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Unformatted text preview: American University of Sharjah
Civil Engineering Department CVE 341 – WATER RESOURCES
ASSIGNMENT 7
Q.1) Water flowing in a wide channel encounters a 22cm high bump at the bottom of the
channel. If the flow depth is 1.2 m and the velocity is 2.5 m/s before the bump, determine if the
flow is chocked over the bump, and discuss.
flow
(Answers yc=0.97m & Ec=1.46m3/s)
97m Assumptions 1 The flow is steady. 2 Frictional effects are negligible so that there is no dissipation of mechanical
Frictional
energy. 3 The channel is sufficiently wide so that the end effects are negligible.
Analysis The upstream Froude number and the critical depth are The flow is subcritical since Fr < 1, and the flow depth decreases over the bump. The upstream, over the bump, and
critical specific energy is We have an interesting situation: The calculations show that Es2 < Ec. That is, the specific energy of the fluid
That
decreases below the level of energy at the critical point, which is the minimum energy, and this is impossible.
Therefore, the flow at specified conditions cannot exist. The flow is choked when the specific energy drops to the
Therefore,
minimum value of 1.46 m, which occurs at a bumpheight of Discussion A bumpheight over 6 cm results in a reduction in the flow rate of water, or a rise of upstream water
level. Therefore, a 22cm high bump alters the upstream flow. On the other hand, a bump less than 6 cm high will
not affect the upstream flow Q.2) Water flow in a wide rectangular channel approaches a 10 cmhigh bump at 1.5 m/s and a
depth of 1m. Estimate
(a)
The water depth y2 over the bump
(b)
The bump height that will cause the crest flow to be critical.
V2
1 .5
Fr =
=
⇒ Fr = 0.479
gy c 9.81 * 1 (Answers y2=0.859m & 0.197m) 2 E = y+ Subcritical flow Q2
1 .5 2
= 1 .0 +
= 1.115m
2 * 9.81
2gA 2 E2=E1∆h=1.015 y 3 − 1.015 y 2 + 0.115 = 0
2
2
There are three real roots y2=0.859m, 0.451m and 0.296. The negative value is physically
impossible. The second solution (0.451m) is supercritical condition for E2 and it is not
possible for this subcritical bump. The first solution is correct.
Q.3) A trapezoidal channel with a bottom width of 5 m and side slopes t = 2 runs on a slope of
0.0005 and carries a discharge of 50 m3/s at normal depth. Take Manning’s n as 0.021 (metric).
a) What is the specific energy of the flow in the channel?
b) Is the flow subcritical or supercritical?
c) What is the alternate depth to the normal depth?
d) What is the critical depth in the channel?
(Answers E=3.07m, Fr=0.359, y=1.12m, yc=1.72m) Y(m)
0.4
0.6
0.8
1
1.116
1.2
1.4
1.6
1.72
1.8
2
2.2
2.4
2.6
2.8
2.95
3
3.2
3.4
3.6
3.8
4
4.2
4.4 A(m^2)
2.32
3.72
5.28
7
8.0709
8.88
10.92
13.12
14.28
15.48
18
20.68
23.52
26.52
29.68
32.155
33
36.48
40.12
43.92
47.88
52
56.28
60.72 Q^2 /(2*g*A^2)
23.674
9.208
4.571
2.600
1.956
1.616
1.069
0.740
0.625
0.532
0.393
0.298
0.230
0.181
0.145
0.123
0.117
0.096
0.079
0.066
0.056
0.047
0.040
0.035 E(m)
24.074
9.808
5.371
3.600
3.072
2.816
2.469
2.340
2.325
2.332
2.393
2.498
2.630
2.781
2.945
3.073
3.117
3.296
3.479
3.666
3.856
4.047
4.240
4.435 y Using Excel
5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 E Q.4) Water flows with a velocity of 3.0 m/s and a depth of 3.0 m in a rectangular channel. (a)
What is the change in water surface elevation produced by a gradual upward change in bed
elevation produced by a gradual upward change in bed elevation (hump) of 30 cm? (b) What
would be the water surface if there were a gradual drop of 30 cm?
(Answers 0.205m drop, 0.1m rise) 1
9 Y(m)
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.495
2.6
2.8
3
3.2
3.4
3.6
3.8
4
4.2
4.4
4.6 A(m^2) Q^2 /(2*g*A^2)
0.4
25.803
0.6
11.468
0.8
6.451
1
4.128
1.2
2.867
1.4
2.106
1.6
1.613
1.8
1.274
2
1.032
2.2
0.853
2.4
0.717
2.495
0.663
2.6
0.611
2.8
0.527
3
0.459
3.2
0.403
3.4
0.357
3.6
0.319
3.8
0.286
4
0.258
4.2
0.234
4.4
0.213
4.6
0.195 t
g 0
9.81 E(m)
26.203
12.068
7.251
5.128
4.067
3.506
3.213
3.074
3.032
3.053
3.117
3.158
3.211
3.327
3.459
3.603
3.757
3.919
4.086
4.258
4.434
4.613
4.795 y b
Q SBM:
E1=0.3+E2
E2=3.4590.30
E2=3.158m
y2=2.495m 5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5
E SBM:
E1+0.3=E2
E2=3.459+0.30
E2=3.758m
y2=3.4m Q.5) Referring to Problem 4, what is the maximum height of the setup that would not affect the
upstream flow condition? What is the minimum width that could exist with a 0.3m stepup
without changing the upstream condition, knowing that the upstream width is 6.0 m?
(Answers 0.428m, 2.105m, 5.64m) c) ...
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 Spring '08
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