Appendix B - HEC 14 - Hydraulics - Engineering

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)/(b^8/3S^1/2)
y/b¹	z = 0	z = 0.25	z = 0.5	z = 0.75	z = 1	z = 1.25	z = 1.5	z = 1.75	z = 2	z = 3
0.02	0.00213	0.00215	0.00216	0.00217	0.00218	0.00219	0.00220	0.00220	0.00221	0.00223
0.03	0.00414	0.00419	0.00423	0.00426	0.00429	0.00429	0.00433	0.00434	0.00437	0.00443
0.04	0.00661	0.00670	0.00679	0.00685	0.00690	0.00690	0.00700	0.00704	0.00707	0.00722
0.05	0.00947	0.00964	0.00980	0.00991	0.01000	0.01010	0.01020	0.01030	0.01030	0.01060
0.06	0.0127	0.0130	0.0132	0.0134	0.0136	0.0137	0.0138	0.0140	0.0141	0.0145
0.07	0.0162	0.0166	0.0170	0.0173	0.0176	0.0177	0.0180	0.0182	0.0183	0.0190
0.08	0.0200	0.0206	0.0211	0.0215	0.0219	0.0222	0.0225	0.0228	0.0231	0.0240
0.09	0.0240	0.0249	0.0256	0.0262	0.0267	0.0271	0.0275	0.0279	0.0282	0.0296
0.10	0.0283	0.0294	0.0305	0.0311	0.0318	0.0324	0.0329	0.0334	0.0339	0.0358
0.11	0.0329	0.0342	0.0354	0.0364	0.0373	0.0380	0.0387	0.0394	0.0400	0.0424
0.12	0.0376	0.0393	0.0408	0.0420	0.0431	0.0441	0.0450	0.0458	0.0466	0.0497
0.13	0.0425	0.0446	0.0464	0.0480	0.0493	0.0505	0.0516	0.0527	0.0537	0.0575
0.14	0.0476	0.0501	0.0524	0.0542	0.0559	0.0573	0.0587	0.0599	0.0312	0.0659
0.15	0.0528	0.0559	0.0585	0.0608	0.0628	0.0645	0.0662	0.0677	0.0692	0.0749
0.16	0.0582	0.0619	0.0650	0.0676	0.0699	0.0720	0.0740	0.0759	0.0776	0.0845
0.17	0.0638	0.0680	0.0717	0.0748	0.0775	0.0800	0.0823	0.0845	0.0867	0.0947
0.18	0.0695	0.0744	0.0786	0.0822	0.0854	0.0883	0.0910	0.0936	0.0961	0.1050
0.19	0.0753	0.0809	0.0857	0.0900	0.0936	0.0970	0.1000	0.1030	0.1060	0.1170
0.20	0.0813	0.0875	0.0932	0.0979	0.1020	0.1060	0.1100	0.1130	0.1160	0.1290
0.21	0.0873	0.0944	0.1010	0.1060	0.1110	0.1150	0.1200	0.1230	0.1270	0.1420
0.22	0.0935	0.1010	0.1090	0.1150	0.1200	0.1250	0.1300	0.1340	0.1390	0.1550
0.23	0.0997	0.1090	0.1170	0.1240	0.1300	0.1350	0.1410	0.1460	0.1510	0.1690
0.24	0.106	0.116	0.125	0.133	0.139	0.146	0.152	0.157	0.163	0.184
0.25	0.113	0.124	0.133	0.142	0.150	0.157	0.163	0.170	0.176	0.199
0.26	0.119	0.131	0.142	0.152	0.160	0.168	0.175	0.182	0.189	0.215
0.27	0.126	0.139	0.151	0.162	0.171	0.180	0.188	0.195	0.203	0.232
0.28	0.133	0.147	0.160	0.172	0.182	0.192	0.201	0.209	0.217	0.249
0.29	0.139	0.155	0.170	0.182	0.193	0.204	0.214	0.223	0.232	0.267
0.30	0.146	0.163	0.179	0.193	0.205	0.217	0.227	0.238	0.248	0.286
0.31	0.153	0.172	0.189	0.204	0.217	0.230	0.242	0.253	0.264	0.306
0.32	0.160	0.180	0.199	0.215	0.230	0.243	0.256	0.269	0.281	0.327
0.33	0.167	0.189	0.209	0.227	0.243	0.257	0.271	0.285	0.298	0.348
0.34	0.174	0.198	0.219	0.238	0.256	0.272	0.287	0.301	0.315	0.369
0.35	0.181	0.207	0.230	0.251	0.270	0.287	0.303	0.318	0.334	0.392
0.36	0.190	0.216	0.241	0.263	0.283	0.302	0.319	0.336	0.353	0.416
0.37	0.196	0.225	0.251	0.275	0.297	0.317	0.336	0.354	0.372	0.440
0.38	0.203	0.234	0.263	0.289	0.311	0.333	0.354	0.373	0.392	0.465
0.39	0.210	0.244	0.274	0.301	0.326	0.349	0.371	0.392	0.412	0.491
0.40	0.218	0.254	0.286	0.314	0.341	0.366	0.389	0.412	0.433	0.518
0.41	0.225	0.263	0.297	0.328	0.357	0.383	0.408	0.432	0.455	0.545
0.42	0.233	0.279	0.310	0.342	0.373	0.401	0.427	0.453	0.478	0.574
0.43	0.241	0.282	0.321	0.356	0.389	0.418	0.447	0.474	0.501	0.604
0.44	0.249	0.292	0.334	0.371	0.405	0.437	0.467	0.496	0.524	0.634
0.45	0.256	0.303	0.346	0.385	0.442	0.455	0.487	0.519	0.548	0.665
0.46	0.263	0.313	0.359	0.401	0.439	0.475	0.509	0.541	0.547	0.696
0.47	0.271	0.323	0.371	0.417	0.457	0.494	0.530	0.565	0.600	0.729
0.48	0.279	0.333	0.384	0.432	0.475	514.000	0.552	0.589	0.626	0.763
0.49	0.287	0.345	0.398	0.448	0.492	0.534	0.575	0.614	0.652	0.797
0.50	0.295	0.356	0.411	0.463	0.512	0.556	0.599	0.639	0.679	0.833
0.52	0.310	0.377	0.438	0.496	0.548	0.599	0.646	0.692	0.735	0.906
0.54	0.327	0.398	0.468	0.530	0.590	0.644	0.696	0.746	0.795	0.984
0.56	0.343	0.421	0.496	0.567	0.631	0.690	0.748	0.803	0.856	1.070
0.58	0.359	0.444	0.526	0.601	0.671	0.739	0.802	0.863	0.922	1.150
0.60	0.375	0.468	0.556	0.640	0.717	0.789	0.858	0.924	0.988	1.240
0.62	0.391	0.492	0.590	0.679	0.763	0.841	0.917	0.989	1.060	1.330
0.64	0.408	0.516	0.620	0.718	0.809	0.894	0.976	1.050	1.130	1.430
0.66	0.424	0.541	0.653	0.759	0.858	0.951	1.040	1.130	1.210	1.530
0.68	0.441	0.566	0.687	0.801	0.908	1.010	1.100	1.200	1.290	1.640
0.70	0.457	0.591	0.722	0.842	0.958	1.070	1.170	1.270	1.370	1.750
0.72	0.474	0.617	0.757	0.887	1.010	1.130	1.240	1.350	1.450	1.870
0.74	0.491	0.644	0.793	0.932	1.070	1.190	1.310	1.430	1.550	1.980
0.76	0.508	0.670	0.830	0.981	1.120	1.260	1.390	1.510	1.640	2.110
0.78	0.525	0.698	0.868	1.030	1.180	1.320	1.460	1.600	1.730	2.240
0.80	0.542	0.725	0.906	1.080	1.240	1.400	1.540	1.690	1.830	2.370
0.82	0.559	0.753	0.945	1.130	1.300	1.470	1.630	1.780	1.930	2.510
0.84	0.576	0.782	0.985	1.180	1.360	1.540	1.710	1.870	2.030	2.650
0.86	0.593	0.810	1.030	1.230	1.430	1.610	1.790	1.970	2.140	2.800
0.88	0.610	0.839	1.070	1.290	1.490	1.690	1.880	2.070	2.250	2.950
0.90	0.627	0.871	1.110	1.340	1.560	1.770	1.980	2.170	2.360	3.110
0.92	0.645	0.898	1.150	1.400	1.630	1.860	2.070	2.280	2.480	3.270
0.94	0.662	0.928	1.200	1.460	1.700	1.940	2.160	2.380	2.600	3.430
0.96	0.680	0.960	1.250	1.520	1.780	2.030	2.270	2.500	2.730	3.610
0.98	0.697	0.991	1.290	1.580	1.850	2.110	2.370	2.610	2.850	3.790
1.00	0.714	1.020	1.330	1.640	1.930	2.210	2.470	2.730	2.990	3.970
1.05	0.759	1.100	1.460	1.800	2.130	2.440	2.750	3.040	3.330	4.450
1.10	0.802	1.190	1.580	1.970	2.340	2.690	3.040	3.370	3.700	4.960
1.15	0.846	1.270	1.710	2.140	2.560	2.960	3.340	3.720	4.090	5.520
1.20	0.891	1.360	1.850	2.330	2.790	3.240	3.680	4.090	4.500	6.110
1.25	0.936	1.450	1.990	2.520	3.040	3.540	4.030	4.490	4.950	6.730
1.30	0.980	1.540	2.140	2.730	3.300	3.850	4.390	4.900	5.420	7.390
1.35	1.02	1.64	2.29	2.94	3.57	4.18	4.76	5.34	5.90	8.10
1.40	1.07	1.74	2.45	3.16	3.85	4.52	5.18	5.80	6.43	8.83
1.45	1.11	1.84	2.61	3.39	4.15	4.88	5.60	6.29	6.98	9.62
1.50	1.16	1.94	2.78	3.63	4.46	5.26	6.04	6.81	7.55	10.40
1.55	1.20	2.05	2.96	3.88	4.78	5.65	6.50	7.33	8.14	11.30
1.60	1.25	2.15	3.14	4.14	5.12	6.06	6.99	7.89	8.79	12.20
1.65	1.30	2.27	3.33	4.41	5.47	6.49	7.50	8.47	9.42	13.20
1.70	1.34	2.38	3.52	4.69	5.83	6.94	8.02	9.08	10.10	14.20
1.75	1.39	2.50	3.73	4.98	6.21	7.41	8.57	9.72	10.90	15.20
1.80	1.43	2.62	3.93	5.28	6.60	7.89	9.13	10.40	11.60	16.30
1.85	1.48	2.74	4.15	5.59	7.01	8.40	9.75	11.10	12.40	17.40
1.90	1.52	2.86	4.36	5.91	7.43	8.91	10.40	12.40	13.20	18.70
1.95	1.57	2.99	4.59	6.24	7.87	9.46	11.00	12.50	14.00	19.90
2.00	1.61	3.12	4.83	6.58	8.32	10.00	11.70	13.30	14.90	21.10
2.10	1.71	3.39	5.31	7.30	9.27	11.20	13.10	15.00	16.80	23.90
2.20	1.79	3.67	5.82	8.06	10.30	12.50	14.60	16.70	18.70	26.80
2.30	1.89	3.96	6.36	8.86	11.30	13.80	16.20	18.60	20.90	30.00
2.40	1.98	4.26	6.93	9.72	12.50	15.30	17.90	20.60	23.10	33.40
2.50	2.07	4.58	7.52	10.60	13.70	16.80	19.80	22.70	25.60	37.00
2.60	2.16	4.90	8.14	11.60	15.00	18.40	21.70	25.00	28.20	40.80
2.70	2.26	5.24	8.80	12.60	16.30	20.10	23.80	27.40	31.00	44.80
2.80	2.35	5.59	9.49	13.60	17.80	21.90	25.90	29.90	33.80	49.10
2.90	2.44	5.95	10.20	14.70	19.30	23.80	28.20	32.60	36.90	53.70
3.00	2.53	6.33	11.00	15.90	20.90	25.80	30.60	35.40	40.10	58.40
3.20	2.72	7.12	12.50	18.30	24.20	30.10	25.80	41.50	47.10	68.90
3.40	2.90	7.97	14.20	21.00	27.90	34.80	41.50	48.20	54.60	80.20
3.60	3.09	8.86	16.10	24.00	32.00	39.90	47.80	55.50	63.00	92.80
3.80	3.28	9.81	18.10	27.10	36.30	45.50	54.60	63.50	72.40	107
4.00	3.46	10.8	20.2	30.5	41.1	51.6	61.9	72.1	82.2	122
4.50	3.92	13.5	26.2	40.1	54.5	68.8	82.9	96.9	111	164
5.00	4.39	16.7	33.1	51.5	70.3	89.2	108	126	145	216
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/D	A/D²	R/D	(αQn)/ (D^8/3S^1/2)	(αQn)/ (y^8/3S^1/2)	y/D	A/D²	R/D	(αQn)/ (D^8/3S^1/2)	(αQn)/ (y^8/3S^1/2)
0.01	0.0013	0.0066	0.00007	15.04	0.51	0.4027	0.2531	0.239	1.442
0.02	0.0037	0.0132	0.00031	10.57	0.52	0.4127	0.2562	0.247	0.415
0.03	0.0069	0.0197	0.00074	8.56	0.53	0.4227	0.2592	0.255	1.388
0.04	0.0105	0.0262	0.00138	7.38	0.54	0.4327	0.2621	0.263	1.362
0.05	0.0147	0.0325	0.00222	6.55	0.55	0.4426	0.2649	0.271	1.336
0.06	0.0192	0.0389	0.00328	5.95	0.56	0.4526	0.2676	0.279	1.311
0.07	0.0294	0.0451	0.00455	5.47	0.57	0.1626	0.2703	0.287	1.286
0.08	0.0350	0.0513	0.00604	5.09	0.58	0.4724	0.2728	0.295	1.262
0.09	0.0378	0.0575	0.00775	4.76	0.59	0.4822	0.2753	0.303	1.238
0.10	0.0409	0.0635	0.0097	4.49	0.60	0.4920	0.2776	0.311	1.215
0.11	0.0470	0.0695	0.0118	4.25	0.61	0.5018	0.2799	0.319	1.192
0.12	0.0534	0.0755	0.0142	4.04	0.62	0.5115	0.2821	0.327	1.170
0.13	0.0600	0.0813	0.0167	3.86	0.63	0.5212	0.2842	0.335	1.148
0.14	0.0668	0.0871	0.0195	3.69	0.64	0.5308	0.2862	0.343	1.126
0.15	0.0739	0.0929	0.0225	3.54	0.65	0.5405	0.2988	0.350	1.105
0.16	0.0811	0.0985	0.0257	3.41	0.66	0.5499	0.2900	0.358	1.084
0.17	0.0885	0.1042	0.0291	3.28	0.67	0.5594	0.2917	0.366	1.064
0.18	0.0961	0.1097	0.0327	3.17	0.68	0.5687	0.2933	0.373	1.044
0.19	0.0139	0.1152	0.0365	3.06	0.69	0.5780	0.2948	0.380	1.024
0.20	0.1118	0.1206	0.0406	2.96	0.70	0.5872	0.2962	0.388	1.004
0.21	0.1199	0.1259	0.0448	2.87	0.71	0.5964	0.2975	0.395	0.985
0.22	0.1281	0.1312	0.0492	2.79	0.72	0.6054	0.2987	0.402	0.965
0.23	0.1365	0.1364	0.0537	2.71	0.73	0.6143	0.2998	0.409	0.947
0.24	0.1449	0.1416	0.0585	2.63	0.74	0.6231	0.3008	0.416	0.928
0.25	0.1535	0.1466	0.0634	2.56	0.75	0.6319	0.3042	0.422	0.910
0.26	0.1623	0.1516	0.0686	2.49	0.76	0.6405	0.3043	0.429	0.891
0.27	0.1711	0.1566	0.0739	2.42	0.77	0.6489	0.3043	0.435	0.873
0.28	0.1800	0.1614	0.0793	2.36	0.78	0.6573	0.3041	0.441	0.856
0.29	0.1890	0.1662	0.0849	2.30	0.79	0.6655	0.3039	0.447	0.838
0.30	0.1982	0.1709	0.0907	2.25	0.80	0.6736	0.3042	0.453	0.821
0.31	0.2074	0.1756	0.0966	2.20	0.81	0.6815	0.3043	0.458	0.804
0.32	0.2167	0.1802	0.1027	2.14	0.82	0.6893	0.3043	0.463	0.787
0.33	0.2260	0.1847	0.1089	2.09	0.83	0.6969	0.3041	0.468	0.770
0.34	0.2355	0.1891	0.1153	2.05	0.84	0.7043	0.3038	0.473	0.753
0.35	0.2450	0.1935	0.1218	2.00	0.85	0.7115	0.3033	0.453	0.736
0.36	0.2546	0.1978	0.1284	1.958	0.86	0.7186	0.3026	0.458	0.720
0.37	0.2642	0.2020	0.1351	1.915	0.87	0.7254	0.3018	0.485	0.703
0.38	0.2739	0.2062	0.1420	1.875	0.88	0.7320	0.3007	0.488	0.687
0.39	0.2836	0.2102	0.1490	1.835	0.89	0.7384	0.2995	0.491	0.670
0.40	0.2934	0.2142	0.1561	1.797	0.90	0.7445	0.2980	0.494	0.654
0.41	0.3032	0.2182	0.1633	1.760	0.91	0.7504	0.2963	0.496	0.637
0.42	0.3130	0.2220	0.1705	1.724	0.92	0.7560	0.2944	0.497	0.621
0.43	0.3229	0.2258	0.1779	1.689	0.93	0.7612	0.2921	0.498	0.604
0.44	0.3328	0.2295	0.1854	1.655	0.94	0.7662	0.2895	0.498	0.588
0.45	0.3428	0.2331	0.1929	1.622	0.95	0.7707	0.2865	0.498	0.571
0.46	0.3527	0.2366	0.201	1.590	0.96	0.7749	0.2829	0.496	0.553
0.47	0.3627	0.2401	0.208	1.559	0.97	0.7785	0.2787	0.494	0.535
0.48	0.3727	0.2435	0.216	1.530	0.98	0.7817	0.2735	0.489	0.517
0.49	0.3827	0.2468	0.224	1.500	0.99	0.7841	0.2666	0.483	0.496
0.50	0.3927	0.2500	0.232	1.471	1.00	0.7854	0.2500	0.463	0.463
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
Resource Center (Atlanta)
404-562-3908
cynthia.nurmi@dot.gov

Updated: 04/07/2011

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

Contact:

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