TABLE for finding, very nearly, the velocity and discharge from Cylindrical Water Pipes or Sewers when the diameter and fall are given." Any t co of the four quantities, the velocity, discharge diameter, and fall or inclination, being given, the others can be found in THE TABLE from inspec tion. SEE TABLE XIII. Height in ft. due to frietion per mile of length. hy. dri pipe or sewer. The VELOCITY IN INCHES PER SECOND is given in the first horizontal line for each inclination or fall; and the DisCHARGE IN CUBIC FEET PER MINUTE in the next following one. 1 in. Jiam. 2 in. diam. 3 in. diam. 4 in. diam. 5 in. diam. 6 in. diam. diam. diam. diam. diam. 05 2.9 4.6 6.8 9.6 2.5 3.8 8.6 9.1 4.3 68 3.1 4.7 8.7 1.4 8.5 23.9 31.2 6.9 11.1 11.9 1.7 3.6 14-8 20.8 10 4 135 7.1 23.6 8.7 12.8 15.9 16.9 12.6 35.1 46.0 11-2 15.1 18:4 4.9 20.2 50-2 5.4 12.0 13.5 17.6 18.7 20-0 15 30.6 41-3 54-1 5.7 12.9 14.5 18.8 16 9.9 32-8 6.1 9.2 15:4 17.1 2.9 16.7 24-7 34.8 46.8 61.3 6.4 14:4 •17 6.3 10.2 17.1 18.9 23.5 24-9 11-6 18.6 7.1 10.8 21.7 23.3 12.3 40.7 54-8 71-7 7.7 11.6 14.7 28:4 3.6 7.5 13.2 21.2 31.2 43.9 8.4 18.8 29-2 31.0 -23 8.2 14.4 23.1 34.1 84.5 9.4 20.9 28.3 30.5 26 9.2 37 8 53.3 71-7 93.8 26.4 200 10.6 23.8 -29 10:4 35.2 150 12.5 28.1 .34 50.9 71-6 52.8 100 15-9 24.1 7.4 15.6 27.3 43.8 64 6 90-9 58.7 90 16.9 46 2.8 130-2 170-3 66. 80 18.1 27.5 55.2 59:4 31.2 49.9 73-7 103-7 139 6 182-7 75-4 7019-6 30.0 49.6 55.1 59-7 33.8 54.1 64.4 68.4 72.5 79-8 112-3 151-2 197-7 88 60 21.5 32.6 37.1 59.3 65.5 105.6 50 24.0 36.4 45.8 53.9 *65 4.0 11.2 23.5 41.3 66.2 73.1 132. 40 27.4 41.6 75 4-5 77.1 83.6 90-1 95.8 101-5 12.8 75-7 1117 157-2 211 6 276.8 176 30 32.6 49.5 62-5 91.7 99.5 107 2 114-0 120.8 *89 320 56.3 90-0 132 9 187-1 251-8 329.4 212.2 25 36.4 92.2 1024 1111 119 7 1273 1349 *99 6.0 629 1006 148 4 208-9 281-2 367-9 264-1 20 41.7 63'3 1056 | 117 3 1272 137-0 1457 154 4 1-14 6.9 19.6 40.9 720 115 1 169-9 239 2 3219 421.2 352 15 49'6 75.3 95.0 111.7 125 6 1396 1631 1734 183 8 1.35 48.3 85-6 137 0 202 2 284-6 383 1 501-2 528 10 63-3 96.0 121-2 142 4 160-2 1780 1929 207 9 2211 2343 1.73 10 5 109 2 174-7 257-8 362-9 488 5 639-0 TABLE for finding, very nearly, the velocity and discharge from Cylindrical Water Pipes or Sewers, when the diameter and fall are given. Any two of the four quantities, the velocity, discharge, diameter, or inclination teing given, the others can be found in THE TABLE from inspection. SEE TABLE XIII. Height in ft. dne to frie ien per mile! of length draulic ineli- Me n hy ipe or sewer. The VELOCITY IN INCHES PER SECOND is given in the first horizontal line for each inclinacion or fall; and the DISCHARGE IN CUBIC FEET PER MINUTE in the next following one. 12 in. diam. 8 12 8 8 66 75-4 88 60 88 344 506 105 6 50 98 106 712 132 523 959 1251 114 121 128 384 565 795 1070 1396 40 119 124 130 138 146 153 467 665 908 1224 1597 2031 2529 176 30 133 144 155 165 174 183 770 1082 1456 1900 2417 1591 1981 Heads in inches due to the velocity and junetion. Best Velocities in inches, per second, due to heads. 204 2122 223 234 245 3848 of great practical utility in solving all questions connected with water-pipes and sewers discharging fullydiluted sewage. In using it, interpolate, by inspection, for intermediate diameters or inclinations. For greater diameters, divide those given by 4, and multiply the corresponding velocity found in the table by 2, and the corresponding discharge in the table by 32. If the object be to find the size of the channel, divide greater given velocities by 2, and multiply the diameters or inclinations found from the table by 4; also divide greater discharges by 32, and multiply the diameters found from the table by 4. The small auxiliary table, p. 29, embodied in the larger one, is of great use in making allowance for the velocity and orifice of entry in short pipes, before finding the head due to friction. The table also gives the different diameters and inclinations which, taken together, give the same velocity or discharge; and it enables, from inspection, to select that relation of diameter to declivity which is best suited for other engineering aspects of the question. Taken in connexion with TABLES VIII., XI., XII., and XIII., this table completes the means of finding, by inspection, the dimensions, inclinations, velocities, and discharges of every class of waterchannel or sewage-conduit required in engineering practice. TABLE XIV. gives the comparative values of English and French measures; and TABLE XV. gives the weight, specific gravity, and ultimate strength and elasticity of various materials with which the engineer has to operate. SECTION II. FORMULE FOR THE VELOCITY, AND DISCHARGE, FROM ORIFICES, WEIRS, AND NOTCHES.-COEFFICIENTS OF AND DISCHARGE.-PRAC TICAL REMARKS ON THE USE OF THE FORMULE. The quantity of water discharged in a given time through an aperture of a given area in the side or bottom of a vessel, is modified by different circumstances, and varies more or less with the form, position, and depth of the orifice; but the discharge may be easily found, when the velocity and the contraction of the fluid vein has been determined. VELOCITY. If g be the velocity acquired by a heavy body falling from a state of rest for one second, in vacuo, then it has been shown by writers on mechanics, that the velocity v per second acquired by falling from a height h, will be = The numerical value of g varies with the latitude; then it shall be assumed that 2 g 772-84 inches = 64.403 feet. These will give for measures in inches, v = 27·8 √h,* and h = and for measures in feet, شوح 772.84 = '001293o, * The velocities for different heights are given in column number 1, TABLE II. v = 8·025 √h, and h = 2.2 = 64.403 •01553 v2. If v be in feet, and h in inches, then v = 2·317 √h, and h 2,2 5.367 = •1864 v2.* COEFFICIENT OF VELOCITY. Let the vessel A B C D, Fig. 1, be filled with water to the level E F: then it has been found, by experi ment, that the velocity of discharge through a small orifice o, in a thin plate, at the distance of half the diameter outside it, in the vena-contracta, will be very nearly that due to a heavy body falling freely from the height h, of the surface of the water E F, above the * The force of gravity increases with the latitude, and decreases with the altitude above the level of the sea, but not to any considerable extent. If λ be the latitude, and h the altitude, in feet, above the mean sea level, then it may be generally taken that in which R, the radius of the earth at the given latitude is equal to 20887600 (1 + 0016 cos 2λ). |