H-flumes

’ to 5d PARSHALL FWMES95 90 es eo 70 601 0.02 0.05 0.10 0.20 0.50 4PERCENTAGE OF SUBMERGENC HEAD LOSS AH THROUGH FLUME in metresFigure 7.20 Head-loss through Parshall flumes (10-50 feet wide)7.5 H-flumes7.5.1 DescriptionOn natural streams where it is necessary to measure a wide range of discharges, astructure with a V-type control has the advantage of providing a wide opening athigh flows so that it causes no excessive backwater effects, whereas at low flows itsopening is reduced so that the sensitivity of the structure remains acceptable. To servethis purpose the U.S. Soil Conservation Service developed the H-type flume, of whichthree geometrically different types are available. Their proportions are shown in Figure7.21. They are:HS-flumesOf this ‘small’ flume, the largest size has a depth D equal to 0.305 m (1 ft) and amaximum capacity of 0.022 m3/s.248

H-flumesOf this ‘normal’ flume, the largest size has a depth D equal to 1.37 m (4.5 ft) anda maximum capacity of 2.36 m3/s.HL-flumesThe use of this ‘large’ flume is only recommended if the anticipated discharge exceedsthe capacity of the normal H-flume. The largest HL-flume has a depth D equal to1.37 m (4.5 ft) and a maximum capacity of 3.32 m3/s.Since all three types are calibrated measuring devices, they should be constructed instrict accordance with the drawings in Figure 7.21. It is especially important that theslanting opening be bounded by straight sharp edges, that it has precisely the proportionaldimensions shown, and that it lies in a plane with an inclination of the exactdegree indicated in Figure 7.21. All cross sections of the flume should be symmetricalabout the longitudinal axis. The flume floor should be truly level. All plates shouldbe flat and should display no appreciable warp, dent, or other form of distortion.All three types of flume should be located downstream of a rectangular approachchannel which has the same bottom width as the entrance of the flume, i.e., 1.05Dfor the HS-flumes; 1.90D for the H-flumes; and 3.20D for the HL-flumes. The minimumlength of this approach channel is 2D. In practice, the flume sections are frequentlyconstructed from sheet steel or other suitable material, while the approach sectionis made of concrete, masonry, etc. The two parts should be given a watertight joinwith the use of bolts and a gasket. The bolts should be suitable for both fasteningand levelling the flume. To prevent silting in the approach channel, its longitudinalslope may vary from flat to about 0.02.The upstream head ha is measured in the flume at a well defined location whichis shown separately for each flume in Figure 7.21. The piezometric head should bemeasured in a separate well having a piezometer tap immediately above the flumebottom. Since the head is measured at a location of accelerating flow and where streamlinesare curved it is essential that the piezometer tap be located in its precise positionif accurate flow measurements are to be obtained.To assure reliable head readings despite heavy sediment loads and the accompanyingsediment deposition in the flume, an 1-to-8 sloping floor was provided for H-flumes. This false floor concentrates flows along the side wall having the stilling wellintake. Low flows can scour the sediment from the little channel formed along thiswall. The proportions of the sloping floor for the H-flume are given in Figure 7.22.If the H-flume is equiped with a false floor the true flow rate differs slightly fromthe figures given in Table 7.14. The percentage deviation in the free flow rate is shownin Figure 7.23.249

k 1 . 0 5 D dFRONT ELEVATIONkl.5D-4SIDE ELEVATIONH-FLUMEF l . 1 0 4\\1.35D \\\1 . 9 D 4 k 1 . 3 5 D dw0.3DSIDE ELEVATION0.50FRONT ELEVATIONw0.25DSIDE ELEVATIONFigure 7.21 Dimensions of the types HS-, H- and HL-flume (after Holtan, Minshall & Harrold 1962)250

Figure 7.23 Deviation in free flow rate through H-flumes with a sloping floor from rating tables 7.14 forH-flumes with a flat floor (after Gwinn)7.5.2 Evaluation of dischargeAll three types of H-flumes have a rather arbitrary control while an upstream piezometrichead ha is measured at a station in the area of water surface drawdown. Underthese circumstances, the only accurate method of finding a head-discharge relationshipis by calibration in a hydraulic laboratory. Based on this calibration, an empiricalformula, expressing the discharge in m3/s as a function of the head ha in metres, couldbe established of the general formlog Q = A + B log ha + C[log hal2 (7-6)Values of the numbers A, B, and C appear in Table 7.12 for each flume type. BasedTable 7. I2 Data on three types of H-flumesFlume Flume depth D Maximum Number in Equation 7-6 Ratingtype capacity tableft m m3/sx A B CHS 0.4 ,122 2.27 -0.4361 +2.5151 +0.1379 7.13.aHS 0.6 ,183 6.14 -0.4430 +2.4908 +0.1657 7.13.bHS 0.8 ,244 12.7 -0.4410 +2.4571 +0.1762 7.13.cHS 1.0 ,305 22.3 -0.4382 +2.4193 +0.1790 7.13.dH 0.5 .I52H 0.75 ,229H 1 .o ,305H 1.5 ,457H 2.0 ,610H 2.5 ,762H 3.0 ,914H 4.5 1.379.1726.953.51503095428572366+0.0372f0.0351+0.0206f0.0238f0.0237+0.0268+0.0329+O.OS88+ 2.6629+2.6434+2.5902+2.5473+ 2.49 18+ 2.4402+2.3977+2.3032+O. I954+0.2243+0.2281+0.2540+0.2605+0.2600+0.2588f0.25477.14.a7.14.b7.14.c7.14.d7.14.e7.14.f7.14.g7.14.hHL 3.5 1:07 2370 +0.3081 +2.3935 +0.2911 7.15.aHL 4.0 1.22 3298 +0.3160 +2.3466 +0.2794 7.15.b252

Ion Equation 7-6, calibration tables were prepared for each flume; see Tables 7.13 forthe HS-flumes, Table 7.14 for the H-flumes and Table 7.15 for the HL-flumes.The error in the modular discharge given in Tables 7.13,7.14 and 7.15 may be expectedto be less than 3%. The method by which this error is to be combined with othersources of error is shown in Annex 2.7.5.3 Modular limitThe modular limit is defined as the submergence ratio h,/h, which produces a 1%reduction from the equivalent modular discharge as calculated by Equation 7-6. Resultsof various tests showed that the modular limit for HS- and H-flumes is h,/h,= 0.25, for HL-flumes this limit is 0.30. Rising tailwater levels cause an increase ofthe equivalent upstream head ha at modular flow as shown in Fig.7.24. Because ofthe complex method of calculating submerged flow, all HS- and H-flumes should beinstalled with a submergence ratio of less than 0.25 (for HL-flumes 0.30).e/.aSubmergence ratio b/haSubmergence ratio hZ/h,Figure 7.24a/b Influence of submergence on the modular head of HS-, H-, and HL-flumes. (Data on HLflumesbased on personal communication, Gwinn 1977)253

7.5.4 ' Limits of applicationThe limits of application of all H-flumes are:a. The inside surface of the flume should be plane and smooth while the flume dimensionsshould be in strict accordance with Figure 7.21.b. The practical lower limit of h, is mainly related to the accuracy with which h, canbe determined. For heads less than 0.06 m, point gauge readings are required to. obtain a reasonably accurate measurement. The lower limit of ha for each typeof flume can be read from Tables 7.13 to 7.15.c. To obtain modular flow the submergence ratio h,/h, should not exceed 0.25.d. To prevent water surface instability in the approach channel, the Froude numberFr, = v,/(gA,/B>'/z should not exceed 0.5.Table 7.13a Free-flow discharge through 0.4 ft HS-flume in I/sha .O00 ,001. .O02 .O03 .O04 .O05 .O06 .O07 .O08 .O09(ml0.010.020.030.040.050.060.070.080.090.100.110.0 I20.0490.1 I30.2080.3350.4970.6970.9351.211.541.900.0150.0540.1210.2190.3500.5160.7190.9611.25I .571.940.0170.0590.1300.2300.3650.5340.7410.9881.281.611.980.0200.065O. 1380.2420.3800.5530.7641 .o11.31I .642.020.024 0.0270.071 0.0770.147 0.1560.255 0.2670.396 0.4120.573 0.5920.787 0.8111.04 1.071.34 1.371.68 1.712.06 2.100.0310.0840.1660.2800.4280.6120.8351.10I .401.752.150.0350.0910.1760.2930.4450.6330.8601.131.441.792.190.0390.0980.1860.3070.4620.6540.8841.161.471.832.230.044o. 1050.1970.3210.4800.6750.9101.191.501.872.27Table 7.13b Free-flow discharge through 0.6 ft HS-flume in I/sha ,000 .O01 .O02 .O03 .O04 .O05 .O06 .O07 .O08 .O09(m)0.02 0.0640.03 0.1410.04 0.2510.05 0.3950.06 0.5770.07 0.7970.08 1 .O60.09 1.36o. IO 1.710.11 2.100.12 2.530.13 3.02O. I4 3.560.15 4.14O. I6 4.780.17 5.470.0700.1500.2630.4120.5970.821I .O91.391.742.142.583.073.614.204.855.550.0760.1600.2770.4290.6180.8461.111.431.782.182.633.123.674.274.925.620.083 0.0910.170 0.1810.290 0.3040.446 0.4630.639 0.6600.871 0.8961.14 1.171.46 1.491.82 1.862.22 2.272.68 2.723.18 3.233.73 3.784.33 4.394.98 5.055.69 5.770.0980.1910.3180.48 10.6820.922I .201.531.902.312.773.283.844.465.125.840.106 '0.2020.3330.5000.7040.9481.231.561.932.352.823.343.904.525.195.920.1140.2140.3480.5180.7270.9751.261.601.972.402.873.393.964.585.265.99O. 1230.2260.3630.5370.7501 .o01.301.632.012.442.923.454.024.655.336.070.1310.2380.3790.5570.773I .O31.331.672.062.492.973.504.084.725.406.14254

OTable 7.13~ Free-flow discharge through 0.8 ft HS-flume in I/sha .O00 .O01 .O02 .O03 .O04 .O05 ,006 ,007 ,008 ,009( 40.03 0.227 0.239 0.252 0.266 0.2800.04 0.294 0.308 0.324 0.339 0.355 0.371 0.388 0.404 0.422 0.4400.05 0.458 0.476 0.495 0.514 0.534 0.554 0.574 0.595 0.617 0.6380.06 0.660 0.683 0.706 0.729 0.753 0.777 0.802 0.827 0.852 0.8780.07 0.904 0.931 0.958 0.986 1.01 1.04 1.07 1.10 1.13 1.160.08 1.19 1.22 1.25 1.29 1.32 1.35 1.38 1.42 1.45 1.490.09 1.52 1.56 1.59 1.63 1.67 1.70 1.74 1.78 1.82 1.860.10 1.90 1.94 1.98 2.02 2.06 2.10 2.15 2.19 2.23 2.280.11 2.32 2.37 2.41 2.46 2.50 2.55 2.60 2.65 2.69 2.740.12 2.79 2.84 2.89 2.94 2.99 3.05 3.10 3.15 3.20 3.260.13 3.31 3.37 3.42 3.48 3.54 3.59 3.65 3.71 3.77 3;830.14 3.89 3.95 4.01 4.07 4.13 4.19 4.25 4.32 4.38 4.450.15 4.51 4.58 4.64 4.71 4.77 4.84 4.91 4.98 5.05 5.120.16 5.19 5.26 5.33 5.40 5.48 5.55 5.62 5.70 5.77 5.850.17 5.92 6.00 6.08 6.15 6.23 6.31 6.39 6.47 6.55 6.630.18 6.71 6.79 6.88 6.96 7.04 7.13 7.21 .... 7.30 7.39 7.470.19 7.56 7.65 7.74 7.82 7.91 8.00 8.10 8.19 8.28 8.370.20 8.47 8.56 8.65 8.75 8.84 8.94 9.04 9.14 9.23 9.330.21 9.43 9.53 9.63 9.73 9.83 9.94 10.0 10.1 10.2 10.40.22 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.40.23 11.5 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.5 12.60.24 12.7Table 7.13d Free-flow discharge through 1 .O ft HS-flume in I/sha .O00 .OOI ,002 .O03 .O04 ,005 .O06 .O07 ,008 .O09(m)0.04 0.3390.05 0.5210.06 0.7460.07 1 .o20.08 1.330.09 I .690.10 2.100.11 2.550.12 3.060.13 3.620.14 4.230.15 4.900.16 5.620.17 6.400.18 7.230.19 8.130.20 9.080.21 10.10.22 11.20.23 12.30.24 13.50.25 14.80.26 16.10.27 17.50.28 19.00.29 20.60.30 22.20.355 0.372 0.3890.542 0.563 0.5840.771 0.797 0.8221.04 1.07 1.101.36 1.40 1.431.73 1.77 ' 1.812.14 2.18 2.232.60 2.65 2.703.11 3.17 3.223.68 3.74 3.804.30 4.36 4.434.97 5.04 5.1 15.69 5.77 5.856.48 6.56 6.647.32 7.41 7.508.22 8.31 8.419.18 9.28 9.3810.2 10.3 10.411.3 11.4 11.512.4 12.6 12.713.6 13.8 13.914.9 15.1 15.216.3 16.4 16.517.7 17.8 18.019.2 19.3 19.520.7 20.9 21.022.30.407 0.425 0.443 0.462 0.4820.606 0.629 0.651 0.674 0.6980.849 0.875 0.902 0.930 0.9581.14 1.17 1.20 1.23 1.261.47 1.50 1.54 1.58 1.611.85 1.89 1.93 1.97 2.012.27 2.32 2.36 2.41 2.462.75 2.80 2.85 2.90 2.963.28 3.33 3.39 3.45 3.503.86 3.92 3.98 4.04 4.1 14.49 4.56 4.63 4.69 4.765.18 5.25 5.32 5.40 5.475.92 6.00 6.08 6.16 6.246.73 6.81 6.89 6.98 7.067.58 7.67 7.76 7.85 7.948.50 8.60 8.69 8.79 8.899.48 9.58 9.69 9.79 9.8910.5 10.6 10.7 10.8 11.011.6 11.7 11.9 12.0 12.112.8 12.9 13.0 13.2 13.314.0 14.2 14.3 14.4 14.515.3 15.5 15.6 15.7 15.916.7 16.8 17.0 17.1 17.318.1 18.3 18.4 18.6 18.719.6 19.8 19.9 20.1 20.221.2 21.4 21.5 21.7 21.80.5010.7220.9861.301.652.052.513.013.564.174.835.546.327.158.048.989.9911.112.213.414.716.017.418.920.422.0255

Table 7.14a Free-flow discharge through 0.5 ft H-flume in m3/s x(l/s).O00 .O02 .O04 .O06 .0080.010.020.030.040.03 10.1190.2720.4970.044O. I450.3110.5510.0590.1720.3530.6090.077 0.0970.203 0.2360.398 0.4460.669 0.7330.050.060.070.080.090.8011.19I .672.252.930.871I .281.782.373.070.9461.371.892.513.231 .o2 1.101.47 1.572.00 2.122.64 2.783.38 3.550.100.110.120.13O. 143.714.615.636.788.053.884.815.857.028.324.065.016.087.278.604.24 4.425.21 5.426.31 6.547.53 7.798.88 9.17Table 7.14b Free-flow discharge through 0.75 ft H-flume in (l/s).o00 .O02 .O04 .O06 .0080.010.020.030.040.050.060.070.080.090.100.110.120.130.140.150.160.170.180.190.200.210.220.0440.1550.3390.6000.9451.381.912.543.284.135.106.187.408.7410.211.813.615.517.619.822.224.80.0610.1860.3840.6621 .O31.482.032.683.444.315.306.427.659.0310.512.214.015.918.020.322.725.30.0800.2200.4330.7281.111.582.152.833.614.505.526.657.929.3210.912.514.416.318.520.823.225.80.1030.2560.4860.797I .201.692.282.973.784.705.736.908.199.6111.212.914.716.718.921.223.726.40.1280.2960.5410.869I .291.802.413.133.954.895.967.148.469.9111.513.215.117.219.421.724.226.9256

Table 7.14~ Free-flow discharge through 1 .O ft H-flume in m3/s x(I/s)haha(m) .O00 .O02 .O04 .O06 .O08 (m) ,000 .O02 .O04 .O06 .O080.00 0.15 11.0 11.3 11.7 12.0 12.30.01 0.127 0.157 0.16 12.7 13.1 13.4 13.8 14.20.02 0.190 0.226 0.265 0.308 0.236 0.17 14.5 14.9 15.3 15.7 16.10.03 0.403 0.455 0.511 0.571 0.634 0.18 16.5 16.9 17.4 17.8 18.20.04 0.701 0.771 0.845 0.922 1.00 ' 0.19 18.7 19.1 19.6 20.0 20.50.05 1.09 1.18 1.27 1.37 1.47 0.20 21.0 21.4 21.9 22.4 22.90.06 1.57 1.68 1.79 1.91 2.03 0.21 23.4 23.9 24.5 25.0 25.50.07 2.16 2.28 2.42 2.56 2.70 0.22 26.1 26.6 27.2 27.7 28.30.08 2.84 2.99 3.15 3.31 3.47 0.23 28.9 29.4 30.0 30.6 31.20.09 3.64 3.82 3.99 4.18 4.36 0.24 31.8 32.4 33.1 33.7 34.20.10 4.56 4.75 4.95 5.16 5.37 0.25 35.0 35.6 36.3 37.0 37.60.11 5.59 5.81 6.04 6.27 6.50 0.26 38.3 39.0 39.7 40.4 41.10.12 6.74 6.99 7.24 7.50 7.76 0.27 41.8 42.6 43.3 44.0 44.80.13 8.03 8.30 8.58 8.86 9.15 0.28 45.5 46.3 47.1 47.9 48.60.14 9.45 9.75 10.1 10.4 10.7 0.29 49.4 50.2 51.0 51.9 52.70.30 53.5Table 7.14d Free-flow discharge through 1 .5 ft H-flume in I/s0.000.010.02 0.269 0.316 0.3670.03 0.542 0.608 0.6770.04 0.910 0.996 1.090.05 1.38 1.49 1.600.06 1.75 2.08 2.210.07 2.64 2.78 2.940.08 3.43 3.60 3.780.09 4.34 4.54 4.740.10 5.38 5.60 5.830.11. 6.54 6.78 7.040.12 7.83 8.10 8.380.13 9.25 9.55 9.860.1410.8 11.1 11.50.15 12.5 12.9 13.20.16 14.4 14.8 15.10.17 16.4 16.8 17.20.18 18.5 19.0 19.40.19 20.8 21.3 21.80.20 23.3 23.8 24.30.21 25.9 26.5 27.00.22 28.7 29.3 29.90.23 31.7 32.3 33.00.24 34.9 35.5 36.20.421 0.4790.751 0.8291.18 1.281.71 1.832.35 2.493.10 3.263.96 4.154.95 5.166.06 6.297.30 7.568.67 8.9610.2 10.511.8 12.213.6 14.015.5 16.017.6 18.119.9 20.422.3 22.824.9 25.427.6 28.230.5 31.133.6 34.236.9 37.50.25 38.2 38.9 39.6 40.3 41.00.26 41.7 42.5 43.2 43.9 44.70.27 45.4 46.2 47.0 47.8 48.50.28 49.3 50.1 51.0 51.8 52.60.29 53.4 54.3 55.1 56.0 56.80.30 57.7 58.6 59.5 60.4 61.30.31 62.2 63.1 64.1 65.0 66.00.32 66.9 67.9 68.8 69.8 70.80.33 71.8 72.8 73.8 74.9 75.90.34 76.9 78.0 79.0 80.1 81.20.35 82.3 83.4 84.5 85.6 86.70.36 87.8 89.0 90.1 91.3 92.40.37 93.6 94.8 96.0 97.2 98.40.38 99.6 101 102 103 1050.39 106 107 108 110 1110.40 112 114 115 116 1180.41 119 120 122 123 1250.42 126 127 129 130 1320.43 133 135 136 138 1390.44 141 142 144 145 1470.45 148 150257

Table 7.14e Free-flow discharge through 2.0 ft H-flume in m3/s x(I/s)ha(m) .O00 .O02 .O04 .O06 ,008ha(m) .O00 .O02 .O04 ,006 ,0080.000.010.02 0.469 0.535 0.6060.03 0.681 0.760 0.844 0.932 1.020.04 1.12 1.22 1.33 1.44 1.550.30 61.90.31 66.60.32 71.50.33 76.60.34 81.962.967.672.577.783.063.868.673.578.784.164.769.574.679.785.265.770.575.680.886.30.05 1.67 1.79 1.92 2.05 2.190.06 2.33 2.48 2.63 2.79 2.950.07 3.11 3.29 3.46 3.64 3.830.08 4.02 4.21 4.41 4.62 4.830.09 5.04 5.27 5.49 5.72 5.960.35 87.50.36 93.20.37 99.20.38 1050.39 11288.694.41 O0107I I389.795.6I02IO81 I490.996.7103I091 I692.097.91041 IO1 I70.10 6.20 6.45 6.70 6.96 7.220.1 I 7.49 7.76 8.04 8.33 8.620.12 8.91 9.22 9.52 9.84 10.20.1310.5 10.8 11.1 11.5 11.80.14 12.2 12.5 12.9 13.3 13.70.40 1180.41 1250.42 1320.43 1400.44 147120127I34141148121128I35I43150I23130I37I441521241311381461540.15 14.0 14.4 14.8 15.2 15.60.16 16.1 16.5 16.9 17.3 17.80.17 18.2 18.7 19.1 19.6 20.10.18 20.5 21.0 21.5 22.0 22.50.19 23.0 23.5 24.1 24.6 25.10.45 1550.46 1630.47 1720.48 1800.49 189157165173182191I58I67175I84193160I68I77186I951621701791871960.20 25.7 26.2 26.8 27.3 27.90.21 28.5 29.1 29.7 30.2 30.90.22 31.5 32.1 32.7 33.3 34.00.23 34.6 35.3 35.9 36.6 37.30.24 38.0 38.7 39.4 40.1 40.80.50 1980.51 2080.52 2170.53 2270.54 23720021021922924020221 122 123 12422042132232332442062152252352460.25 41.5 42.2 42.9 43.7 44.40.26 45.2 46.0 46.7 47.5 48.30.27 49.1 50.0 50.7 51.5 52.30.28 53.2 54.0 54.9 55.7 56.60.29 57.5 58.3 59.2 60.1 61.00.55 2480.56 2590.57 2700.58 2810.59 2930.60 30525026 1272283295307252263274286297309254265276288300256267279290302258

Table 7.14f Free-flow discharge through 2.0 ft H-flume in m3/s x(l/s)ha(m) ,000 .O02 ,004 .O06 .O08ha(m) .O00 .O02 .O04 .O06 .O080.000.010.020.03 0.820 0.9120.04 1.33 1.450.649 0.7321.01 1.11 1.221.57 1.69 1.820.40 1250.41 1320.42 1390.43 1470.44 155126134141149156128I35142150I581291361441521601311381451531610.05 1.96 2.100.06 2.71 2.880.07 3.59 3.780.08 4.60 4.820.09 5.75 5.992.25 2.40 2.553.05 3.23 3.413.98 4.18 4.395.04 5.27 5.516.24 6.50 6.760.45 1630.46 1710.47 1800.48 1890.49 198165173181I90I9916617518319220 11681761851942031691781871962050.10 7.02 7.300.11 8.44 8.750.12 10.0 10.30.13 11.7 12.10.14 13.6 14.07.58 7.86 8.159.05 9.36 9.6810.7 11.0 11.412.4 12.8 13.214.4 14.8 15.20.50 2070.51 2160.52 2260.53 2360.54 24720921822823924921 122023024 125 12132222322432532152242342452550.15 15.6 16.00.16 17.6 18.20.17 20.1 20.60.18 22.6 23.10.19 25.2 25.816.4 16.9 17.318.7 19.1 19.621.1 21.6 22.123.6 24.2 24.726.4 26.9 27.50.55 2570.56 2680.57 2800.58 2910.59 30326027 128229330526227328429630826427528629831026627728930 I3130.20 28.1 28.70.21 31.1 31.70.22 34.2 34.90.23 37.6 38.40.24 41.1 41.929.2 29.8 30.532.3 33.0 33.635.6 36.2 36.939.0 39.7 40.442.6 43.4 44.10.60 3150.61 3270.62 3400.63 3530.64 3663173303433553693203323453583713223353483613743253373 503633770.25 44.9 45.60.26 48.8 49.60.27 52.9 53.70.28 57.2 58.10.29 61.7 62.746.4 47.2 48.050.4 51.2 52.054.6 55.4 56.359.0 59.9 60.863.5 64.5 65.40.65 3800.66 3930.67 4080.68 4220.69 43738239641042544038539941342844338840241643 I44639 I4054194344490.30 66.4 67.30.31 71.3 72.30.32 76.4 77.40.33 81.7 82.80.34 87.2 88.30.35 93.0 94.10.36 98.9 1000.37 105 1060.38 112 1130.39 118 11968.3 69.3 70.373.3 74.3 75.378.5 79.5 80.683.9 85.0 86.189.5 90.6 91.895.3 96.5 97.7101 102 104108 109 110114 115 117121 122 .I240.70 4520.71 4670.72 4830.73 4990.74 5150.75 5324554704865025195354584 7448950652253946 1477493509525542464480496512529259

Table 7.14g Free-flow discharge through 3.0 ft H-flume in m3/s x(I/s)ha(4-0.000.010.030.040.050.060.070.080.090.100.1 10.120.13O. 140.150.160.170.180.190.200.210.220.230.240.250.260.270.280.290.300.310.320.330.340.350.360.370.380.390.400.410.420.430.440.450.460.470.480.49.O00 .O02 .O04 .O06 ,0080.959 1.06 1.18 1.29 1.411.54 1.67 1.81 1.95 2.092.25 2.40 2.57 2.74 2.913.09 3.27 3.46 3.66 3.864.06 4.28 4.49 4.72 4.955.18 5.42 5.66 5.92 6.176.43 6.70 6.98 7.26 7.547.83 8.13 8.44 8.75 9.069.38 9.71 10.0 10.4 10.711.1 11.4 11.8 12.2 12.512.9 13.3 13.7 14.1 14.514.9 15.4 15.8 16.2 16.717.1 17.6 18.0 18.5 19.019.4 19.9 20.4 20.9 21.421.9 22.4 23.0 23.5 24.024.6 25.1 25.7 26.3 26.827.4 28.0 28.6 29.2 29.830.4 31.1 31.7 32.3 33.033.6 34.3 35.0 35.6 36.337.0 37.7 38.4 39.1 39.840.5 41.3 42.0 42.8 43.544.3 45.1 45.8 46.6 47.448.2 49.0 49.8 50.7 51.552.3 53.2 54.0 54.9 55.856.6 57.5 58.4 59.3 60.261.2 62.1 63.0 64.0 64.965.9 66.8 67.8 68.8 69.870.8 71.8 72.8 73.8 74.975.9 77.8 78.0 79.1 80.281.2 82.3 83.4 84.5 85.786.8 87.9 89.1 90.2 91.492.5 93.7 94.9 96.1 97.398.5 99.7 101 102 103105 106 107 109 110111 112 114 115 116118 119 120 122 123125 126 127 129 130132 133 135 136 138139 141 142 144 145147 148 150 151 153154 156 158 159 161163 164 166 167 169171 173 174 176 178179 181 183 185 186188 190 192 194 195197 199 201 203 205207 208 210 212 214ha(m) .O00 .O02 .O04 .O06 .O080.50 2160.51 2260.53 2460.54 2570.55 2680.56 2790.57 2900.58 3020.59 3140.60 3260.61 3390.62 3520.63 3650.64 3780.65 3920.66 4060.67 4200.68 4350.69 4500.70 4650.71 4810.72 4970.73 5130.74 5290.75 5460.76 5630.77 5810.78 5990.79 6170.80 6350.81 6540.82 6730.83 6930:84 7130.85 7330.86 7530.87 7740.88 7950.89 8170.90 83921822824825927028 129330431732934 I35436838 139540942343845346848450051653355056758460262063965867769771773775777880082 I84322023025126127228329530731933 134435737038439841242644145647 148750351953655357058860662464366268170 172 174 I76278380482684822223225326327428629730932 1334347360373387400415429444459475490506523539556574592610628647666685705725745766787808830852224234255266277288300312324336349362376389403418432447462478494510526543560577595613632650669689709729749770791813835857260

Table 7.14h Free-flow discharge through 4.5 ft H-flume in m3/s x IO” (I/s)ha(m) ,000 ,002 .O04 .O06 .O08ha(m) .O00 .O02 .O04 .O06 .O080.000.010.020.03 1.39 1.530.04 2.17 2.351.68 1.842.53 2.722.002.9 I0.40 1520.41 1600.42 1690.43 1770.44 186154162170179188I 551641721811901571651741831921591671761841930.05 3.12 3.320.06 4.22 4.460.07 5.48 5.750.08 6.90 7.200.09 8.49 8.823.53 3.764.70 4.956.02 6.317.52 7.839.17 9.523.985.216.608.169.880.45 1950.46 2050.47 2140.48 2240.49 23419720721622623619920821822823820 12102202302402032122222322430.10 10.2 10.60.11 12.2 12.60.12 14.3 14.70.13 16.5 17.00.14 19.0 19.511.0 11.413.0 13.415.1 15.617.5 18.020.0 20.511.813.816.118.521.00.50 2450.51 2550.52 2660.53 2770.54 28924725726828029 124926027 I28229425 12622732842962532642752872980.15 21.6 22.10.16 24.4 25.00.17 27.4 28.00.18 30.5 31.20.19 33.9 34.622.7 23.225.6 26.228.6 29.231.9 32.535.3 36.023.826.830.033.236.70.55 3010.56 3130.57 3250.58 3370.59 3503033153273403533053173303433553083203323453583103223353483610.20 37.4 38.20.21 41.2 42.00.22 45.1 45.90.23 49.3 50.10.24 53.6 54.538.9 39.742.7 43.546.8 47.651.0 51.855.4 56.340.444.348.452.757.20.60 3630.61 3770.62 3900.63 4050.64 4193663803934074223693823964104253713853994134273753884024164300.25 58.1 59.10.26 62.9 63.90.27 67.8 68.90.28 73.0 74.10.29 78.4 79.560.0 61.064.8 65.869.9 70.975.1 76.280.6 81.761.966.872.077.382.80.65 4330.66 4480.67 4630.68 4790.69 49543645 146648249843945447048550 144245747348850444546047649 15070.30 84.0 85.10.31 89.8 91.00.32 95.8 97.00.33 102 1030.34 109 11086.3 87.492.2 93.498.3 99.5105 106Ill 11388.694.61011071 I40.70 5110.71 5270.72 5440.73 5610.74 57851453054756458251753455 I56858552053755457 15895245405575755920.35 115 1170.36 122 1240.37 129 1310.38 137 1380.39 144 146118 119125 126132 134140 141148 14912112813514315126 1

Table 7.14h Free-flow discharge through 4.5 ft H-flume in m3/s x(I/s) (cont.)ha(m) .O00.O02.O04,006,008ha(m) .O00 .O02 .O04 .O06 .0080.75 5960.76 6140.77 6320.78 6500.79 66959961763665467360362 I63965867760662564366268 161062864766668 51.05 1281 12871.06 1310 13161.07 1339 13451.08 1368 13741.09 1398 140312921321I350I380140912991327I35613861415i30413331362139214210.80 6890.81 7080.82 7280.83 7480.84 76969371273275277369671673675777770072074076 178 17047247447657861.10 1427 14341.11 1458 14641.12 1489 14951.13 1520 15261.14 1551 15581440147015011532I5641446147615071539I570145214821513154515770.85 7900.86 8110.87 8330.88 8550.89 87779481583785988 179882084 I8638868028248468688908078288508728941.15 1583 15901.16 1616 16221.17 1648 16551.18 1681 16881.19 1715 172215961629166116951728I6031635166817011735160916421675170817420.90 8990.91 9220.92 9460.93 9690.94 99390492795097499890993295597910039139369609841 O0891894 196598810131.20 1749 17561.21 1783 17901.22 1818 18251.23 1853 18601.24 1889 189617631797I832I8671903I769I804I839I8751910177618111846188219180.95 10180.96 10420.97 10680.98 10930.99 111910231047107310981 I241028105210781 IO31 I2910321057108311081 I341037I062108811141 I401.25 1925 19321.26 1961 19691.27 1998 20061.28 2035 20431.29 2073 20811939197620132050208819471983202020582096195419912028206621041.00 11451.01 11721.02 11981.03 12261.04 125311501 I771204123 I12591 I561 I821209123712651161118812151242I2701 I661 I9312201248I2761.30 2111 21191.31 2150 21581.32 2189 21971.33 2228 22361.34 2268 22762127216522052244228421342173221222522292214221812220226023001.35 2308 23171.36 2349 23572325236623332341262

Table 7.15a Free-flow discharge through 3.5 ft HL-flume in I/s (m3/s xha(m) .O00 .O02 ,004 .O06 .0080.050.060.070.080.094.86 5.196.58 6.958.55 8.9810.79 I 1.2713.29 13.825.527.349.4111.7514.365.867.739.8612.2514.926.228.1410.3212.7715.480.100.1 I0.120.130.140.150.160.170.180.190.200.210.220.230.240.250.260.270.280.2916.06 16.6519.11 19.7522.44 23.1426.05 26.8129.96 30.7834.17 35.0538.69 39.6343.51 44.5148.65 49.7154.10 55.2317.2420.4023.8527.5831.6135.9440.5845.5350.7956.3817.8521.0724.5728.3632.4536.8441.5446.5551.8857.5318.4721.7525.3129.1633.3137.7642.5247.5952.9958.7059.89 61.0866.00 * 67.2772.45 73.7979.25 80.6586.39 87.8693.88 95.42101.73 103.35109.95 1 I I .64118.53 120.30127.49 129.3362.2968.5475.1382.0689.3496.98104.98113.34122.07131.1863.5269.8376.4983.4990.8498.55106.62115.06123.86133.0564.7571.1477.8684.9392.36100.14108.28116.79125.67134.930.300.310.320.330.340.350.360.370.380.39136.83 138.74146.55 148.54156.66 158.73167.17 169.32178.07 180.30189.38 191.69201.10 203.50213.24 215.72225.80 228.36238.78 241.43140.67150.55160.82171.48182.55194.02205.91218.21230.94244.09142.61152.57162.92173.66184.81196.36208.33220.72233.53246.77260.45274.56289.12304. I2319.58335.50351.88368.73386.05403.86422.15440.92460. I9479.96500.24521.02542.32564.13586.47609.34144.57154.61165.03175.86187.09198.73210.78223.25236.15249.470.400.410.420.430.440.450.460.470.480.49252.19 254.92266.04 268.86280.33 283.24295.06 298.06310.25 313.34325.89 329.07341.99 345.27358.56 361.93375.60393.12379.07396.68257.68271.70286.17301 .O8316.45332.28348.57365.32382.35400.26263.23277.43292.08307.18322.73338.74355.21372.16389.58407.48425.86444.74464.11483.98504.35525.24546.64568.5659 I .o0613.970.500.510.520.530.540.550.560.570.580.59411.12 414.77429.60 433.35448.57 452.43468.04 472.00488.01 492.07508.49 512.65529.48 533.74550.98 555.34573.00 577.47595.55 600.13418.45437. I3456.30475.97496.14516.82538.02559.7358 I .96604.72263

.Table 7.15a (cont.) Free-flow discharge through 3.5 ft HL-flume in I/s (m3/s x 10-7ha(4 .O00 .O02 .O04 .O06 .0080.600.610.620.630.640.650.660.670.680.69618.63642.25666.40691.10716.35742.16768.52795.46822.96851.03623.3 I647.0367 I .30696.1 I72 I .47747.39773.87800.91828.52856.71628.01651.84676.22701.14726.61752.64779.23806.39834.12862.42632.74656.67681.16706.1973 I .77757.91784.6181 1.89839.73868. I5637.48661.53686.1271 1.26736.95763.21790.02817.41845.37873.910.700.710.720.730.740.750.760.770.780.79879.68908.92938.75969. I71000. I91031.821064.051096.901130.36I 164.45885.49914.84944.79975.331006.471038.221070.571103.541137.131171.34891.31920.78950.85981.511012.771044.641077.121 I10.211143.921 178.26897.16926.75956.93987.711019.101051.081083.69I1 16.901150.741185.20903.03932.74963.04993.941025.441057.561090.281123.621157.581192.170.800.810.820.830.840.850.860.870.880.890.900.9 I0.920.930.940.950.960.970.980.991199.171234.521270.501307.131344.411382.341420.921460.171500.091540.67158 I .941623.881666.511709.831753.851798.561843.991890.121936.971984.531206.191241.661277.781314.54I35 I .941390.001428.721468.1 O1508. I51548.871590.271632.351675.121718.581762.731807.591853.161899.431946.421994. I31213.231248.831285.081321.971359.501397.691436.541476.061516.241557.101598.631640.851683.751727.351771.651816.651862.351908.771955.912003.761220.301256.031292.401329.421367.091405.411444.391484.041524.361565.351607.021649.381692.421736. I61780.591825.731871.581918.141965.422013.421227.401263.251299.751336.901374.701413.151452.271492.051532.501573.631615.441657.931701.111744.991789.561834.851880.841927.541974.962023.1 II .o0 2032.82 2042.57 2052.35 2062.15 2071.981.01 2081.85 2091.74 2101.66 2111.61 2121.59I .o2 2131.60 2141.64 2151.71 2161.81 2171.94I .O3 2182.10 2192.28 2202.50 2212.75 2223.03I ... o4 22zz __. . 31 . 2243.67~~ .2254.04 2264.44 2274.86I .o5 2285.32 2295.81 2306.33 2316.87 2327.45I .O6 2338.06 2348.70 2359.37 2370.07264

Table 7.15b Free-flow discharge through 4 ft HL-flume in I/s (m3/s xha(m) .o00 .O02 .O04 .O06 .0080.050.060.070.080.095.387.269.41I I .8414.565.731.679.8812.3615.136.108.0910.3512.9015.726.488.5210.8413.4416.326.868.961 1.3413.9916.930.100.110.120.130.140.150.160.170.18' 0.1917.5520.8424.4328.3232.5137.0141.8346.9752.4458.2418.1921.5425.1829.1333.3837.9542.8348.0453.5759.4418.8422.2425.9529.9634.2738.9043.8549.1254.7260.6519.4922.9626.7330.7935.1739.8644.8850.2155.8861.8820.1623.6927.513 I .6536.0940.8445.9251.3257.0563.120.200.210.220.230.240.250.260.270.280.2964.3770.8577.6784.8492.37100.26108.51117.14126.14135.5265.6472.1879.0786.3293.92101.88110.21118.91127.99137.4566.9273.5380.4987.8195.48103.52I 1 I .92120.69129.85139.3868.2174.9081.9389.3 I97.06105.17113.64122.50131.73141.3469.5276.2783.3890.8398.65106.83115.38124.31133.62143.310.300.3 I0.320.330.340.350.360.370.380.39145.29155.45166.00176.96188.31200.08212.26224.86237.88251.33147.29157.53168.16179.20190.63202.48214.75227.43240.54254.08149.31159.62170.34181.45192.97204.90217.25230.02243.21256.84151.34161.73172.53183.72195.32207.34219.77232.62245.90259.61153.39163.86174.73186.01197.69209.79222.3 I235.24248.61262.410.400.410.420.430.440.450.460.470.480.49265.22279.54294.30309.51325.18341.29357.87374.92392.43410.42268.05282.46297.31312.61328.36344.57361.24379.39395.99414.07270.89285.39300.33315.72331.57347.87364.6338 I .86399.51417.75273.76288.34303.38318.86334.79351.18368.04385.37403.16421.44276.64291.32306.44322.01338.03354.52311.47388.89406.78425.150.500.510.520.530.540.550.560.570.580.59428.88447.83467.27487.20507.63528.56550.0057 I .94594.40617.39432.6345 I .68471.22491.25511.78532.81554.34576.39598.96622.04436.41455.55475.19495.315 15.94537.07558.71580.87603.53626.72440.20459.44479.17499.40520. I3541.36563.10585.36608.1363 I .43440.00463.35483.18503.51524.33545.67567.51589.87612.75636.15265

Table 7.15b (cont.) Free-flow discharge through 4 ft HL-flume in l/s (m3/s xha(m) .O00 .O02 .O04 .O06 .0080.600.610.620.630.640.650.660.670.680.69640.89664.92689.49714.60740.24766.44793.18820.48848.34876.76645.66669.80694.47719.68745.44771.74798.59826.00853.98882.51650.44674.69699.47724.79750.65777.07804.03831.55859.64888.29655.25679.60704.49729.92755.89782.41809.49837.13865.32894.09660.08684.54709.53735.07761.15787.79814.97842.72871.03899.910.700.710.720.730.740.750.760.770.780.79905.75935.31965.46996.181027.491059.391091.88I1 24.981158.681192.9891 1.62941.30971.551002.391033.821065.841098.451131.671165.491199.92917.51947.30977.671008.631040.181072.31I105.051138.381172.321206.88923.42953.33983.821014.891046.561078.8111 11.671145.121179.191213.86929.36959.38989.991021.181052.961085.3411 18.311151.891186.071220.870.800.810.820.830.840.850.860.870.880.891227.901263.441299.591336.371373.79141 1.831450.521489.841529.821570.441234.961270.621306.901343.811381.341419.521458.331497.791537.891578.651242.041277.821314.231351.261388.931427.231466. I71505.761545.991586.881249.151285.051321.591358.741396.541434.961474.041513.751554.121595. I31256.281292.311328.971366.251404.171442.731481.931521.771562.271603.420.900.910.920.930.940.950.960.970.980.99161 1.731653.671696.281739.551783.501828. I31873.441919.431966.122013.501620.061662.141704.881748.291792.371837.141882.581928.711975.542023.061628.421670.631713.511757.051801.271846.171891.751938.021984.992032.651636.811679.1 51722.161765.841810.20.I855231900.751947.361994.462042.261645.231687.701730.841774.661819.151864.321910.181956.732003.97205 I .9 II .o01.01I .o21 .O31 .O41 .o51 .O61 .O71 .O8I .O92061.582110.362159.852210.062260.972312.612364.982418.07247 I .902526.472071.282120.202 169.842220.18227 I .242323.032375.542428.782482.762537.47208 1 .O12130.072179.852230.34228 I .542333.472386. I32439.522493.642548.502090.762139.972189.892240.52229 1.872343.952396.752450.282504.552559.562100.552149.902199.962250.732302.232354.452407.40246 I .O825 15.492570.651.101.111.121.131.141.151.161.171.181.192581.772637.832694.632752.192810.5 I2869.602929.452990.073051.473113.652592.932649.132706.092763.802822.272881.502941.513002.293063.843126.182604.1 12660.462717.572775.432 8 3 4. O 52893.442953.603014.543076.253 138.742615.322671.822729.082787.092845.872905.412965.733026.8 I3088.683151.332626.562683.212740.622798.792857.722917.412977.883039. I33101.153 163.96I .201.213176.613240.373189.303253.213202.023266.093214.773279.003227.553291.94266

I’7.6 Selected list of referencesAckers, P. and A.J.M. Harrison 1963. Critical-depth flumes for flow measurement in open channels. Dept.of Sci. &Industrial Research. Hydraulic Res. Sta., Hydr. Research Paper No. 5. London.Balloffet, A. 1951. Critical flow meters (Venturi flumes). Proc. ASCE. 81, Paper 743.Bennett, R.S. 1972. Cutthroat flume discharge relations. Thesis presented to Colorado State University,Fort Collins, Col., in partial fulfillment of requirements for the degree of Master of Science.Bos, M.G. 1985. Long-throated flumes and broad-crested weirs. Martinus Nijhoff Publishers, Dordrecht.p 141.Bos, M.G. and Y, Reinink 198 I. Head loss over long-throated flumes. Journal of the Irrigation and DrainageDivision, ASCE, Vol. 107, IRI, pp.87-102.Blau, E. 1960. Die modelmässige Untersuchung von Venturikanälen verschiedener Grösse und Form. Veröffentlichungender Forschungsanstalt fiir Schiffahrt, Wasser- und Grundbau 8. Akademie Verlag,Berlin.British Standards institution 1965. Methods of measurement of liquid flow in open channels. BS3680. Part4. Weirs and flumes. 4A: Thin plate weirs and venturi flumes.Caplan, F. 1963. Nomograph for Free Flow Discharge through a Parshall Flume. Water & Sewage Works.Clemmens, A.J., J.A. Replogle & M.G. Bos 1987. Flume: a computer model for estimating flow ratesthrough long-throated measuring flumes, U.S. Dept. of Agriculture, ARS-57, p.64.Eggleston, K.O. 1967. Effects of boundary geometry on critical and subcritical flow through measuringflumes. Utah Water Research Laboratory. College of Engineering, Utah State University. Logan, Utah.Engel, F.V.A.E. 1934. The venturi flume. The Engineer. London. Vol. 158. Aug. 3, pp. 104-107. Aug.10,pp. 131-133.Fane, A.C. 1927. Report on flume experiments on Sirhind Canal. Punjab Irrigation Branch. Paper 1 IO,Punjab Eng. Congress.Gwinn, Wendell R. and Donald A. Parsons. 1976. Discharge equations for HS, H, and HL flumes. J.of the Hydraulics Div. ASCE, Vol. 102. No. HY I., pp. 73-88.Harvey, W.B. 1912. Harvey’s Irrigation Outlet. Punjab Irrigation Branch.Holtan, H.N., N.E. Minchal and L.L. Harrold. 1962. Field manual for research in agricultural hydrology.Soils & Water Conservation Research Div., Agricultural Research Service, Agricultural HandbookNo.224. Washington D.C.Idelcik, I.E. 1969. Memento des pertes de charge. Collection du Centre de recherche et d’essais de Chatou.Eyrolles. Paris.Inglis, C.C. 1929. Notes on standing wave flumes and flume meter falls. Public Works Dept. TechnicalPaper No. 15. Bombay.Jameson, A.H. 1930. The development of the venturi flume. Water & Water Engineering. March 20, pp.105- 107.Khafagi, A. 1942. Der Venturikanal. Theorie und Anwendung. Diss. Driickerei AG. Gebr. Leemann &Co., Zurich.Parshall, R.L. 1945. Improving the Distribution of Water to Farmers by Use of the Parshall MeasuringFlume. Soil Conservation Service. Bull. 488. U.S. Dept. of Agriculture and Colorado Agricultural ExperimentStation. Colorado A and M College. Fort Collins, Colorado.Parshall, R.L. 1950. Measuring Water in Irrigation Channels with Parshall Flumes and Small Weirs. SoilConservation Circular No. 843. U.S. Dept. of Agriculture.Parshall, R.L. 1953. Parshall Flumes of Large Size. Bull. 426-A (Reprint of Bull. 386). Colorado Agric.Experiment Sta., Colorado State University, Fort Collins, Colorado.Peterka, A.J. 1965. Water Measurement Procedures. Irrigation Operators’ Workshop. Hydraulics LaboratoryReport No. Hyd.-552. Bureau of Reclamation, November I5 (unpublished).Robinson, A.R. 1957. Parshall Measuring Flumes of Small Sizes. Technical Bulletin No. 61. AgriculturalExperiment Station. Colorado State University. Fort Collins, Colorado.Robinson, A.R., and A.R. Chamberlain. 1960. Trapezoidal flumes for open channel flow measurement.Trans. Amer. Soc. Agri. Engnrs. Nr. 2, pp. 120-128.Robinson, A.R. 1965. Simplified Flow Corrections for Parshall Flumes under Submerged Conditions. CivilEngineering ASCE.Robinson, A.R. 1968. Trapezoidal flumes for measuring flow in irrigation channels. Agr. Res. Service ARS41-140. U.S. Dept. ofAgriculture. 15 pp.267

Schuster, J.C.(Ed.). 1970. Water measurement procedures. Irrigation operators’ workshop. Report on REC-OCE-70 pp.49.Skogerboe, G.V., M.L. Hyatt, R.K. Anderson, and K.O. Eggleston 1967. Design and calibration of submergedopen channel flow measurement structures. Part 3: Cutthroat flumes. Report WG31-4. UtahWater Res. Laboratory. College of Engineering. Utah State University. Logan, Utah.Skogerboe, G.V. and M.L. Hyatt 1967. Analysis of submergence in flow measuring flumes. J. of the HydraulicsDiv., ASCE . Vol. 93, No. HY4, Proc. Paper 5348. pp. 183-200.Skogerboe G.V., M.L. Hyatt, J.D. England and J.R. Johnson 1967. Design and Calibration of submergedopen channel flow measurement structuies. Part 2. Parshall flumes. Report WG 3/-3. Utah Water ResearchLaboratory. College of Eng. Utah St. University. Logan, Utah.Skogerboe, G.V., and M.L. Hyatt 1967. Rectangular cutthroat flow measuring flumes. J. of the Irrigationand Drainage Div. ASCE, Vol. 93, No. IR4. pp. 1-33.Skogerboe, G.V., R.S. Bennett, and W.R. Walker 1972. Generalized discharge relations for cutthroatflumes. J. of the Irrig. and Drainage Div. ASCE, Vol. 98. No. IR4. pp. 569-583.U.S. Department of the Interior 1967. U.S. Bureau of Reclamation: Water measurement manual. SecondEd. Denver, Colorado, 327 pp.Ven Te Chow 1959. Open channel hydraulics. McGraw-Hill Book Comp., New York. pp. 680.Wells, E.A., and H.B. Gotaas 1956. Design of Venturi flumes in circular conduits. J. Sanit. Engng. Div.,ASCE. Paper No. 2937. pp.749-77 I.268