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Hydraulic Design of Energy Dissipators for Culverts and Channels
Hydraulic Engineering Circular Number 14, Third Edition

Appendix B: Critical Depth And Uniform Flow For Various Culvert And Channel Shapes

Figure B.1 (SI). Critical Depth Rectangular Section (Normann, et al., 2001)

Curve that provides critcal depth as a function of the quantity Q divided by (N times B). The relationship is y sub c equals 0.467 times the cube root of ((Q divided by B) squared). Note: y sub c cannot exceed top of box.

Figure B.1 (CU). Critical Depth Rectangular Section (Normann, et al., 2001)

Curve that provides critcal depth as a function of the quantity Q divided by (N times B). The relationship is y sub c equals 0.315 times the cube root of ((Q divided by B) squared). Note: y sub c cannot exceed top of box.

Figure B.2 (SI). Critical Depth of Circular Pipe

Curves that provides critcal depth as a function of Q for pipe diameters ranging in size from 300 to 4500 millimeters. Note: y sub c cannot exceed top of pipe.

Figure B.2 (CU). Critical Depth of Circular Pipe

Curves that provides critcal depth as a function of Q for pipe diameters ranging in size from 1 to 15 feet. Note: y sub c cannot exceed top of pipe.

Figure B.3 (SI). Critical Depth Oval Concrete Pipe Long Axis Horizontal

Curves that provides critcal depth as a function of Q for pipe sizes ranging from 575 by 365 millimeters to 3840 by 2440 millimeters. Note: y sub c cannot exceed top of pipe.

Figure B.3 (CU). Critical Depth Oval Concrete Pipe Long Axis Horizontal

Curves that provides critcal depth as a function of Q for pipe sizes ranging from 23 by 14 inches to 151 by 97 inches. Note: y sub c cannot exceed top of pipe.

Figure B.4 (SI). Critical Depth Oval Concrete Pipe Long Axis Vertical

Curves that provides critcal depth as a function of Q for pipe sizes ranging from 365 by 575 millimeters to 2440 by 3840 millimeters. Note: y sub c cannot exceed top of pipe.

Figure B.4 (CU). Critical Depth Oval Concrete Pipe Long Axis Vertical

Curves that provides critcal depth as a function of Q for pipe sizes ranging from 14 by 23 inches to 97 by 151 inches. Note: y sub c cannot exceed top of pipe.

Figure B.5 (SI). Critical Depth Standard C.M. Pipe-Arch

Curves that provides critcal depth as a function of Q for pipe-arch sizes ranging from 610 by 460 millimeters to 1800 by 1200 millimeters. Note: y sub c cannot exceed top of pipe.

Figure B.5 (CU). Critical Depth Standard C.M. Pipe-Arch

Curves that provides critcal depth as a function of Q for pipe-arch sizes ranging from 25 by 16 inches to 72 by 44 inches. Note: y sub c cannot exceed top of pipe.

Figure B.6 (SI). Critical Depth Structural Plate C.M. Pipe-Arch

Curves that provides critcal depth as a function of Q for pipe-arch sizes ranging from 1850 by 1400 millimeters to 5050 by 3070 millimeters. Note: y sub c cannot exceed top of pipe.

Figure B.6 (CU). Critical Depth Structural Plate C.M. Pipe-Arch

Curves that provides critcal depth as a function of Q for pipe-arch sizes ranging from 6 foot 1 inch by 4 foot 7 inch to 16 foot 7 inch by 10 foot 1 inch. Note: y sub c cannot exceed top of pipe.

Table B.1. Uniform Flow in Trapezoidal Channels by Manning's Formula
Values of (αQn)/(b8/3S1/2)
y/b1z = 0z = 0.25z = 0.5z = 0.75z = 1z = 1.25z = 1.5z = 1.75z = 2z = 3
0.020.002130.002150.002160.002170.002180.002190.002200.002200.002210.00223
0.030.004140.004190.004230.004260.004290.004290.004330.004340.004370.00443
0.040.006610.006700.006790.006850.006900.006900.007000.007040.007070.00722
0.050.009470.009640.009800.009910.010000.010100.010200.010300.010300.01060
0.060.01270.01300.01320.01340.01360.01370.01380.01400.01410.0145
0.070.01620.01660.01700.01730.01760.01770.01800.01820.01830.0190
0.080.02000.02060.02110.02150.02190.02220.02250.02280.02310.0240
0.090.02400.02490.02560.02620.02670.02710.02750.02790.02820.0296
0.100.02830.02940.03050.03110.03180.03240.03290.03340.03390.0358
0.110.03290.03420.03540.03640.03730.03800.03870.03940.04000.0424
0.120.03760.03930.04080.04200.04310.04410.04500.04580.04660.0497
0.130.04250.04460.04640.04800.04930.05050.05160.05270.05370.0575
0.140.04760.05010.05240.05420.05590.05730.05870.05990.03120.0659
0.150.05280.05590.05850.06080.06280.06450.06620.06770.06920.0749
0.160.05820.06190.06500.06760.06990.07200.07400.07590.07760.0845
0.170.06380.06800.07170.07480.07750.08000.08230.08450.08670.0947
0.180.06950.07440.07860.08220.08540.08830.09100.09360.09610.1050
0.190.07530.08090.08570.09000.09360.09700.10000.10300.10600.1170
0.200.08130.08750.09320.09790.10200.10600.11000.11300.11600.1290
0.210.08730.09440.10100.10600.11100.11500.12000.12300.12700.1420
0.220.09350.10100.10900.11500.12000.12500.13000.13400.13900.1550
0.230.09970.10900.11700.12400.13000.13500.14100.14600.15100.1690
0.240.1060.1160.1250.1330.1390.1460.1520.1570.1630.184
0.250.1130.1240.1330.1420.1500.1570.1630.1700.1760.199
0.260.1190.1310.1420.1520.1600.1680.1750.1820.1890.215
0.270.1260.1390.1510.1620.1710.1800.1880.1950.2030.232
0.280.1330.1470.1600.1720.1820.1920.2010.2090.2170.249
0.290.1390.1550.1700.1820.1930.2040.2140.2230.2320.267
0.300.1460.1630.1790.1930.2050.2170.2270.2380.2480.286
0.310.1530.1720.1890.2040.2170.2300.2420.2530.2640.306
0.320.1600.1800.1990.2150.2300.2430.2560.2690.2810.327
0.330.1670.1890.2090.2270.2430.2570.2710.2850.2980.348
0.340.1740.1980.2190.2380.2560.2720.2870.3010.3150.369
0.350.1810.2070.2300.2510.2700.2870.3030.3180.3340.392
0.360.1900.2160.2410.2630.2830.3020.3190.3360.3530.416
0.370.1960.2250.2510.2750.2970.3170.3360.3540.3720.440
0.380.2030.2340.2630.2890.3110.3330.3540.3730.3920.465
0.390.2100.2440.2740.3010.3260.3490.3710.3920.4120.491
0.400.2180.2540.2860.3140.3410.3660.3890.4120.4330.518
0.410.2250.2630.2970.3280.3570.3830.4080.4320.4550.545
0.420.2330.2790.3100.3420.3730.4010.4270.4530.4780.574
0.430.2410.2820.3210.3560.3890.4180.4470.4740.5010.604
0.440.2490.2920.3340.3710.4050.4370.4670.4960.5240.634
0.450.2560.3030.3460.3850.4420.4550.4870.5190.5480.665
0.460.2630.3130.3590.4010.4390.4750.5090.5410.5470.696
0.470.2710.3230.3710.4170.4570.4940.5300.5650.6000.729
0.480.2790.3330.3840.4320.475514.0000.5520.5890.6260.763
0.490.2870.3450.3980.4480.4920.5340.5750.6140.6520.797
0.500.2950.3560.4110.4630.5120.5560.5990.6390.6790.833
0.520.3100.3770.4380.4960.5480.5990.6460.6920.7350.906
0.540.3270.3980.4680.5300.5900.6440.6960.7460.7950.984
0.560.3430.4210.4960.5670.6310.6900.7480.8030.8561.070
0.580.3590.4440.5260.6010.6710.7390.8020.8630.9221.150
0.600.3750.4680.5560.6400.7170.7890.8580.9240.9881.240
0.620.3910.4920.5900.6790.7630.8410.9170.9891.0601.330
0.640.4080.5160.6200.7180.8090.8940.9761.0501.1301.430
0.660.4240.5410.6530.7590.8580.9511.0401.1301.2101.530
0.680.4410.5660.6870.8010.9081.0101.1001.2001.2901.640
0.700.4570.5910.7220.8420.9581.0701.1701.2701.3701.750
0.720.4740.6170.7570.8871.0101.1301.2401.3501.4501.870
0.740.4910.6440.7930.9321.0701.1901.3101.4301.5501.980
0.760.5080.6700.8300.9811.1201.2601.3901.5101.6402.110
0.780.5250.6980.8681.0301.1801.3201.4601.6001.7302.240
0.800.5420.7250.9061.0801.2401.4001.5401.6901.8302.370
0.820.5590.7530.9451.1301.3001.4701.6301.7801.9302.510
0.840.5760.7820.9851.1801.3601.5401.7101.8702.0302.650
0.860.5930.8101.0301.2301.4301.6101.7901.9702.1402.800
0.880.6100.8391.0701.2901.4901.6901.8802.0702.2502.950
0.900.6270.8711.1101.3401.5601.7701.9802.1702.3603.110
0.920.6450.8981.1501.4001.6301.8602.0702.2802.4803.270
0.940.6620.9281.2001.4601.7001.9402.1602.3802.6003.430
0.960.6800.9601.2501.5201.7802.0302.2702.5002.7303.610
0.980.6970.9911.2901.5801.8502.1102.3702.6102.8503.790
1.000.7141.0201.3301.6401.9302.2102.4702.7302.9903.970
1.050.7591.1001.4601.8002.1302.4402.7503.0403.3304.450
1.100.8021.1901.5801.9702.3402.6903.0403.3703.7004.960
1.150.8461.2701.7102.1402.5602.9603.3403.7204.0905.520
1.200.8911.3601.8502.3302.7903.2403.6804.0904.5006.110
1.250.9361.4501.9902.5203.0403.5404.0304.4904.9506.730
1.300.9801.5402.1402.7303.3003.8504.3904.9005.4207.390
1.351.021.642.292.943.574.184.765.345.908.10
1.401.071.742.453.163.854.525.185.806.438.83
1.451.111.842.613.394.154.885.606.296.989.62
1.501.161.942.783.634.465.266.046.817.5510.40
1.551.202.052.963.884.785.656.507.338.1411.30
1.601.252.153.144.145.126.066.997.898.7912.20
1.651.302.273.334.415.476.497.508.479.4213.20
1.701.342.383.524.695.836.948.029.0810.1014.20
1.751.392.503.734.986.217.418.579.7210.9015.20
1.801.432.623.935.286.607.899.1310.4011.6016.30
1.851.482.744.155.597.018.409.7511.1012.4017.40
1.901.522.864.365.917.438.9110.4012.4013.2018.70
1.951.572.994.596.247.879.4611.0012.5014.0019.90
2.001.613.124.836.588.3210.0011.7013.3014.9021.10
2.101.713.395.317.309.2711.2013.1015.0016.8023.90
2.201.793.675.828.0610.3012.5014.6016.7018.7026.80
2.301.893.966.368.8611.3013.8016.2018.6020.9030.00
2.401.984.266.939.7212.5015.3017.9020.6023.1033.40
2.502.074.587.5210.6013.7016.8019.8022.7025.6037.00
2.602.164.908.1411.6015.0018.4021.7025.0028.2040.80
2.702.265.248.8012.6016.3020.1023.8027.4031.0044.80
2.802.355.599.4913.6017.8021.9025.9029.9033.8049.10
2.902.445.9510.2014.7019.3023.8028.2032.6036.9053.70
3.002.536.3311.0015.9020.9025.8030.6035.4040.1058.40
3.202.727.1212.5018.3024.2030.1025.8041.5047.1068.90
3.402.907.9714.2021.0027.9034.8041.5048.2054.6080.20
3.603.098.8616.1024.0032.0039.9047.8055.5063.0092.80
3.803.289.8118.1027.1036.3045.5054.6063.5072.40107
4.003.4610.820.230.541.151.661.972.182.2122
4.503.9213.526.240.154.568.882.996.9111164
5.004.3916.733.151.570.389.2108126145216
  • 1 for y /b less than 0.04, use of the assumption R = y is more convenient and more accurate than interpolation in the table.
  • y = depth of flow, m (ft)
  • Q = discharge by Manning's Equation, m3/s (ft3/s)
  • n = Manning's coefficient
  • S = channel bottom and water surface slope
  • α = units conversion = 1.49 for SI, 1 for CU
  • z = side slope, 1:z (V:H)
  • b = bottom width
  • Source: USBR (1974)
Table B.2. Uniform Flow in Circular Sections Flowing Partly Full
y/DA/D2R/D(αQn)/ (D8/3S1/2)(αQn)/ (y8/3S1/2) y/DA/D2R/D(αQn)/ (D8/3S1/2)(αQn)/ (y8/3S1/2)
0.010.00130.00660.0000715.040.510.40270.25310.2391.442
0.020.00370.01320.0003110.570.520.41270.25620.2470.415
0.030.00690.01970.000748.560.530.42270.25920.2551.388
0.040.01050.02620.001387.380.540.43270.26210.2631.362
0.050.01470.03250.002226.550.550.44260.26490.2711.336
0.060.01920.03890.003285.950.560.45260.26760.2791.311
0.070.02940.04510.004555.470.570.16260.27030.2871.286
0.080.03500.05130.006045.090.580.47240.27280.2951.262
0.090.03780.05750.007754.760.590.48220.27530.3031.238
0.100.04090.06350.00974.490.600.49200.27760.3111.215
0.110.04700.06950.01184.250.610.50180.27990.3191.192
0.120.05340.07550.01424.040.620.51150.28210.3271.170
0.130.06000.08130.01673.860.630.52120.28420.3351.148
0.140.06680.08710.01953.690.640.53080.28620.3431.126
0.150.07390.09290.02253.540.650.54050.29880.3501.105
0.160.08110.09850.02573.410.660.54990.29000.3581.084
0.170.08850.10420.02913.280.670.55940.29170.3661.064
0.180.09610.10970.03273.170.680.56870.29330.3731.044
0.190.01390.11520.03653.060.690.57800.29480.3801.024
0.200.11180.12060.04062.960.700.58720.29620.3881.004
0.210.11990.12590.04482.870.710.59640.29750.3950.985
0.220.12810.13120.04922.790.720.60540.29870.4020.965
0.230.13650.13640.05372.710.730.61430.29980.4090.947
0.240.14490.14160.05852.630.740.62310.30080.4160.928
0.250.15350.14660.06342.560.750.63190.30420.4220.910
0.260.16230.15160.06862.490.760.64050.30430.4290.891
0.270.17110.15660.07392.420.770.64890.30430.4350.873
0.280.18000.16140.07932.360.780.65730.30410.4410.856
0.290.18900.16620.08492.300.790.66550.30390.4470.838
0.300.19820.17090.09072.250.800.67360.30420.4530.821
0.310.20740.17560.09662.200.810.68150.30430.4580.804
0.320.21670.18020.10272.140.820.68930.30430.4630.787
0.330.22600.18470.10892.090.830.69690.30410.4680.770
0.340.23550.18910.11532.050.840.70430.30380.4730.753
0.350.24500.19350.12182.000.850.71150.30330.4530.736
0.360.25460.19780.12841.9580.860.71860.30260.4580.720
0.370.26420.20200.13511.9150.870.72540.30180.4850.703
0.380.27390.20620.14201.8750.880.73200.30070.4880.687
0.390.28360.21020.14901.8350.890.73840.29950.4910.670
0.400.29340.21420.15611.7970.900.74450.29800.4940.654
0.410.30320.21820.16331.7600.910.75040.29630.4960.637
0.420.31300.22200.17051.7240.920.75600.29440.4970.621
0.430.32290.22580.17791.6890.930.76120.29210.4980.604
0.440.33280.22950.18541.6550.940.76620.28950.4980.588
0.450.34280.23310.19291.6220.950.77070.28650.4980.571
0.460.35270.23660.2011.5900.960.77490.28290.4960.553
0.470.36270.24010.2081.5590.970.77850.27870.4940.535
0.480.37270.24350.2161.5300.980.78170.27350.4890.517
0.490.38270.24680.2241.5000.990.78410.26660.4830.496
0.500.39270.25000.2321.4711.000.78540.25000.4630.463
  • y = depth of flow, m (ft)
  • D = diameter of pipe, m (ft)
  • A = area of flow m2 (ft2)
  • R = hydraulic radius, m (ft)
  • Q = discharge by Manning's Equation, m3/s (ft3/s)
  • n = Manning's coefficient
  • S = channel bottom and water surface slope
  • α = units conversion = 1.49 for SI, 1 for CU
  • Source: USBR (1974)
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Cynthia Nurmi
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cynthia.nurmi@dot.gov

Updated: 04/07/2011
 

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