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## Hydraulic Design of Energy Dissipators for Culverts and ChannelsHydraulic 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)

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

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

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

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

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

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

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

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

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

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

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

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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### Contact:

Cynthia Nurmi
Resource Center (Atlanta)
404-562-3908
cynthia.nurmi@dot.gov

Updated: 04/07/2011

United States Department of Transportation - Federal Highway Administration