvr Nit rate AicN01 iss.s J69.9
.Sili<'a .• Sil>. GU.I 30.0 1.67 0.60
1.14
0.14
Silicon • Si :!Ii.I 7.03 2.18 0.46
Sodium. , Na .. 2:1.0 23.0 0.60 J.68
Sodium llkarhunate Nall CO,. H4.0 M.O
Sodium Disulf.&L1:t Na.llSO,. 120.
Sodium Dis.ullitP. NallS01• 104.
1.06
Sodium Carbr.netc Na�C01 lllt:L 63.0 0.94 2.86
SuJium Carlutnillfe N"'1C0,· 10lhO :!t<G. 148. 0.35 1.17
Sodium Chluridu . NaCl !JK . .'.", 5�.5 0.85
Sodium llypl.)(:hloril., . Na\.10. 7-l.;j 37.3 0.67 1.49
0.HO
1.25
Sodium Hydrate NoOll. 40.0 40.0 e.ss
Sodium Nitrate NaN01 KJ.0 k5.0 1.70
Sodium NiLrite. NaNA.>, 69 0 34.5 0.7:l 1.31l
Sodium Oxlde Na,O , 62.0 31.0 1.61 0.62
'fri-sodKun l'hu.:sph&Lt!. Na11'0,·J2H,O (IK.7'1� 1'10,) 3K0.2 126. 7 o to 2.53
1.09
'I'rf-eodlum l'hcs. tauhydruua) Na11'0,(4:l.:!'�i;, · 1'�0,) 164.0 !,,l.7 0.91 2.39
Di-sodium I'hoaphato . . Na1IIP01·121110 (19.R''.� l'·1U,) 3!'1H,t 119.4 0.4�
Di-aodium l'huJt, (:,,nl,ydrouit) Natll i-o, (&0% l'i<>.) . 142.0 47.3 1.06 0.95
Mono-sodium l'ht1!1J1hate NalL!'0,· 1110 (51.4% l 1U,>. 1ax.1 46.0 1.09 0.9'l
1
Mono-eud. phos. (anhydr,,�) NaH�l'O• (:i9.1% 1'10•) l:!O.n 40.0 1.25 IUSO
0.68
Mcta-t•hnllJ)hale (ll•Kan) NaP<h (69% 1',lh) 10�.o 31.0 1.-17
Sodium Sulra1e. . , . , Na,SO,· JOll:0 . 322.1 161.1 0.31 3.22
Sodium Sulfate ... NatSO, H2.1 71.0 0.70 1.42
Sodium Thio�ulraLt!. N•:S20,. l:!H.l 15/i.1 O.G3 1.59
Sodium T1•trathionate. Na1S,Ot. 270.2 135.1 0.87 2.71
Sodium Sulfite Na,801 126.1 K:l.O 0.79 1.27
Sulfur (Valence 2) S" 3". I 16.0 3.f3 0.32
Sulfur ( valence 4) S"" 3:!.l K.O:! 6.25 0.16
SuHur ( Val,•nce 6) S""" az.t 5.34 9.10 0.11
Sullur l>ioxidc . SO,. s,.1 :t:!'.O
Tin .. . Sn • 119.
'Water. 11,0. 1�.o 9 nu 6.56 0.18
Zinc . Zn 65.4 32.7 J.54 0.65
ACID RADI<:Al.S
Dkarbonate . ucu, . 61.0 61.0 0.82 l."2
Carhonatf'-. co.. 60.0 30.0 1.67 .60
Carbon J)iO:Lida CO,. H.O 22.0 2.27 .4-1
Chloride. Cl. 35.5 35,5 1.41 , 71
Iodide 126.9 t:W.9 0.40 2.64
Nltrate NO, 62.0 6t.O 0.81 1.24
Hydratu. OH: I 7.0 17.0 2.94 0.34
l'husphatc. r-o.. 95.0 31.7 1.6H 0.63
l'ho�phoroua Oxide l'10,. 142.0 23.7 2.11 0.47
1
Su l1lde . : : .. s. 32.1 16.0 3.11 0.32
Sul late so •. 96.1 4M.O 1.04 0.96
Hutrur Trio•lde. so,. 80.1 40.0 1.26 0.HO
ACIDS
llydru"l!n . . H. , . 1.0 1.0 50.00 0.02
At'..-lic Ai:ld . HC,U.01 60.1 60.1 0.83 1.20
Carbonic Acid . HrC01. 62.0 31.0 1.61 0.62
llydro<:hloric Acid IICI .. 36.5 36.5 1.37 0.73
l'hoat>huric Acid HJl'O,. 9•.o 32. 7 r.ss 0.65
Suttur oua Acid . !liSO,. M2.l 41.1 1.22 0.82
Sulfuric Acid. H�O,. 9K.l 4�.o J.02 0.9H
Hydrogen Sulfidff, H1S. ..
!th11KanoW1 Acid . ll1Mn01. 10,.9 62.6 0.96 1.05

Appendix 621


A-30.
Grains Per U.S. Gallons-
Pounds Per 1000 Gallons

A. To convert grains per U.S. gal-
lons to pounds per moo gallons
multiply by the factor 0.143.
B. To convert pounds per I ooo gal-
Ions to grains per U.S. gallons
multiply by the factor 7.0.
Exam pie:
1. 4-5 grains/U. S. gallon X 0.143 = o.644 lbs./1000 gals.
2. 0.5 lbs./1000 gallons X 7.0 = 3.5 gr.iins/U. S. gal.



A-31.
Parts Per Million-
Pounds Per 1000 Gallons

A. To convert puts per million to
pounds per IOOO gallons divide
by the factor 120.
B. To convert pounds per IOOO gal-
lons to parts per million multi-
ply by the factor 120.
Example:
r , 39 parts/million
= o. 325 lhs./ 1 ooo ga Is.
120 ·
2. 0.167 lhs.z'rooo gals. X 120 = 20 parts/million


A-32.
Coagulant, Acid, and Sulfate- I ppm Equivalents

ppm
I Ppm. pprn SOJ us CaC01 ppm ppm ppm
1 Ppm FQTnrnl11 nf Alkalinity Increase Na2S01 CO, Total Solids
t,..:amP nr ("hf"mic'al Chomh-al Roduct.ion Increase Increase Increeaa

Filtrr Alum Ah(S0,)1 · J8lh0 0.4:i 0.4� 0.61 0.40 l 0.16
Ammunia Alum Ali(SO,)I · (:\'"II ,)1S01 · 241ll0 0.31 O.H 0.63 0.29 0.27
Potash Alum Ah(SO,)I · K1�0, · :!'11110 0.32 0.43 0.60 0.28 0.30
c:opprra1 (fprr,11.U sulfate) F('.SO, · 71110 0.36 0.36 0.61 0.31 0.13
Chlorine t ed Coppr-r as FeSO, · 7H,O+ (},C:1,) 0.54 0.36 0.61 0.48 0.18
Fer ric Su[fatr (lOO,..� J-'P•(S0,)1) F(',{�0.)1 0.75 0.76 1.07 0.66 0.27
Sulfuric J\dd-!)�% 111.SO, LOO LOO 1.42 0.88 0.36
SuHuric Al'iri-!13.2';, (66° Df?) n.so, 0.95 0.95 L35 O.Rt 0.34
Sultur!c Ar-id -77. 7S� (60° DP) n-so, 0.79 0.79 l.13 0.70 0.28
Salr f"11.k"- 9f,'::'"; Na,�n. 0.66 0.95 1.00
��-��������-'-��������� ...... ����'--���-'-���---''--���'--����
By permission, The Permutit Co., Inc., Data Book, J 953.

622 Applied Process Design for Chemical and Petrochemical Plants


A-33.
Alkali and Lime-1 ppm Equivalents
Alkalinity A Frf'P C(h T.H. u CaCO,
NamP. Fnrmule, Increase Reduct ion Inceceee
I l'pm I l'pm ppm ppm ppm
Sodium nicarhvnale NaJIC01 0.60
Soda AP.h (il6,...() NarO .. 99.16,..� Na,C01) Na1C"01 0.94 0.41
Cauatic Soda (767,i Na!O =-- 9�.06':'() NaOH} NaOI! J.23 J.08
Chrmical Lime (Qukklimr- l'sually 9()7" CaO) f'aO J.61 1.0 1.61
Hydrated Lim" [ll,=ua'ly n"t f'a(OH)1) C"a(Oll)I J.26 1.11 J.26
By permission, The Permutit Co., Inc., Data Book, 1953.






A-34 .
Sulfuric, Hydrochloric Acid Equivalent CaCO, }';quivah·rit
lo onf" lb. Acid
Spl'r·ific
Name Formula (;ravily C"nnrPnlrallor, GramB/Liter Lbs, Grain I
60° /60°F.
Sul luric Acid 60° n- n.so, 1.70{,9 77.67% 1325 • 7�26 Dt,4.8
Sulfuric Ac-id 66" Be H1SO, ).RJ[i4, 93.19';� 1710 .9[,09 6657
SuHuric Al'id 9Rr:� 11,SO, J.S407 98.00% 1804 1.0000 7000
Hvdrochlnrlc Arid IR':c Be IIC"I 1.1417 21.n�-o 319 .3S31 26�2
By permission, The Permutit ce., Inc., Data Book, 1953.

Appendix 623

A-35.




ASME FLANGED AND
DISHED HEADS
IDDCHART

OD - Outside Diameter
THK - Thickness
OH - Overall Height
SF - Straight Flange
RD - Radius of Dish
For "Overall Height" add length of straight flange to IDD given, plus thickness ICR - Inside Corner Radius
of material.
IDD - Inside Depth of Dish
Use when RD EQUALS DIAMETER


o;-r-f: l/,s� v,� !1/u" J/e" '/,11," »· Y•a" %"' 1 Vu ... 'I, I,,,. I r
12 'f, 1,95 1.92 2.0J 2 09
14 '/1 2.29 2.26 2.27 2 35
16 I 2 63 2 60 2.51 2.62
-�
18 1Ya 2 97 2.94 2.9! �I
___!0 1V, J,31 3.28 325 3.22
22 H� 3,73 J,75 3.67 3 64 On
24 1Yi 4,00 3.97 3.93 3.90
26 2'/4 4 72 4 69 1..66 463 Application
28 2V, 4,99 4.96 4 92 4 89
30 211.t 5.25 5.22 5 19 5 16
32 2'/, 5.52 5 48 5 45 5 42
34 2V, 5.78 1 5.75 5 72 5.69
36 2114 6 05 6.02 5.98 5.95 --�
38 3 6 78 6 74 6 71 6 66 6 65 6.62 s.ss 6 56 6 53 6 sn fi 44 6 38
40 3 7 04 7.01 6.98 695 6 91 6 88 6.85 6.82 6 79 6 76 6 70 6,64
42 3 7 31 7,27 7,24 7 2·1 7.18 7 15 t 12 7,08 7 05 7 02 6 96 6 90
44 3 7 51 7 54 7 51 7.47 7 44 7.41 7.38 7 35 7 32 7.29 7 22 7 16
46 3 7.84 7 80 7 77 7.74 7.71 7.68 1.64 7 61 7 58 7.55 7 49 7 43
48 3 6.10 8.07 8.04 8.00 7.97 7.94 7 91 7 BB 7 85 7 Bl 7,75 7 69
50 3 B 37 6.Jd 8.30 6.27 B 24 8.21 817 8.i4 8.11 8.08 8.02 795
52 Jl/1 9.09 9.06 9.03 8.99 8 96 8 93 8 9J 8.87 8.84 8.80 8.74 8,68
54 3¥, 9 35 9.32 9.29 9.26 9 23 9 19 9.16 9.13 9, 10 9 07 9 01 8 94
56 33/, 9.62 9.59 9.56 9.52 9 49 9.46 9.43 9.40 9.36 9,33 9.27 9.21
I 58 3% 9.89' 9.85 9.82 9.79 9.76 9,72 9.69 9.65 9 63 9 60 9.53 9.47
60 JJ/, 10 15 10 12 'O 09 10.05 10 02 9 99 9 95 9.93 9.89 9.86 9.80 9.74
62 3.l/, 10.42 10.39 10 35 10 32 10 29 10 26 10.22 10.19 10.16 10 13 10.06 10.0J
64 4V, 10.99 10 95 10 92 10,89 10 86 10.83 10.79 10 76 10 73 10 70 1064 10,57
66 4% 11.25 1122 11 19 1116 1 I 12 11 09 11 06 11.03 10.99 10.96 10.90 10,64
68 4Y. 11.52 11 49 11 45 11 42 11.39 n.ss 11 32 11.29 I i.26 11 23 i 116 11 10
70 4Y• 11.78 11.75 11 72 11 69 11 65 11.62 11 59 11 56 11.53 i i.49 11 43 11,37
72 41/.. 12.35 12 32 12.29 12.26 12.22 12.19 12, 16 12.13 12.10 12.06 12.00 11.94
74 411, 12.62 12.59 12.55 12.52 12.49 12.46 12.43 12 39 12.36 12.33 12.27 12 20
_76 4¥, 12.89 12.85 12.82 1279 12.76 12.72 12.69 12.66 i2 03 12 59 12 53 12.47
78 0'4 13.15 13.12 13.09 13,05 13.02 12.99 12.96 12 92 12 89 12 86 12.80 12.73
80 5 13 57 13 54 13 50 13.47 13.44 13.41 13.37 13 34 13 31 13 26 13 21 13.15
82 5 '3 64 13 60 13.77 13.74 13.70 13 67 !364 13 61 13 57 13 54 13 48 13.41
84 SJ/, 14 56 1'.52 14.49 14.46 14.43 14 39 1d.36 14 33 14 30 14 27 14 20 t4 i4
86 SJ/• 14 82 14 79 14 76 14 72 14 69 14 66 14 63 14 60 1• 56 11. 53 14.47 14 40
BB 5¥, 15,09 15 OS 15 02 14.99 14.96 14.92 14.89 14.66 14 83 14 80 14.73 1467
!UI 5¥, 15.35 15 32 15.29 15.26 15.22 15 19 15 16 15 !3 i5 09 is 06 15 00 14 93
92 SI/, 15.62 15.59 15 55 15 52 15 49 1516 15 42 15.39 15.36 15.33 15.26 15 20
94 5¥, 15.69 15,85 15.82 15 79 15 75 15 72 15.69 15.66 15.62 15.59 15.53 15.46
96 6V, 16 6i 16 57 16 54 i6 51 16 46 161.4 i6.4' 16 36 16 35 16 32 16 25 1619
98 61/2 '6.87 16 84 '6 61 16 77 16 74 1671 1668 1664 16 6i 16 56 16.52 16.45
100 6� 11 17 '.4 i 7 10 17 07 17 04 i? 01 16 97 16*tft9' 16 68 16 85 16 78 16 72
102 6Y2 17 40 '17 37 17 34 17 31 17 27 1724 1721 1718 17 ·,<! 11·,·1 17 05 16.98
104 6\,1 17.67 17.64 17 60 1157 17 54 17 51 17 47 17.44 17 41 17.38 17 31 17 25
106 6'h 17 94 17 90 17 87 17 84 17 80 1777' 17,74 17.7i 17 67 17 64 "17 58 17 51
108 6'h 18 20 18 17 i3,14 18 1D 16.07 18.04 16 00 17 97 17.94 17 91 i7 64 17.76
110 tv. i8 92 'B 89 18.86 i3.82 1879 18 76 18 13 18.69 ia.es i8 63 18 57 18.50
112 tv. is 19 '.9 15 19.12 i9.09 19.06 :9.02 18.99 18.96 18.93 !8.89 18 83 18 77
114 711, 19.45 19.,12 10 39 19 36 19 32 19 29 19.26 19.23 19.19 19.16 i9.10 19 03
116 7Y, ;9}2 19 69 i965 1962 19 59 19 56 19 52 19 49 19 46 i9 43 19 36 19 30
I 118 7V4 19.99 19 95 19.92 19 89 19 85 19 82 19.79 19 76 19 72 19 69 19 63 ;9,55
i 120 7V4 20 2,5 20.22 20 19 20 15 20 i2 20.G9 20 05 20.02 ;9 99 19 96 19 89 ;9 83
By permission, Hackney-Brighton, a division of Trinity Industries,

624 Applied Process Design for Chemical and Petrochemical Plants

A-35.





ELLIPTICAL HEADS
(2:1 RATIO)

ID
- Inside Diameter
l OH - Overall Height
OH THK - Thickness
SF
- Straight Flange
100 - Inside Depth of Dish
x - STANDARD
I - INQUIRE

SIZES AND THICKNESSES OF HEADS
-
v,, 11/16, 1111, 2V4, 4, x
:v,, IV1a, :v,, 1J&. 1Va, 1'¥9, 2'h, 41/4, 5,
� :v,. v, ,;,,. 7/16 '¥, l:V1& 1 1V, 1¥, 1:V, 1'/, 2 2:V, 3 3V, 3 1 h 3:V, 4v, 4:V, 5V, 5 1 11 5:V, 6 6V, 7 8 D
D
6 x x x x x x x I I I - 6
8 x x x x x x x x x I 8
10 x x x x x x x x x x x x 10
12 x x x x x x x x x x x x x x I 12
14 x x x x x x x x x x x x x x I 14
16 x x x x x x x x x x x x x x I 16
18 x x x x x x x x x x x x x x I .. 18
20 x x x x x x x x x x x x x x I 20
22 x x x x x x x x x x x x x x x 22
24 x x x x x x x x x x x x x x x x I 24
30 x x x x x x x x x x x x x x x x I 30
36 x x x x x x x x x x x x x x x x x x 36
42 x x x x x x x x x x x x x x x x x x x x 42 -- 'Nm
:..lS
48 x x x x x x x x x x x x x x x x x x x x I 48 J:J°9.
54 x x x x x x x x x x x x x x x x x x x x x I I 54 I»-·
-(')
-·111
60 x x x x x x x x x x x x x x x x x x x x x x x x I I 60 .£.-
66 x x x x x x x x x x x x x x x x x x x x x x x I I 66
72 x x x x x x x x x x x x x x x x x x x x x x x I I 72
78 x x x x x x x x x x x x x x x x x x x x x x I I 78
84 x x x x x x x x x x x x x x x x x x x x x I I 84
90 x x x x x x x x x x x x x x x x x x x x x I I 90
96 x x x x x x x x x x x x x x x x x x x x x I I 96
102 x x x x x x x x x x x x x x x x x x x x x I I 102
108 x x x x x x x x x x x x x x x x x x x x x I I 108
114 x x x x x x x x x x x x x x x x x x x x x I I 114
120 x x x x x x x x x x x x x x x x x x )( x x I I 120












By permission, Hackney-Brighton, a division of Trinity Industries.

Appendix 625
A-35.





80-10® HEADS


OD - Outside Diameter
THK - Thickness
OH - Overall Height
SF - Straight Flange
RD - Radius of Dish
ICR - Inside Corner Radius
IDD - Inside Depth of Dish
Meeting all A.S.M.E. Unfired Pressure Vessel
Code requirements, the 80-10' Head permits
significantly higher pressures than other
configurations selected for the same service.
Figure 1. The 80-10·•· Head is named for its unique
INTERNAL PRESSURE COMPARISON dimensions-the dish radius equals 80% of the
head diameter and the inside corner radius
equals 10% of the head diameter. These
304 S.S., 100 P.S.I., 100°F dimensions compare to 100% and 6%
I respectively for A.S.M.E. F&D Heads.

� ·"'"'


� -30THK � -+ �� -- � -t,,,,tC...- ��� f-- � ----:::;;--IIIIF'----:::;a,..-=-+- ��� --,


L.20THK�-:Ji,J,c_���-t11�""-:::.,.,--=,f--�+-�-+����--t-���--i
I so-io-
RD= 80% OD
ICR = 10% 00
40" ID 60"10 80"10 100" ID 120'" ID
:=tgure 2.
EXTERNAL PRESSURE COMPARISON
I
304 s.s., �o P.s.1., 100°F
f-.70THK � -+- ���� +- ��� -4 ���� --+- �� ,c- � -t7 �� ---:::.-'!
ASME F&D
RD = 100% OD-------"
ICR = 6% OD














40" ID 60"10 80"10 100" ID 120" ID
By permission, Hackney-Brighton, Division of Trinity Industries.

Index






Accounting, plant construction costs, 48 Compressible fluids, 101, 102-112 Stokes' law, 226, 230
Cost accumulation, 49 Calculation, 112 Stokes-Cunningham law, 226, 230
Affinity laws, 201, 202, 203 Pressure drop, chart, 102, 103, 111 Dust, mist, particle collector performance
Air In leakage, vacuum systems, see Computer aided drafting, 17 chart, 229
vacuum systems Condensate, flashing flow, 135-142, 147 Dusts, particle sizes, 225
Air pressure drop, table, 106 Charts, 142, 143 Dusts, hazard class, 521-523
Chart, 114 Control valve pressure drop, 90 Explosion characteristics, 524
Orifice flow, 107 Calculations, 90-96 Efficiency, centrifugal pumps, 200
Air, absolute viscosity, 132 Cost estimates, plant, 45--49 Ejector control, 380
Low absolute pressure calculations, 129 Accounting, 48 Ejector systems, 343, 344, 351
Low pressure system, 129 Chemical Engineering Plant Cost Index, 47 Air inleakage, table, 366, 367
American Petroleum Institute, 399 Cost accumulation, diagram, 49 Applications, 345
American Society of Mechanical Equipment, 45 Calculations, 359-366
Engineers, 399 Marshall and Swift Equipment Cost Chilled water refrigeration, 350
API Codes, 399 Index,47 Comparison guide, 357, 375
API oil field separators, 239 Nelson Index, 47 Evacuation time, 380, 381
API, heat absorbed from fire, 451-453 Plant, 45, Charts, 382
Babcock steam formula, 103, 107, 108 Six-tenths factor, 4 7 Example, 381
Back pressure, 401 Yearly cost indices, 4 7 Features, 345
Effect of, ,107, 108 Critical flow, safety-relief, 438 Installation arrangements, 351
Baffles, Lank mixing, 31 l Back pressure, 440 Pump-down time, 380
Diagrams, 330 Sonic flow, 138 Selection procedure, 374
Bag filters/separators, 270 Critical flow, see Sonic Specification form, 377
Bag materials, 274 Cyclone separators, 259-269 Specifications, 373
Cleaning, 272, 273 Design. 260-265 Steam jet comparison, 356
Heavy dust loads, 271 Efficiency chart, 263 Types of loads, 359
Specifications, 271 Hydroclones, 265-267 Ejectors, 346
Temperature range, 271 Pressure drop, 263, 261 Applications, 353
Bins, silos, hoppers venting, 516 Scrubber, 269 Barometric condenser, 249, 376
Blast pressure, 496 Webre design, 265 Booster, 370
Blowdown, 404 Deflagration venting nomographs, Calculations
Boiling liquid expanding vapor 509-512 Actual air capacity, 362
explosion, 504 Design Air equivalent, 360
Brake horsepower, centrifugal pumps, 200 Factor of safety, flow, 56 A.ir/water vapor mixture, chart, 364, 365
Driver horsepower, 201 Design operating pressures, 33, 34 Air/water vapor, 359
Burst pressure, 405, 456 Guide, 36 Capacity at ejector suction, 369
Cartridge filters, 274-278 Maximum operating pressure, 33 Capacity for process vapor, 362
"Capture mechanism," 279 Diaphragm metering pump, 214 Evacuation time, 371, 380
Edge filter, 278 DIERS,finalreports,523 Load for steam surface condenser, 367
Filter media, table, 278 Discharge coefficients, liquid flow, C,, Non-condensables, 362, 363
Micron ratings, 277 chart, 118 Size selection, 371
Reusable elements, 281 Dowtherm(R) pressure drop, charts, 94, 113 Steam pressure factor, 373
Sintered metal, 280 Draft tubes, mixing, 309, 313 Steam requirements, 372
Types, 276, 277, 279 Dust clouds, 517 Steam/air mixture temperature, 361
Wound vs. pleated, 276, 277 Dust explosions, 513 Total weight saturated mixture, 362
Centrifugal pumps, operating Calculations, 513 Capacity, 358
characteristics, 177-180 Dust separator, applications, 278 Discharge, pressure, 358
Calculations, see hydraulic performance Characteristics, 234 Effect of excess steam pressure, 358
Capacity, 180 Table, 232 Effects of back pressure, 359
Hydraulic characteristics, 180 Dust venting nomographs, 514-520 Effects of wet steam, 356
Performance curves, 180-182 Calculations, 513-517 Inter-and-after condenser, 351
Centrifugal separator, 256, 257 Dust, mist calculations, 226--236 Load variation, 370
Combination, 257 Brownian movement, 226, 236 Materials of construction, 347
Chilled water refrigeration, steamjets, 349 Drag coefficients, chart, 235 Molecular weight. entrainment, chart, 360
Coalescer, 258 Intermediate law, 226 Performance, 358, 370, 375
Codes, 399 Newton's law, 226, 228 Relative comparison, 357




626

Index 627
Selection procedure, 374 Relief device set pressure, 451 Scale reference, 16
Steam pressure, 353, 358, 376 Unvented gas vessels, 454 Symbols, 19-22
Steam/air mixture temperature, 361 Fittings, see pipe, fittings and valves Types, 4
Surface condenser, 349 Flame arrestors, 480 Utility, 6, l l
Temperature and entrainment. chart, 360 Flame distortion, Dares, 532, 533 Fluid flow, 52
Temperature approach, 375 Flammability, 484 Fluids, Newtonian, 52
Therrnocornpressors, 378 Flammable limits, 485 Non-Newtonian, 52
Types, 346, 347 Flammable liquid, 484 Free air, 461
Vacuum range guide, 348, 354 Auto-ignition temperature, 485 Friction factor, 53-i32
Water, 378 Explosive range, 485 Chart. 55
Ejectors, steam/water requirements, 371 Fire point, 485 Fanning, 55
Electrical charge on tanks, 537 flammability, limits, 485 Friction factor, 68,
Electrical precipatators, 280 Flash point, 484 Low pressure air chart, 132
Applications, 280, 282 Ignition point, 485 Moody, 55
Concept of operation, 281 Lower explosive limits, 485 Relative roughness, pipe, 132
Emergency relief, 450 Spontaneous heating, 485 Friction losses, 181; also see Chapter 2
Engineering, plant development, 46 Upper explosive limits, 483 Friction, head loss, 68
Equipment symbols, 19-2 l Flammable mixtures, 486 Compressible fluids, 101
Abbreviations, 25 Aqueous solutions, 496 Factor, 68
Instruments, 21, 26. 29 Calculations, 486, 49 l Vacuum lines, 131
Piping, 22 Ignition, 493 Gas constants, R, 378
Valve codes, 26 Pressure effects, 492, 493 Gravity settlers, 228
Equivalent feet (flow). 86 Temperature, effects, 491 Head, 180-200
Estimated design calculation Lime, Flare stacks, 523 Calculations, 183, 184, 183
37, 39 Height, 330, 331 Discharge, 180, 187
Equipment, 38 Purging, 534 Friction, 183
.Job record time accumulation, 40 Sizing, 528-534 Liquid, 183
Process total, 39 Flare>s, 523, 528 Net positive suction, 188-192
Examples, 83, 86, 92, 94, 99, 100, 104, 107, Knock-out pots, 523 NPSH calculations, 190-194
112, 119, 121, 122. 127, 128, 135, 139, Seal tanks, 523, 527 Performance, 197
183, 186, 190, 191, 192, 194, 197, 200, Sizing, 328, 529 Pressure, 183
203, 206. 209, 225, 236, 245, 252, 319, Smokeless, 328 Relations to other characteristics, 200
350, 360, 361, 36�!. 353, 367, 371, 372, Systems, 323, 527 Static, 183
376, 380. 406,440, 457,463, 465, 466, Flash point, flammable liquid, 484 Suction lift, 184
469, 470. 474,480, 491, 501, 503, 504, Flashing liquids, pressure drop, 134 Suction, 180, 184
508, 514 Chart, 141, 142 Total, 180
Expansion factor, Y, (llow), 82, 114 Line sizing, 135--146 Velocity, 187
Charts, 116 Flow, 32-82 Heat and Material balances, 8
Explosion calculations, 499-504 Compressible, 32, 54, 101 Heat transfer, mixing, 330, 425-427
Estimating destruction, 501 Expansion factor, Y, 82 Chart, 330
Overpressure, 502 Incompressible, 52 Overall coefficients, 332
Pressure piling, 501, 504 Laminar, 77 Vertical plate coil, 331
Relief sizing, 505 Nozzles and orifices, 82, 83 Hindered settling velocities, 231, 236
Scaled distance, 502, 503 Vapors and gases, 54 Horsepower, centrifugal pump driver. 201
Schock front velocity, 503 Flow, long natural gas lines, 120 Hydraulic performance, calculations,
TNT equivalent, 49<}-504 American Gas Association method, 121 180-188
Explosion characteristics of dusts, 515 Complex pipe systems, 122 Centrifugal pumps, 181
Explosion suppression, 518 Low pressure air, steam, 131 Discharge systems, 187
Explosion venting, gases/vapors, 504 Panhandle formula, 120, 121 Example calculation, 186
Blcves, 504 Panhandle-A formula, 121 Flow friction losses, 185, 186
Explosions, 482 Parallel system, 122 Friction losses, pipe, see Chapter 2
Blast pressure. 496 Series system, 122 Friction, 188
Combustion, 482 Transmission factors, 120 Pressure head, 184-186
Confined,482 Wevmouth formula, 120 Static head, 184-186
0
Damage, 498-501 Flowsheet symbols, 17 Suction head, 184, 183
Deflagration, 482 Equipment abbreviations, 23 Suction lift, 184, 185
Detonation. 483 Instruments, 29 Suction systems, 186
Explosions emergency relief, 450 Flowsheets, 1-11 Hydroclones, 263-267
Explosions, vapor cloud, 520 Block diagram, 4 Application system, 267
Explosive limits, 485 Combined process and piping, 5, 10 Ignition, flammable mixtures, 193
External fires, see fires Instrumentation. 3 Impellers, centrifugal, reducing diameter, 203
Factors of safety, Ilow, 56 Isometric, 6, 7, 11 Impellers,
Fiber bedv'pads impingement separator, Material balance, 12 Affinity laws, 201-203
254, 255 Mechanical, 3, 9 Comparison of types, chart, l 77
Fires, emerge1cy relief, 450-454 Pictorial, 13 Enclosed, 1 71
External, 450, 463 Piping. 3 Inducer, 171
Heat absorbed, 451 Process, 3 Open, 171

628 Applied Process Design for Chemical and Petrochemical Plants

Reducing diameter, 203 Mixers, range of operation, 289 Mixing performance, 306
Semi-enclosed, 1 70 Chart to examine types, 296 Blending, 324
Semi-open, 170 Draft tubes, 309. 313 Emulsions, 324
Impingement separators, 246, 257 Flow patterns, 291 Extraction, 324
Chevron style, 248, 255 Jet, 325, 326 Gas-liquid contacting, 324
Efficiencies, 246 Selection guide, 289 Gas-liquid dispersion, 325
Knitted wire mesh, 216 Mixing applications, 288 Liquid-liquid dispersion, 325, 326
York-vane efficiencies, 248 Blending, 300 Mixing vortex, 311
Inertial centrifugal separators, 266, 268 Gas dispersion, 325 Motionless mixing, see static mixing
Kinetic energy, pump system, 187 Motion, 300 National Fire Protection Association, 399
Larnella plate classifiers, 239 Mixing concepts, fundamentals, 297 Net positive suction head, 160-194
Line sizing work sheet, 107 Actual motor horsepower, 307 Available from system, 160, 188, 189,
Lines in vacuum service, 135-111 Axial flow, 291 190, 208
Line symbols, 17, 23 Baffle diagrams, 318 Boiler feed water pump, 194
Numbering, 23 Baffles, 311 Calculations, 189-191
Lined centrifugal pumps, 171 Calculations, 297 Corrections, 192, 193
Liquid-solid particle, separators, 228 Characteristic curves, 306 Required by pump, 180, 181, 182, 188-190
Baffle type specifications, 248 Draft tubes, 309, 312, 313 Newton's law, chart, 226
Baffle type, 247, 248 Entrainment, 309 NFPA Codes, 398
Centrifugal, 256, 259-261 Flow number, 298 Nomenclature, 154, 221, 284, 339, 397, 537
Chevron-vane, 248, 235 Flow patterns, 309-313 Nozzle, flow, 82
Comparison chart, 230 Flow, 298 NPSH (available from system, A), 160
Cyclone, 259 Froude number, 304 NPSH (required by pump, R), 160
Specification form, 268 Heat transfer, 312 Operating pressure, 408
Vane, 259 In baffled tanks, 301 Operational check-list, safety relief, 428
Wire mesh, 246 Performance relationships, mixing Orifice areas, relief valves, 43 7
York-vane, 218 variables, 306 Sharp edge, 440
Low pressure storage Power consumption of impellers, chart, Orifice, flow, 82, 83, 119
Pressure-vacuum relief, 466 312, 313 Air, table, 107
Manhours, calculation, 37-10 Power number, 299 Overpressure, 403
Material of construction, centrifugal Power relationships, 301, 316 Causes, 427
pumps, 211 Power, 299 Packing, shaft, 171-1 72
Pipes, 18, 27, 28 Process results, 316, 323, 321 Lantern gland, 171
Maximum Allowable vVorking Pressure, Pumping number, 400 Mechanical seals, 171-172
code, 399,405,406,408 Radial flow, 291 Stuffing box, 1 71
Mechanical seals, 1 71-177 Reynolds number, 299, 303 Particle sizes, 224, 225
Fundamentals, 172 Scale up, 312-318 Air-borne particles, 227
Inside, 172 Shear rate, 315 Characteristics, 226
Installations, 173 Similarity for scale up, 312, 313 Dispersed, chart, 226
Lubrication, 174 Dynamic, 313 Terminal velocity, 228
Outside, 173 Geometric, 312, 313 Physical properties, water vapor, 378
Seal flush system, 1 76 Kinematic, 313 Saturated steam, 379
Tandem, 177 Turbulence, 323 Pipe material specifications, 27
Mechanical separations, 224 Mixing heat transfer Pipe sizing, non-Newtonian flow, 133
Mechanical vacuum systems, 342 External jackets, 326-328 Pressure drop, chart, 131
Applications, 352, 353 Helical coils, 312, 326, 327 Slurries, 134-139
Barometric in iercondenser, 349 Vertical coils, 326, 327 Vacuum conditions, 128
Evacuation times, 387 Mixing impellers, 290-297 Pipe, fittings and valves, 56-65, 69, 70
Operating range, 355 Anchor, 290-329 Comparison with tubing, 63, 64
Performance curves, 386 Blending, 321, 326 Flanged, 61, 62
Pump down, 380 Characteristic curves, 306 Industry sizes, usual, 59
Surface inter I after condenser, 349 Chan Lo examine turbine applications, 296 Lined, 59, 60
System diagrams, 383 Efficiency of propellers, 299 Relative roughness, 68
Mists, particle sizes, 225 Flow of propellers. 298, 299 Socket weld, 57
Mixers, jet, 325, 326 Flow pauerns, 309-312 Threaded, 57
Mixers, mechanical components, 289 Gas-Liquid contacting, 324, 326 Welded, 65, 66
Baffles, 311 General !is t im pe1lers, 291 Piping system, 54
Coils, 312 Helical, 290, 329 Plam layout, 45
Draft tubes, 309, 313 Liquid-liquid dispersion, 326 Checklist, 46
Drive and gears, 306, 308 Multiple, 297 Development, 46
Impeller, location, 322 Performance relations, variables, 306 Plant models, 8, 15
Impeller types, 290, 291-295 Propeller, 290 Planning, 8
Materials of construction, 307 Scale up, 312, 314-317, 332 Plot plans, 6, 14
Motor horsepower, actual, 307, 318 Turbines, 290, 291 Pressure drop,
Shaft, 306 Turbulence, 326 Air, table, 106
Specifications, 308, 310 Types performance, 297 Calculations, 61, 67, 71-86, 87-89, 96
Tanks, 320 Mixing of liquids, 288 Compressible fluids, IOI, 103, 104

Index 629

Con trol valves, 90-96 Steam service, 426 Lined, 171
Dowtherrn liquid, friction loss chart, 94 Type,400 Turbine type, 169
Dowtherrn vapor, l 1 � Valves, parts, 412 Pumps, centrifugal system performance, 197
Equivalent feel concept, 86 Pressure-vacuum relief, 466 Affinity laws, 201-203
Equivalent feet, non-viscous liquids, 89 Calculations, 469 Branch piping, 200
Fittings, 71 Emergency venting, 476-479 Calculations, 199
Flashing liquids, 134-146 Equipment (valves), 468, 478, 480 Effects of performance changes, 201-203
Flow coefficients, Cv, for valves, 81 Fire exposure, 4 79 Head curve for single pump, 198
Friction loss, 68 Free air, 469, 474 Relations between head, horsepower,
Incompressible fluid, 71 Specification work sheet, 481 capacity and speed, 200
Laminar flow, 77, 78, 86 Thermal outbreathing, 468, 469 Temperature rise 207-209
Liquid lines, chart, 92 Vacuum in breathing, 468, 469, 475 Viscosity corrections, 203-207
Long natural gas pipe lines, 120 Process check list, 35 Purging, flare stack systems, 535
Non-water liquids, 99 Process design organization, 1, 2 Reciprocating pumps, 215-219
Pipe, 71 Calculations, 37-39 Flow patterns, 219
Resistance coefficient, K, 71, 72, 73-77, Costs, 43 Specification form, 219
78-80 Manhours, 40-43 Relief areas, 437
Resistance of fittings, 69, 70 Scope, 2 External fires, 451, 453
Resistance of valves, 81 Process engineer, role, 3 Sizing, 434, 436
Steam, 103 Activity analysis, 36 Relief sizing, explosions gases/vapors, 505
Sudden enlargement zconuacuon. 70, 80 Estimated design manhours, 37 Deflagration venting, 506, 507
Total line, 64 Time planning, 36 High strength venting, 508
Two-phase flow, 124-127 Process planning, scheduling, flow sheet Low strength venting, 508
Vacuum lines, 128-134 design, 1 NFPA Code, 506
Velocities, 85, 89, 90 Process results, mixing, 316, 323, 324 Venting (deflagration) nomographs, AP!,
Velocities, chart, 91 Process safety, 399 509-512
Velocity head, 71 Properties of gases/vapors, 439 Venting, dusts, ( deflagration),
Water flow calculations, 96 Pumping of liquids, 160 nomograph, API, 514-520
Water flow, table, 93, 97, 98 Pumps centrifugal, 161-164 Relief valves, 400
Pressure level relationships, AJ."\JSl Standards, 161 Code requirements, 415, 420
Closing, 411 Bearings, 168 Installation, 422, 429-434
Conform to Codes, 409, 410 Boiler feed water high pressure, 167 Safety-relief, 400
Relieving, 411 Brake horsepower, 200 Relieving pressure, 411-417
Resealing, 411 Capacity-head ranges, 165 Resistance coefficient, K, (flow), 71, 72
Rupture disks, L.d O Casing, 165 Flow coefficient, C,,, 81, 83
Set pressur� (relieving), 425, 455 Double suction, 166, 167 Pipe sizing, 83, 84, 86
Simmer, 412 Efficiency, 200 Sudden contraction, 80
Vacuum, 466 High speed, 169 Sudden enlargement, 80
Valves, 409 Illustrations, 161, 164 Tables/ charts, 73- 76, 77, 78-80
Pressure levels chart, 53 Impellers, 164, 170 Valves, 81
Reference, 56 In parallel, 177, 178 Resistance, equivalent feet, design, 86-89
Pressure piling, explosion, 501 In series, 176, 178 Chart, 87, 88
Pressure, Liquid horsepower, 200 Reynolds number. 55, 67
Accumulation, 403 Materials of construction, 211 Calculations, 68
Levels, 409, 410 Mixed flow, 169 Chart, 110
Operating, 408, 410 Multistage, 167 Rotary pumps, 206
Over, 403 Operating curves, 180 Selection, 214-
Relieving, 411 Packing, shaft, 170 Type, 213
Pressure-relief terms/ definitions, 403 Performance curves, 180, 181, 182, 197 Roughness, relative, 68
External fires, 450 Rotative speed, 197 Chart, 68
Relief areas, 437 Seals, shaft, 168 Runaway reactions, 405
Pressure-relieving devices, 399, 435-455 Selection guide, 178, 179 Runaway reactions, DIERS, 521-523
Balanced. valves, 400, 405, 407, 441 Single stage, 164 Rupture, disk, 401, 418, 435, 455
Calculation of relief areas. 436, 440, Single stage, single impeller, 174 Burst pressure, 455
441,449 Specifications, 209 Calculations, non-explosive, 455, 459
Conventional valves, 400, 402, 407, 438 Stuffing box, packing, 171 Code pressure levels, 410
External fires, 450, 453 System performance, 197, 198 Effects of temperature, 458
Genera, Code requirements, 412, 415, Temperature rise, 207, 208, 209 Graphite, 418-'-120, 424
420-425 Turbine, 169 Installation, ,122, 423
Installation, 429-434 Turbine type performance, 178 Liquids, 462
Materials of construction, valves, 402, Vertical in-line, 165, 175 Low pressure, 418, 421
404,405 Vertical multistage, 168 Manufacturing range, 434, 456
Pilot operated valves, 400, 406, 407 Vertical propeller, 169 Metal, 411
Rupture disks, 401, 418, 451, 455 Viscosity correction, 203-207 Non-fire, 465
Selection/application, 427, 434 Pumps classes, 161 Quick opening, 414, 415
Sizing, 436-441, 449, 434, 453 Basic pans, centrifugal, 164 Reverse buckling, 413
Special. 401 Design standardization, 161 Selection features, 434

630 Applied Process Design for Chemical and Petrochemical Plants

Sizing, 451, 453, 455, 459, 462 Steam pressure drop, 103 Operating chart, 385
Sonic flow, 461 Chart, 109 Operating range, 386
Types, illustrations, 411-421 Stokes law, chart, 226 Performance curve, 386
Rupture disk, liquids, 462, 466 Sump design, vertical pumps, 212 Rotary displacement pump, 397
Rupture disk/ pressure-relief valves Sylvan chart, 224, 229 Rotary lobe blowers, 390, 392, 394
combination, 463 Tanks, above ground, API std., 468 Rotary lobe performance curves,
Safety relief valve, 400 Refrigerated tanks, 478 395, 396
See Relief valve Storage, 469 Rotary vane performance chart, 389
Safety valve, 400, 434 Temperature rise, centrifugal pump, 207-209 Rotary vane, 388, 394
Safety, vacuum, 343 Terminal particle velocity, 228, 230 Screw-type lobe, mechanical seal,
Scale-up, mixing, 312, 314-316 Particles, different densities, 238 382,392
Design procedure, 316-318 Single spheres, 274 Screw-type rotary lobe blower, 390-391
Schedules/summaries Solids in air, 237 Vacuum relief, 435
Equipment, 30, 31 Solids in water, 237 Pressure/vacuum, 435, 466
Lines, 23, 24 Test pressure, piping, 18 Vacuum systems, 343
Screen particle size, 225 Thickeners and settlers/decanters, Absolute pressure conversions, 363
Scrubber, spray, 269, 270 Decanter, 242 Airinleakage, 366
Impingement, 269, 272 Gravity decanter, illustration, 243, 244 Calculations, 366-375
Separator applications, liquid particles, 235 Happel/Jordan method, 241 Dissolved gases release, 368
Liquid particles, 235 Horizontal gravity, 239 Estimated air inleakage, table, 366
Separator selection, 224, 225 Lamella classifiers, 239 Evacuation time, 371
Comparison chart, 230 Settler vessel, illustration, 240 Maximum air leakage, chart, 367
Efficiency, 231 Time planning and scheduling, process Specific air inleakage rates, 368
Size ranges, solid-solid and solid- design, 36 Temperature approach, 375
liquid, 267 Total head, centrifugal pumps, 180, 183 Classifications, 343
Separator, wall wiper, 265 Discharge, 205 Diagrams, 380
Physical arrangements, 265 Head curve, 198 Pressure drop, 353
Set pressures, safety relief valves, 425 Suction head, 184, 186 Pressure levels, 343, 352
Simmer pressure, 412 Suction lift, 184, 186 Pressure terminology, 348
Sizes, air-borne solids, 227 Type, 184 Pump down example, 381
Dispersed, 226 Tubing, 63, 64 Pump down time, 380
Sizing, safety relief, 436, 437-441 Two-phase flow, 124 Thermal efficiency, 384
API liquid valve, 444 Calculations, 125-127 Valve codes, 26
Balanced valves, 441 Flow patterns, chart, 124 Valves, see pipe, fittings, and valves
Conventional valves, 438 System pressure drop, 125 Vapor cloud explosions, 520
Critical back pressure, 440 Types of flow, 124, 125 Velocities, fluid flow, 85, 89, 90
Effects of two-phase flow, 437 Utilities check list, process design, 34 Vacuum lines, 133
Hydraulic expansion, 441 Vacuum, Velocity head, 71
Rupture disks, 434 Absolute, 53 Venting (deflagration) nornographs, API,
Sub-critical flow, 449 Air systems, 129 508-511
Slurry flow, process pipe, 142-147 F1ow calculation methods, 129 Venting dust deflagration
Regimes, 143 Gage (gauge), 53 nomographs, APT, 514-520
Sonic flow, safety relief, 438 Line sizing, 128 Venting dusts, 521
Rupture disk, 460, 461 Pressure drop, 128 Venting, low pressure storage, 466
Sub-sonic flow, 461 Vacuum capacities and operating ranges, Calculations, 469-479
Sonic or critical flow, 115, 125 table, 344, 355 Work sheet, 481
Calculations, 125 Ejectors, 344, 357 Vessels,
Velocity, 126 Integrated systems, 344 External fires, 450
Specific speed, 194-197 Liquid ring pumps, 344 Unwetted gas only vessels, fire, 454
Impeller designs, 194 Rotary lobe blowers, 344 Viscosity correction, centrifugal pumps,
Upper limits, chart, 195-197 Rotary piston pumps, 344 203-207
Specifications, Rotary vane pumps, 344 Chart, 204, 205, 207
Rupture disk, 455 Vacuum equipment, 343 Vortex, 190
Safety relief valves, 454, 467, 481 Applications diagram, 352 Water hammer, 98
Specifications, centrifugal pumps, 209 ASME Code, 344 Wire mesh separators, 246, 247
Spray nozzle particle size, 225 Pumps, 382 Calculations, 247-254
Standards and Codes, 31, 32, 33 Steamjets, 357 Efficiency, 248, 250
Static electricity, 536 Vacuum flow, Installation, 251-253
Static mixing, 332 Friction losses, air steam, 131 k-value for mesh, table, 249
Applications, 336 Pressure losses chart, 134 Mesh patterns, 247
Calculations, 337, 338 Vacuum pumps, mechanical, 382 Pressure drop, 249, 251
Materials of construction, 337 Liquid ring pumps, 383-385 Specifications form, 254
Principles of operation, 335 Liquid ring volume displaced/ Vapor velocity, 247, 250
Type of equipment 334-338 evacuation, 387 Wire mesh types, 24-8





Applied Process Design for

Chemical and Petrochemical Plants

Volume 1 Third Edition


Completely revised and updated throughout, this new edition of the all-time
best-selling process industry classic is now more valuable than ever. Volume 1 of
this three-volume set is the definitive guide for process engineers and designers. It
covers a complete range of basic day-to-day operation topics such as the latest
ASME Code requirements; design and assembly of piping systems; selection of
mechanical equipment; manpower requirements; pump types, ratings, and selec-

tions· separation of liquid and solid particles from vapor; and methods for liquid
and gas :fl.ow and pumping of liquids.
This expanded edition introduces new design methods and is packed with
examples, design charts, tables, and performance diagrams to add to the practical
understanding of how selected equipment can be expected to perform in the
process situation. A major addition is the comprehensive chapter on process
safety and pressure relief devices that incorporates industrial safety design con-

siderations, ranging from new devices and components to updated venting
requirements for low-pressure storage tanks to the latest NFPA methods for siz-
ing rupture disks and bursting panels, and more.

All three volumes of Applied Process Design for Chemical and Petrochemical

Plants serve the practicing engineer by providing organized de-sign procedures,
equipment suitable for application selection, and charts in readily usable form.
Process engineers, designers, and operators will find more chemical and petro-
chemical plant design data in:

Volume 2/Second Edition, which covers distillation and packed towers, and
contains material on azeotropes and ideal and non-ideal systems.
Volume 3/Second Edition, which covers heat transfer, refrigeration systems,
compression surge drums, and mechanical drivers.


Ernest E. Ludwig, a registered professional chemical engineer in Louisiana, is a
Fellow of the American Institute of Chemical Engineers and a past member of the
American Society of Mechanical Engineers. He is a consulting engineer in Baton
Rouge, specializing in plant design, operations, industrial fires and explosions,
and management in the chemical and petrochemical industry.



Cover design by Martin H. Vtves PRODUCT #5025
ISBN 0-88415-025-9
00 00
GI P Gulf Professional Publishing , JU
p O
an imprint of Butterworth-Heinemann
150251 ,