IMAGE EVALUATION TEST TARGET (MT-3) V > //W i Wo «L? Jr? ^ ///// <\, % ^^- y /A, 1.0 I.I - lilM J 40 1.25 1.4 1^ lllitt Hi 2.0 I™ 1.6 V] <^ /a 'el c^. c*] *3 A^ 'i \ ///, Photographic Sciences Corporation 4, \ \ cF \\ ■-^ ^ \ "^A*^ % "•b^ ;\ 23 WEST MAIN STREET WEBSTER, N.Y. 14580 (716) 872-4503 Q- Q>. O^ CIHM/ICMH Microfiche Series. CIHM/ICMH Collection de microfiches. Canadian Institute for Historical Microreproductions Institut canadien de microreproductions historiques 1980 Technical and Bibliographic Notes/Notes techniques et bibliographlques The Institute has attempted to obtain the best original copy available for filming. Features of this copy which may be bibliographically unique, which may alter any of the images in the reproduction, or which may significantly change the usual method of filming, art checked below. L'Institut a microfilm* le meilleur exemplaire qu'il lui a 6X6 possible de se procurer. 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Les diagrammes suivants illustrent la mdthode. 1 2 3 32X 1 2 3 4 5 6 K 7 / Hydraulic Tables. APPLICABLE FOR WATER PIPES AND SEWERS, BY E, H, KEATING, HAUFAX, NOV/v SCOTIA. 'h' TABIiE I. S=Tho sine of tlio 8lopc=7=tho hyilraulic indiniition in onu foot. F=The fall in fcot per mile, or tho height in feet duo to friction per mile of length. /=The nionn hydraulic inclination: i=Thc length of tho pipe or sower. A=The head duo to friction. For most purposes and where the pipe or sewer is long, h may bo regarded as the total head. i. i n • This table was originally prepared— without the colvunn of velocities —with tlie view to simplify calculations for velocity and discharge by means of M. DuBuat's formula expressed in Jlnglish inches V-- in which 306.590 (r ^ - .1032) — .2906 (r ^ — -1032) V= the velocity in inches per second. f = the mean radius or hydraulic depth in inches. S = the sine of the slope ; and also to facilitate similar calculations by means of_Mr. Leslie's table of constants given in Beardniore's Hydrology, whe-e -^ [ is first required to be found ; and from Mr. Neville's table* for finding tho velocity in fci^ per second, from the product of the hydraulic mean depths and hydraulic in- clinations. . The application of the table for these purposes needs no explanation. The column of velocities will be found serviceable in detorininiiigthe velocity and discharge not only tlirough a 12 inch pipe, but— with the aid of Table 2— those for any pipe or sewer can readily be obtained. Tho velocities luu'cbcen calculated from DuBuat's formula, as given above, Avhich reduced for a 12 inch pipe, becomes 499.40 V = — .47 (1)5^-%;. %. (I +1.6)^ The results are in all cases a little less than those given in table via of Mr. Neville's work, (page 431). This difference will be explained by re- ferring to that work, (png(> 195). The lornuila used by Mr. ^evllle, in con- structing his table viii, being 307 (r ^ — -1) V ^ ^ .3 (r ^ - .1) (f,) ^ - hyp. log. (I + 1.6) ^ the results from which are stated to be in excess of the true quantities. ^ The inclinations given in the tal)le are from .01 foot per 100 to lo per 100 feet, which are suflicient to meet all ordinary rc(iuirements. This table is also particularly adapted to the use of engineers wlio are in the habit of registering inclinations in feet per 100, as it is only ne- cessary to remove the deciinal point two places to tho rigbt, in the lirst column, in order to obtain the corresponding inclination per 100 feet, ino table, therefore, becomes a useful tab . of gradients, as it gives not only t lo rise or fall in unity, but tho equivalent inclination hi feet per mile and tlio distance required to rise or fall one foot. Seville's Hydraulic Tables, Co-efTicient and Formula, page 220, second edition. 'i 1 1 HydraiUic Tables, Applicable for Water Pipes and Sewers ; by E. PI. Keating. i SLIP To he insprtod bctweoii pa-res 80 and HI in IIk! "Report of ProoeodingB of tho Fourth Annual Meeting of the American Wutei- Works Association." 1884. ERRATA. . ^, In the heading to tho 3rd column, throughout Table 1.— For ''one inch ' read one in. On page 85, 2nd column.— For "61.784" read 61.744. On page 87, 2nd column.— For "9G.G26" road 0G.024. On page 92, 3rd column of Table 2.— For "1.090" read 1.000. .0001 .0002 .0003 .0004 .0006 .OOOG .0007 .0008 .0009 .0010 .0011 .0012 .0013 .0014 .0016 .0018 .0017 .0018 .0019 .0020 .0021 .0022 .0023 .0024 .0025 .0026 .0027 .0028 .0029 .0080 .0031 .0032 .0033 .0034 .0035 .0030 .0037 .0038 .0039 .0040 .0041 .0042 .0043 0.528 1.06(i 1.584 2.112 2.640 8.168 3.696 4.224 4.752 5.280 5.808 6.336 6.864 7.392 7.920 8.448 8.976 9.504 10.032 10.560 11.088 11.616 12.144 12.672 13.200 13.728 14.256 14.784 15.312 15.840 1().368 16.896 1 7.424 17.952 18.480 19.008 19.536 20.064 20.592 21.120 21.648 22.176 22.704 One Inch. 10,000.00 5,000.00 3,333.33 2,500.00 2,000.00 i,(;(;6.67 1,428.57 1,250.00 1,111.11 1,000.00 909.09 833.33 769.23 714.29 666.67 625.00 588.24 555.56 526.32 500.00 476.19 454.56 434.78 416.67 400.00 384.62 370.37 357.14 341.83 333.33 322.68 312.50 303.03 294.12 285.71 277.78 270.27 263.16 256.41 250.00 243.90 23S.10 232.66 100.00 70.71 67.73 50.00 44.72 40.83 37.80 35.36 33.33 31.62 80.15 28.87 27.74 26.73 25.82 25.00 24.26 23.57 22.94 22.30 21.82 21.32 20.85 20.41 20.00 19.61 19.25 18.90 18.57 18.26 17.96 17.68 17.41 17.15 16.90 16.67 16.44 16.22 16.02 15.81 15.62 15.43 15.25 4.76 7.04 8.83 10.86 11.73 12.98 14.16 16.23 16.27 17.26 18.20 19.10 19.98 20.83 21.64 22.46 23.23 24.00 24.74 26.46 26.17 26.86 27.55 28.23 28.89 29.64 30.18 30.82 81.44 82.04 82.64 88.24 33.83 34.43 35.00 35.56 3(;.14 86.69 87.22 87.79 38.30 38.86 39.38 8 Sine of the Slope = .0044 .0045 .0040 .0047 .004S .004'.) .0060 .0051 .0052 .0068 .0054 .0065 .0056 .0067 .0068 .0069 .0060 .0061 .0062 .0068 .0064 .0065 .0066 .0067 .0068 .0069 .0070 .0071 .0072 .0073 .0074 .0076 .0076 .0077 .0078 .0079 .0080 .0081 .0082 .0083 .0084 .0085 .0086 .0087 .0088 F Pull per Mile in Feet. Monn Ilydnuilic Iiicliiiiitioii h [^) M VJ or One Inch. 23.232 23.760 24.288 24.816 26.344 26.872 26.400 26.928 27.466 27.984 28.612 29.040 29,668 30.096 80.624 31.152 31.680 32.208 32.786 33.264 38.792 34.320 34.848 86.876 35.904 36.482 36.960 37.488 88.016 88.544 39.072 39.600 40.128 40.656 41.184 41.712 42.240 42.768 43.296 48.824 44.852 44.880 45.408 45.936 46.464 227.27 222.22 217.39 212.77 208.83 204.08 200.00 196.08 192.31 188.68 185.19 181.82 178.67 175.44 1 72.41 169.49 ' 166.67 168.93 161.29 158.78 156.26 153.85 151.52 149.26 147.06 144.98 142.86 140.85 138.89 136.99 135.14 138.83 181.58 129.87 128.21 126.58 125.00 128.46 121.96 120.48 119.05 117.65 116.28 114.94 113.64 a/T 16.08 14.91 14.75 14.69 14.44 14.29 14.16 14.00 13.87 13.74 1.3.61 13.48 18.36 18.26 13.13 13.02 12.91 12.80 12.70 12.60 12.50 12.40 12.81 12.22 12.18 12.04 11.95 11.87 11.79 11.71 11.63 11.66 11.47 11.40 11.82 11.25 11.18 11.11 11.04 10.98 10.91 10.85 10.78 10.72 10.66 Velocity in Inches per Second in 12" ripe. 39.90 40.43 40 94 41.46 41.96 42.47 42.9(') 48.45 43.96 44.44 44.93 46.42 45.90 46.33 46.82 47.27 47.73 48.25 48.68 49.12 49.57 60.07 60.49 60.94 51.39 61.82 62.26 62.66 53.11 63.52 53.93 54.35 54.83 66.21 65.70 56.09 56.47 66.86 67.33 57.67 58.15 68.49 68.98 59.34 69.77 ft s Sine of the Slope :n= A t K .008'.) .OOUO .00<.)1 .0092 .0003 .0094 ,0096 .0091) .0097 .0098 .0099 .0100 .0101 .0102 .0103 .0104 .0105 .OlOG .0107 .0108 .0109 .0110 .0111 .0112 .0113 .0114 .0115 .0116 .0117 .0118 .0119 .0120 .0121 .0122 .0123 .0124 .0125 .0126 .0127 .0128 .0129 .0180 .0131 .0132 .0183 F Fall per Milo in Feet. = / / S Mean llydniulic Int'linatiun / h 40.992 47.520 48.048 48.576 49.104 49.1)32 50.160 50.688 61.216 51.784 52.272 52.800 53.328 53.856 54.884 54.912 55.440 55.968 56.496 57.024 57.662 58.080 58.608 59.136 59.664 60.192 00.720 61.248 61.776 62.304 62.832 63.360 63.888 64.416 64.944 66.472 66.000 66.528 67.056 67.584 68.112 68.640 69.168 69.696 70.224 ^ = V 7 or One Inch. 112.36 111.11 109.89 108.70 107.63 106.88 106.26 104.17 108.09 102.04 101.01 100.00 99.01 98.04 97.087 96.154 95.238 94.340 93.468 92.693 91.743 90.909 90 090 89.286 88.496 87.719 86.957 86.207 85.470 84.746 84.034 83.333 82.645 81.967 81.301 80.645 80.000 79.866 78.740 78.125 77.519 ,76.923 76.336 75.768 75.188 VT 10.60 10.64 10.48 10.43 10.37 10.31 10.26 10.21 10.15 10.10 10.05 10.00 9.96 9.90 9.85 9.80 9.76 9.71 9.67 9.62 9.58 9.68 9.49 9.46 9.41 9.37 9.33 9.29 9.26 9.21 9.17 9.13 9.09 9.05 9.02 8.98 8.94 8.91 8.87 8.84 8.805 8.77 8.74 8.70 8.67 Velocity in InclicH per Second in 12'^ Pipo. 60.14 60.61 60.96 61.26 61.72 62.11 62.61 62.82 68.31 63.66 63.97 64.39 64.81 66.16 66.59 66.94 66.30 66.65 67.02 67.38 67.75 68.12 68.51 68.89 69.18 69.67 69.87 70.27 70.67 70.98 71.38 71.70 72.12 72.64 72.86 73.19 73.62 73.86 74.30 74.61 74.92 75.28 75.64 75.90 76.25 1 8 F Moiin Wlocily Sine of the Full Ilydrnulln 1 » or in InclioH jxt Slope = A / per Milo in Foot. Inclination I h Vi" Second in 12'' Pipe. One Inch. .0184 70.752 74.627 8.R4 76.00 .oi;{5 71.280 74.074 8.005 76.94 .01 3() 71.808 73.529 8.57 77.28 .0137 72.33<) 72.993 8.54 77.02 .0138 72.804 72.4(i4 8.51 77.95 .0139 73.392 71.942 8.48 78.29 .0140 78.920 71.429 8.46 78.03 .0141 74.448 70.922 8.42 78.97 .0142 74.976 70.423 8.39 79.31 .0143 76.504 09.930 8.36 79.04 .0144 70.082 69.444 8.33 79.98 .0145 76.560 08.905 8.305 80.32 .0140 77.088 08.493 8.275 80.()0 .0147 77.010 08.027 8.25 81.00 .0148 78.141 07.508 8,22 81.33 .0149 78.072 07.114 8.19 81.07 .0150 79.200 O().O07 8.105 81.99 .0151 79.728 60.225 8.14 82.31 .0162 80.250 05.789 8.11 82.03 • .0153 80.784 05.359 8.085 82.95 .0154 81.312 04.935 8.06 83.27 .0155 81.840 04.510 8.03 83.59 .0150 82.308 64.103 8.005 83.91 .0157 82.890 03.094 7.98 84.23 .0158 83.424 03.291 7.955 84.56 .0159 83.952 62.893 7.93 84.87 .0100 84.480 02.500 7.905 85.19 .0101 85.008 02.112 7.88 85.61 .0102 85.530 01.728 7.855 85.83 .0163 80.004 01.350 7.83 80.15 .0104 80.592 60.970 7.81 86.47 .0106 87.120 G0.t)00 7.785 80.79 .0160 87.648 00.241 7.70 87.11 .0107 88.170 69.880 7.74 87.43 .0108 88.704 59.524 7.716 87.76 .0109 89.232 59.172 7.09 88.07 .0170 89.700 58.8'M 7.07 88.39 • .0171 90.288 58.480 7.05 88.70 .0172 90.816 .58.140 7.025 89.01 .0173 91.344 57.S03 7.00 89.32 .0174 91.872 57.471 7.58 89.63 .0175 92.400 57.143 7.50 89.94 .0174 92.928 50.818 7.54 90.26 .0177 93.456 50.497 7.515 90.56 .9178 93.984 66.180 7.495 90.87 9 i = J f f\ 8 F S Menu 7 ^ - VI Vcliioity Sine of tho Full Hvtliiuillo or in Inciic's per Slo))o =^ per Mi'io in Iiu^liiiiition vr Second A t Foot. in 12^' Pipo OuB Inch. .017'.) 94,512 55.80G 7.476 91.18 .0180 05.010 55.55(1 7.456 91.49 .0181 .7*.»2 62.910 7.276 94.20 .01 M 100.820 52.(182 7.255 94 50 .01'.)1 100.848 52.850 7.285 94.80 .011)2 101.87() 52.083 7.216 95.10 .01 '.>S 101.<,i04 51.813 7.20 95.40 .01 '.>4 102.4;;2 51.540 7.18 95.08 .01 •)5 i02.',»(;o 51.282 7.10 95.90 .01 '.)(■) 108.488 51.020 7.146 90 24 .01 '.»7 104.01(5 50.701 7.125 90.52 .01'; 18 104.544 50.506 7.11 90.80 .01<.)0 105.072 50.251 7.09 97.07 .0200 105.(i()0 60.000 7.07 97.27 .0205 108.24 48.780 0.98 99.01 .0210 110.88 47.019 0.90 100 36 .0215 118.52 4(3.512 0.82 101.(39 .0220 11(5.1(1 45.455 0.74 108.08 .0225 118.80 41.444 0.07 104.37 .0280 121.44 48.478 0.59 105.71 .0285 124.08 42.553 0.52 107.05 .0240 12(3.72 41.(307 0.455 108 89 .0245 129.8(1 40.810 0.39 109.73 .0250 182.00 40.000 0.325 111.07 .0255 184.(54 39.210 0.20 112.41 .0200 187.28 38.402 0.20 118.75 .02f,5 139.92 37.730 0.14 115.09 .0270 142.5(1 37.087 0.085 110.43 .0275 145.20 30.804 6.025 117.77 .0280 147.S4 35.714 5.975 119.11 .0285 150.48 35.088 5.92 120.45 .02U0 158.12 34.483 5.87 121.79 .02'.)5 155.7(J 38.898 6.82 128.14 .0800 158.40 3.3.833 5.77 121.38 .0805 1(31.04 32.787 5.726 125.02 .0810 1(33.(18 32.258 5.08 120.80 .0815 100.82 31.740 5.035 128.10 8 s F Monn L] ^ = y^J Velocity Sitio of tlio Full Ih'or Slope ~ per Mil<( in liidinution 1 , • St'COlKl A V Ft't^t. / Vi- hi 12"l'll.o. Oue lucb. 16.949 16.667 ._.. ., . . .-,■ .or,90 .OHOO !',ll.r.2 iM6.H0 4.116 4.08 187.40 18'.i.40 .0610 822.08 16.898 4.06 191.22 .0(;'20 827.8(1 16.129 4.015 198.01 .0»l:',0 882.64 15.878 8.985 1 '.14.86 .0(140 387.92 15.626 8.96 196.68 .o»ir)0 848.20 15.886 8.92 198.50 .OCifiO 848.48 16.162 8.89 200.82 .0C.70 858.76 1 J.926 8.8B 202.14 .0(580 859.04 14.706 8.83 208.9(5 .0(1', 10 864.82 14,498 8.81 205.78 .0700 360.60 14.286 8.78 207.60 .0710 874.88 14.085 8.75 20'.».29 .0720 880.16 18.8K9 8.78 210.98 .07 ao 385.44 18.699 ;5.70 212.67 .0740 890.72 18.614 8.68 214.86 .0760 896.00 18.888 8.66 216.05 .0760 401.28 18.158 8.(58 217.74 .0770 406.66 12.987 3.60 219.4:; .0780 411.84 12.821 3.58 221.12 .0790 417.12 1 2.658 8.56 222.80 .0800 422.40 12.500 8.54 224.48 .0810 .0820 427.68 482.96 12.846 12.195 8.51 8.49 226.16 227.88 .0880 488.24 12.048 8.47 229.61 .0840 448.52 11.9a5 8.46 231.19 .0860 448.80 11.765 8.48 232.87 .0860 464.08 11.628 8.41 284.64 .0870 469.86 11.494 8.89 286.22 .0880 1 464.64 11.864 8.87 287.89 .0890 469.92 11.286 8.85 239.57 .0900 475.20 11.111 8.88 241.25 .0910 480.48 10.989 8.81 242.90 .0920 485.76 10.870 8.80 244.55 .0980 491.04 10.768 8.28 1 246.20 .0940 496.82 10.688 ! 8.26 247.86 .0960 601.60 10.526 8.24 249.41 .0060 606.88 10.417 3.28 j 260.98 .0970 612.16 10.80'.' 8.21 i 262.55 .0980 617.44 10.204 8.194 264.11 .0990 522.72 10.101 8.178 266.68 .1000 528.00 lO.OCK) 8.162 267.24 .1010 688.28 9.901 8.146 268.72 .1020 688.56 9.804 8.180 260.21 .1080 548.84 9.709 3.116 261.70 .1040 649.12 9.615 3.101 268.19 .1050 554.40 9.'J24 8.086 264.68 10 s F Mean 1 Velocity Sine of the Fall Hydraulic in Indies per Slope — per Mile in Inclination / 7t VT Scc( »n<;l A I Feet. in 12^^ Pipe. One Inch. .lOfiO 559.68 9.484 8.071 2C)6.17 .1070 564.9<» 9.346 3.057 267.6(5 .1080 570.24 9.259 3.048 269.15 .1090 576.52 9.174 3.028 270.64 .1100 580.80 9.091 8.015 272.13 .1110 586.08 9.009 3.001 273.60 .1120 591.36 8.929 2.988 275.06 .1130 596.(54 8.850 2.976 276.53 .1140 601.92 8.772 2.961 277.99 .1150 607.20 8.69(5 2.948 279.46 .1160 612.48 8.621 2.936 280.87 .1170 617.76 8.547 2.923 282.29 .1180 623.04 8.475 2.911 283.70 .1190 628.32 8.403 2,898 285.12 .1200 633.t50 8.333 2.886 28(5.53 .1210 638.88 8.2(56 2.874 287.92 .1220 644.16 8.197 2.862 289.:!1 ."^30 649.44 8.130 2.861 290.70 .1^40 654.72 8.0(55 2.889 292.09 .1260 6(50.00 8.000 2.828 293.48 .12(50 6(55.28 7.937 2.817 294.8(5 .1270 (570.56 7.874 2.806 29(5.24 .1280 675.84 7.812 2.796 297.(52 .1290 (581.12 7.752 2.784 299.00 .1300 686.40 7.692 2.773 300.:5» .1310 (591.68 7.634 2.762 301.75 .1320 696.96 7.576 2.752 803.12 .183C 702.24 7.519 2.742 304.49 .1340 707.52 7.463 2.731 805.86 .1350 712.80 7.407 2.721 307.23 .1360 718.08 7.363 2.711 308.55 .1370 723.36 7.299 2.702 309.86 .1880 728.64 7.246 2.692 311.18 .1390 733.92 7.194 2.681 312.49 .1400 739.20 7.148 2.672 813.81 .1410 744.48 7.092 2.663 315.10 .1420 749.76 7.042 2.663 316.39 .1430 755.04 6.993 2.644 317.(58 .1440 760.32 6.944 2.684 318.98 .1450 765.60 6.897 2.626 320.27 .1460 770.88 6.849 2.617 321.53 .1470 776.16 6.803 2.608 822.79 .1480 781.44 6.767 2.600 824.05 .1490 786.72 6.711 2.590 325.31 .1500 792.00 6.667 2.682 326.57 For double the iuclinntion add 40 per cent. II TABLE II i Is a univcisal taMo, by wliioh — with the nicharge through a 10 inch ])ip(' one mile long with a head of 66 feet. The velocity in a 12 inch pipe by tabic 1 i.« 78.52 inches per second, and the multiplier for velocity in a 10 inch pipe by table 2 is 0.907o: 73. 62X<^.9075 -66.72 inches per second, the rcfpiired velocity. For discharge the imdtiplicr by table 2 is 2.474: 78.52X2.474=181.89 cubic feet per minute, the recpiired discharge. ExAMi'i.K 2. — Jvcquired velocity and discharge through a sower 4 feet in diameter, falling at the rate of .05 per 100. From the tables we obtain: 11.78X2.0615-24.18 inches per second, and 11.73Xl-'^-5"lol9 cubic f.-ct per minute. I i TABLE 2. Pliimctcr. Areas. Multipliors for Vclocitv. Multipliers for Dii*('lmrge. 1 2 8 4 6 6 7 8 9 10 1—0 1—2 1—3 1—4 1—6 1—8 1—10 2-0 2—2 2—4 2-0 2—8 a— 8—4 8-8 4-0 6-0 (i— 7—0 8-0 10—0 12—0 .005454 .021816 .04000 .0872() .18685 ,10685 .26725 .8400 .4418 .6464 .7864 1.0690 1.8062 1.7671 2.1816 2.6898 3.1416 8.6860 4.2760 4.0087 5.6850 7.0086 8.7266 10.5501 12.5664 10.6850 28.2744 88.484«) 50.2656 78.5400 113.0076 .2450 .8710 .4608 .6514 .6208 .6891 .7470 .8062 .8562 .9076 1.000 1.085 1.164 1.288 1.808 1.875 1.489 1.404 1.560 1.620 1.672 1.777 1.876 1.071 2.061 2.812 2.588 2.746 2.010 3.206 3.615 .0011 .0067 .0406 .1150 .2405 .4229 .6766 .0084 1.406 1.801 2.474 8.027 5.709 6.700 8.127 10.042 14.276 18.157 22.611 27.541 38.352 30.76 46.60 62.80 81.87 104.07 129.62 226.98 85S.86 628.54 780.06 1208.0 2044.4 '„„t ...ior n!'.1.6 ; A<- result, «„ukl tl.orrfore bo, f..r a 4 ':>.(. i 04X12SI.6X1-0- =M1 <■• "■ I"-'- '"■• ""■" f ." ■ 7 3xl"« fiXO--* ==27?. 0. 11. I..T 111., 'Vliim 1 lull. f. sower 1 1