TABLES AND DATA.
Miner’s Inch Measurement.The term miner’s inchis of California origin, and not known or used in any other locality, it being a method of measurement adopted by the various ditch companies in disposing of water to their customers. The term is more or less indefinite for the reason that the water companies do not all use the same head above the center of the aperture, and the inch varies from 1.36 to 1.73 cubic feet per minute each, but the most common measurement is through an aperture 2 inches high and whatever length is required, and through a plank 11⁄4inches thick, as shown in the engraving, Fig.675. The lower edge of the aperture should be 2 inches above the bottom of the measuring box, and the plank 5 inches high above the aperture, thus making a 6-inch head above the center of the stream. Each square inch of this opening represents a miner’s inch, which is equal to a flow of 11⁄2cubic feet per minute. Time is not to be considered in any calculation based upon a miner’s inch measurement.
Explanation of Weir Dam Measurement.Place a board or plank edgewise across the stream to be measured as illustrated in Fig.676.
This plank will be supported by posts sufficiently strong to resist the pressure likely to be brought upon it by the head of water which will form in the pond above this temporary dam, saw out a gap in the top of the dam whose length should be from two to four times its depth for small quantities of water and longer for larger quantities. The edges of this gap should be beveled toward the intake as represented. The over-fall below the bottom of gap should be not less than twice its depth, that is, twelve inches if the gap is six inches deep, etc.
Drive a stake above the dam at a distance of about six feet from the face of the plank and then obstruct the water until it rises precisely to the bottom of the gap and mark the water level on the stake. Complete the dam so that all the water will be compelled to flow through the gap and when the stream has assumed a regular flow mark the stake at this new level.
Some would prefer to drive the stake with its top precisely level with the bottom edge of gap in dam so that the depth of water in stream may be measured with a rule or steel square placed upon top of this stake at any time after the flow of water has reached its average depth over dam. However the marks upon the stake are preferred by most experts. After the stake has been marked it may be withdrawn and the distance between the first and last marks gives the theoretical flow according to the table, page 391.
Fig. 676.
Fig. 676.
Measurement in an open stream by velocity and cross section.Measure the depth of the water at from 6 to 12 places across the stream at equal distances apart. Add together all the depths in feet and divide by the number of measurements made; this will be the average depth of the stream, which, multiplied by its width, will give its area or cross section. Multiply this by the velocity of the stream in feet per minute which gives the cubic feet per minute of the stream.
Cubic Feet of water per minute that will flow over a Weir one-inch wide and from1⁄8to 207⁄8-inches deep.
INCHES1⁄81⁄43⁄81⁄25⁄83⁄47⁄80.00.01.05.09.14.19.26.321.40.47.55.64.73.82.921.0221.131.231.351.461.581.701.821.9532.072.212.342.482.612.762.903.0543.203.353.503.663.813.974.144.3054.474.644.814.985.155.335.515.6965.876.066.256.446.626.827.017.2177.407.607.808.018.218.428.638.8389.059.269.479.699.9110.1310.3510.57910.8011.0211.2511.4811.7111.9412.1712.411012.6412.8813.1213.3613.6013.8514.0914.341114.5914.8415.0915.3415.5915.8516.1116.361216.6216.8817.1517.4117.6717.9418.2118.471318.7419.0119.2919.5619.8420.1120.3920.671420.9521.2321.5121.8022.0822.3722.6522.941523.2323.5223.8224.1124.4024.7025.0025.301625.6025.9026.2026.5026.8027.1127.4227.721728.0328.3428.6528.9729.2829.5929.9130.221830.5430.8631.1831.5031.8232.1532.4732.801933.1233.4533.7834.1134.4434.7735.1035.442035.7736.1136.4536.7837.1237.4637.8038.15
Example showing the application of the above table
Suppose the Weir to be 66 inches long, and the depth of water on it to be 115⁄8inches. Follow down the left hand column of the figures in the table until you come to 11 inches. Then run across the table on a line with the 11 until under5⁄8on top line you will find 15.85. This multiplied by 66, the length of Weir, gives 1046.10, the number of cubic feet of water passing per minute.
Suppose the Weir to be 66 inches long, and the depth of water on it to be 115⁄8inches. Follow down the left hand column of the figures in the table until you come to 11 inches. Then run across the table on a line with the 11 until under5⁄8on top line you will find 15.85. This multiplied by 66, the length of Weir, gives 1046.10, the number of cubic feet of water passing per minute.
FRICTION-LOSS IN POUNDS PRESSURE, FOR EACH 100 FEET OF LENGTH IN DIFFERENT SIZE CLEAN IRON PIPES DISCHARGING GIVEN QUANTITIES OF WATER PER MINUTE. ALSO VELOCITY OF FLOW IN PIPE, IN FEET PER SECOND.
G. A. Ellis, C. E.
Gallonsdischargedperminute.1⁄2Inch.3⁄4Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.58.1724.63.633.31016.396.07.2513.015. . .. . .10.928.720. . .. . .14.550.425. . .. . .18.178.0Gallonsdischargedperminute.1 Inch.11⁄4Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.52.040.841.310.31104.083.162.611.05156.136.983.922.38208.1712.35.224.072510.219.06.536.403012.327.57.849.153514.337.09.1412.044016.348.010.416.145. . .. . .11.720.250. . .. . .13.124.975. . .. . .19.656.1Gallonsdischargedperminute.11⁄2Inch.2 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.50.910.12. . .. . .101.820.471.020.12152.730.97. . .. . .203.631.662.040.42254.542.62. . .. . .305.453.753.060.91356.365.05. . .. . .407.266.524.091.60458.178.15. . .. . .509.0810.05.112.447513.622.47.665.3210018.239.010.29.46125. . .. . .12.814.9150. . .. . .15.321.2175. . .. . .17.128.1200. . .. . .20.437.5Gallonsdischargedperminute.21⁄2Inch.3 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.251.630.211.130.10503.260.812.270.35754.901.803.400.741006.533.204.541.311258.164.895.671.991509.807.006.812.8517511.49.467.943.8520013.112.479.085.0225016.319.6611.37.7630019.628.0613.611.2350. . .. . .15.915.2400. . .. . .18.219.5450. . .. . .20.425.0500. . .. . .22.730.8Gallonsdischargedperminute.4 Inch.6 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.501.280.09. . .. . .75. . .. . .. . .. . .1002.550.331.130.051503.830.691.700.102005.111.222.270.172506.391.892.840.263007.662.663.400.373508.943.653.970.5040010.24.734.540.6545011.56.015.110.8150012.87.435.670.96
Note.—The quantity of a fluid discharged through a pipe or an orifice is increased by heating the liquid: because heat diminishes the cohesion of the particles, which exists to a certain degree, in all liquids.
Note.—The quantity of a fluid discharged through a pipe or an orifice is increased by heating the liquid: because heat diminishes the cohesion of the particles, which exists to a certain degree, in all liquids.
FRICTION LOSS IN POUNDS PRESSURE, FOR EACH 100 FEET OF LENGTH IN DIFFERENT SIZE CLEAN IRON PIPES DISCHARGING GIVEN QUANTITIES OF WATER PER MINUTE. ALSO VELOCITY OF FLOW IN PIPE, IN FEET PER SECOND.
G. A. Ellis, C. E.
Gallonsdischargedperminute.6 Inch.8 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.2502.840.261.590.075005.670.983.190.257508.512.214.790.531,00011.33.886.380.941,250. . . .. . . .7.971.461,500. . . .. . . .9.572.09Gallonsdischargedperminute.10 Inch.12 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.2501.020.030.710.015002.040.091.420.047503.060.182.130.081,0004.080.322.840.131,2505.100.493.550.201,5006.120.704.260.291,7507.150.954.960.382,0008.171.235.670.492,250. . . .. . . .6.380.632,500. . . .. . . .7.090.773,000. . . .. . . .8.511.11Gallonsdischargedperminute.14 Inch.16 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.5001.040.0170.800.0091,0002.080.0621.600.0361,5003.130.1352.390.0712,0004.170.2343.190.1232,5005.210.3623.990.1883,0006.250.5154.790.2673,5007.290.6975.590.3654,0008.340.9106.380.4724,500. . . .. . . .7.180.5935,000. . . .. . . .7.980.730Gallonsdischargedperminute.18 Inch.20 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.5000.630.005. . . .. . . .1,0001.260.0201.020.0121,5001.890.040. . . .. . . .2,0002.520.0712.040.0422,5003.150.107. . . .. . . .3,0003.780.1503.060.0913,5004.410.204. . . .. . . .4,0005.040.2634.080.1584,5005.670.333. . . .. . . .5,0006.300.4085.110.2446,0007.560.5856.130.3487,000. . . .. . . .7.150.4728,000. . . .. . . .8.170.612Gallonsdischargedperminute.24 Inch.30 Inch.Veloc. in Pipeper second.Friction Lossin pounds.Veloc. in Pipeper second.Friction Lossin pounds.1,0000.720.0050.450.0022,0001.440.0200.910.0063,0002.160.0471.360.0124,0002.880.0671.820.0225,0004.600.1022.270.0356,0004.320.1462.720.0487,0005.040.1963.180.0658,0005.760.2553.630.0839,0006.470.3234.080.10510,0007.190.3984.540.131
Note.—The velocity with which a liquid issues from an infinitely small orifice in the bottom or sides of a vessel that is kept full is equal to that which a heavy body would acquire by falling from the surface level to the level of the orifice.
Note.—The velocity with which a liquid issues from an infinitely small orifice in the bottom or sides of a vessel that is kept full is equal to that which a heavy body would acquire by falling from the surface level to the level of the orifice.
TABLE SHOWING FRICTIONAL HEADS AT GIVEN RATES OF DISCHARGE IN CLEAN CAST IRON PIPES FOR EACH 1000 FEET OF LENGTH,condensed from elaborate tables prepared by Messrs. Geo. A. Ellis and A. H. Howland, Civil Engineers, Boston, Mass.
U. S.gallonsdischargedper minute.U. S. gallonsdischargedpertwenty-fourhours.4-Inch Pipe.6-Inch Pipe.VelocityinFeet.FrictionHead.VelocityinFeet.FrictionHead.Feet.PoundsFeet.Pounds2536000.64.59.26.28.11.0550720001.282.01.87.57.32.141001440002.557.363.191.131.08.471502160003.8316.056.951.702.28.992002880005.1128.0912.172.273.921.702503600006.3743.4718.832.846.002.603004320007.6662.2026.943.408.523.693505040008.9484.2636.503.9711.484.9740057600010.21109.6847.504.5414.896.4545064800011.49138.4359.965.1118.738.1150072000012.77170.5373.875.6723.019.9760086400015.32244.76106.026.8132.8914.25700100800017.87332.36143.987.9444.5419.088001152000. . .. . .. . .9.0857.9525.109001290000. . .. . .. . .10.2173.1231.6710001440000. . .. . .. . .11.3590.0538.9912001728000. . .. . .. . .13.61129.2055.9614002016000. . .. . .. . .15.88175.3875.9716002304000. . .. . .. . .18.15228.6299.018002592000. . .. . .. . .20.42288.90125.1420002880000. . .. . .. . .22.69356.22154.30U. S.gallonsdischargedper minute.U. S. gallonsdischargedpertwenty-fourhours.8-Inch Pipe.10-Inch Pipe.VelocityinFeet.FrictionHead.VelocityinFeet.FrictionHead.Feet.PoundsFeet.Pounds2536000.16.04.02.10.02.015072000.32.10.04.20.04.02100144000.64.29.13.41.11.05150216000.96.60.26.61.22.102002880001.281.01.44.82.36.162503600001.601.52.661.02.54.233004320001.912.13.921.23.75.323505040002.232.851.241.43.99.434005760002.553.681.591.631.27.554506480002.874.612.001.831.58.695007200003.195.642.442.041.93.846008640003.838.033.482.452.721.1870010080004.4710.834.692.863.661.5880011520005.0914.056.083.274.732.0590012900005.7417.687.693.685.932.57100014400006.3821.749.414.087.283.15120017280007.6631.1013.474.9010.384.50140020160008.9442.1318.255.7214.026.071600230400010.2154.8423.756.5318.227.891800259200011.4769.2229.987.3522.969.952000288000012.7785.2736.938.1728.2512.342500360000015.96132.7057.4910.2143.8719.0030004320000. . .. . .. . .12.2562.9227.25U. S.gallonsdischargedper minute.U. S. gallonsdischargedpertwenty-fourhours.12-Inch Pipe.14-Inch Pipe.VelocityinFeet.FrictionHead.VelocityinFeet.FrictionHead.Feet.PoundsFeet.Pounds2536000.07.01. . .. . .. . .. . .5072000.14.02.01.10.01. . .100144000.28.05.02.21.03.01150216000.43.10.04.31.05.02200288000.57.16.07.42.08.04250360000.71.24.10.52.12.05300432000.85.32.14.63.16.07350504000.99.43.18.73.21.094005760001.13.54.23.83.27.124506480001.28.67.29.94.33.145007200001.42.81.351.04.40.176008640001.701.14.491.25.55.2470010080001.981.52.661.46.73.3280011520002.271.96.851.67.94.4190012900002.552.451.061.881.17.51100014400002.843.001.302.081.43.62120017280003.404.261.852.502.02.88140020160003.975.742.492.912.721.18160023040004.547.443.223.333.511.52180025920005.119.364.063.754.411.91200028800005.6711.505.004.175.412.34250036000007.0917.827.725.218.353.62300043200008.5125.5111.056.2511.935.17350050400009.9334.5814.987.2916.146.9940005760000. . .. . .. . .8.3421.009.1045006480000. . .. . .. . .9.3826.4911.47