HEC-RAS PRACTICUM -1 (DUE NOVEMBER 20, 2007)

— David Wagner 2007/11/20 17:56

A rectangular channel 8 ft wide carries 100 ft3/s at a normal depth of 0.5 ft. This channel is connected by a 50-ft long straight wall transition to a rectangular channel 10 ft wide. If the downstream normal depth of flow is 4.16 ft and the Manning resistance coefficient upstream, through the transition and downstream is 0.001,

A. The longitudinal slope of the upstream of the transition

Using the minimum Manning's n flowmaster will accept (0.009), the upstream slope is 0.067601

A=by=8*0.5= 4 ft²; P=b+2y=8+2*0.5= 9 ft; R=A/P=4/9= 0.44 ft; $S_1=({nQ}/{phi A R^{2/3}})^2=({0.001*100}/{1.49*4*0.44^{2/3}})^2=(0.1/3.47)^2=0.0288^2$ =0.00083

S1=0.00083

B. For the conditions specified, does a hydraulic jump occur within the transition?

u_1=Q/A=100/4= 25 ft/s; L_1=D=A/T=4/8= 0.5 ft;

$F_1=u/sqrt{gL}=25/sqrt{32.2*0.5}=25/4.012=$ 6.23 → Supercritical.

$E_1=y_1+{{{u_1}^2}/{2g}}=0.5+{25^2}/{2*32.2}=0.5+9.7=$ 10.2 ft.

A_2=by=10*4.16= 41.6 ft²; u_2=Q/A=100/41.6= 2.4 ft/s; L_2=D=A/T=41.6/10= 4.16 ft;

$F_2=u/sqrt{gL}=2.4/sqrt{32.2*4.16}=2.4/8.80=$ 0.27 → Subcritical.

$E_2=y_2+{{{u_2}^2}/{2g}}=4.16+{2.4^2}/{2*32.2}=4.16+0.089=$ 4.25 ft < 10.2 ft.

∴A Hydraulic Jump Occurs

C. Estimate where within the transition the hydraulic jump takes place.

$E_L=E_1=y_L+{{Q^2}/{2gb^2 y_L}}=y_L+{10000/{2*32.2*b^2 {y_L}^2}}=10.2 right$ ${y_L}^3+{155.28/{b^2}}=10.2{y_L}^2 right$

${y_L}^3-10.2{y_L}^2+{155.28/{b^2}}=0$ ;

$m_1=3{y_L}^2-20.4y_L$

$E_H=E_2=y_H+{{Q^2}/{2gb^2 y_H}}=y_H+{10000/{2*32.2*b^2 {y_H}^2}}=4.25 right$ ${y_H}^3+{155.28/{b^2}}=4.25{y_H}^2 right$

${y_H}^3-4.25{y_H}^2+{155.28/{b^2}}=0$ ;

$m_2=3{y_L}^2-8.5y_L$

l	b	zero	m	yL	ML	zero	m	yH	MH	deltaM
0	8.0			0.50	78.69	0.23	15.91	4.11	76.86	1.82
10	8.4	-0.22	-9.45	0.48	78.74	0.20	16.11	4.12	80.24	-1.51
20	8.8	-0.20	-9.04	0.45	78.78	0.17	16.28	4.13	83.64	-4.86
30	9.2	-0.17	-8.64	0.43	78.82	0.15	16.43	4.14	87.06	-8.24
40	9.6	-0.15	-8.29	0.42	78.85	0.13	16.56	4.15	90.49	-11.64
50	10.0	-0.14	-7.96	0.40	78.89			4.16	93.80	-14.91

The jump occurs between zero and ten feet after the start of the transition.

D. The longitudinal slope of the channel downstream of the transition

Using the minimum Manning's n flowmaster will accept (0.009), the downstream slope is 0.000071

A=by=10*4.16= 41.6 ft²; P=b+2y=10+2*4.16= 18.32 ft; R=A/P=41.6/18.32= 2.27 ft; $S_2=({nQ}/{phi A R^{2/3}})^2=({0.001*100}/{1.49*41.6*2.27^{2/3}})^2=(0.1/107)^2=0.00093^2$ =0.00000087

S2=0.00000087

E. Develop HEC-RAS data files for this situation and confirm that a hydraulic jump occurs in the transition.

Zipped HEC-RAS Project Files

Reach	River Sta	Profile	Q Total	Min Ch El	W.S. Elev	Crit W.S.	E.G. Elev	E.G. Slope	Vel Chnl	Flow Area	Top Width	Froude # Chl
			(cfs)	(ft)	(ft)	(ft)	(ft)	(ft/ft)	(ft/s)	(sq ft)	(ft)
1	2000	PF 1	100.00	90.00	90.50	91.69	100.25	0.000841	25.06	3.99	8.00	6.25
1	1500	PF 1	100.00	89.58	90.08	91.27	99.82	0.000840	25.05	3.99	8.00	6.25
1	1499.*	PF 1	100.00	89.58	90.08	91.26	99.82	0.000845	25.05	3.99	8.04	6.27
1	1498.*	PF 1	100.00	89.58	93.73	91.26	93.87	0.000002	2.98	33.53	8.08	0.26
1	1497.*	PF 1	100.00	89.58	93.73		93.87	0.000002	2.97	33.71	8.12	0.26
1	1496.*	PF 1	100.00	89.58	93.73		93.87	0.000002	2.95	33.88	8.16	0.26
1	1495.*	PF 1	100.00	89.58	93.73		93.87	0.000001	2.94	34.06	8.20	0.25
1	1494.*	PF 1	100.00	89.58	93.73		93.87	0.000001	2.92	34.23	8.24	0.25
1	1493.*	PF 1	100.00	89.57	93.74		93.87	0.000001	2.90	34.49	8.28	0.25
1	1492.*	PF 1	100.00	89.57	93.74		93.87	0.000001	2.88	34.66	8.32	0.25
1	1491.*	PF 1	100.00	89.57	93.74		93.87	0.000001	2.87	34.84	8.36	0.25
1	1490.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.86	35.01	8.40	0.25
1	1489.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.84	35.19	8.44	0.25
1	1488.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.83	35.36	8.48	0.24
1	1487.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.81	35.53	8.52	0.24
1	1486.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.80	35.71	8.56	0.24
1	1485.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.79	35.88	8.60	0.24
1	1484.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.77	36.06	8.64	0.24
1	1483.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.76	36.23	8.68	0.24
1	1482.*	PF 1	100.00	89.57	93.74		93.86	0.000001	2.75	36.40	8.72	0.24
1	1481.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.73	36.67	8.76	0.23
1	1480.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.71	36.84	8.80	0.23
1	1479.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.70	37.02	8.84	0.23
1	1478.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.69	37.19	8.88	0.23
1	1477.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.68	37.36	8.92	0.23
1	1476.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.66	37.54	8.96	0.23
1	1475.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.65	37.71	9.00	0.23
1	1474.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.64	37.89	9.04	0.23
1	1473.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.63	38.06	9.08	0.23
1	1472.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.62	38.23	9.12	0.23
1	1471.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.60	38.41	9.16	0.22
1	1470.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.59	38.58	9.20	0.22
1	1469.*	PF 1	100.00	89.56	93.75		93.86	0.000001	2.58	38.76	9.24	0.22
1	1468.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.56	39.02	9.28	0.22
1	1467.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.55	39.20	9.32	0.22
1	1466.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.54	39.37	9.36	0.22
1	1465.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.53	39.55	9.40	0.22
1	1464.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.52	39.72	9.44	0.22
1	1463.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.51	39.89	9.48	0.22
1	1462.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.50	40.07	9.52	0.21
1	1461.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.48	40.24	9.56	0.21
1	1460.*	PF 1	100.00	89.55	93.76		93.86	0.000001	2.47	40.42	9.60	0.21
1	1459.*	PF 1	100.00	89.55	93.76		93.85	0.000001	2.46	40.59	9.64	0.21
1	1458.*	PF 1	100.00	89.55	93.76		93.85	0.000001	2.45	40.76	9.68	0.21
1	1457.*	PF 1	100.00	89.55	93.76		93.85	0.000001	2.44	40.94	9.72	0.21
1	1456.*	PF 1	100.00	89.54	93.76		93.85	0.000001	2.43	41.21	9.76	0.21
1	1455.*	PF 1	100.00	89.54	93.76		93.85	0.000001	2.42	41.39	9.80	0.21
1	1454.*	PF 1	100.00	89.54	93.76		93.85	0.000001	2.41	41.56	9.84	0.21
1	1453.*	PF 1	100.00	89.54	93.76		93.85	0.000001	2.40	41.73	9.88	0.21
1	1452.*	PF 1	100.00	89.54	93.76		93.85	0.000001	2.39	41.91	9.92	0.20
1	1451.*	PF 1	100.00	89.54	93.77		93.85	0.000001	2.38	42.08	9.96	0.20
1	1450	PF 1	100.00	89.54	93.77		93.85	0.000001	2.37	42.26	10.00	0.20
1	950	PF 1	100.00	89.54	93.77	91.00	93.85	0.000001	2.37	42.25	10.00	0.20

HEC-RAS PRACTICUM -1 (DUE NOVEMBER 20, 2007)

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