To determine the depth of flow upstream of the dam (y) solve the specific head equation (Equation
2.137)
q2
0.93 2
H=
+y=
= 1.89 m
2gy 2
19.62 y 2
or
0.93 2
3
2
y - 1.89 y +
=0
19.62
The solution is
y = 1.87 m
As the normal depth is only 1.52 m, the backwater is
∆y = 1.87 - 1.52 = 0.35 m
That is, the depth upstream of the dam is increased 0.35 m by the 1.22 m high dam when the flow
is 28.32 cms.
2.15 SOLVED PROBLEMS OPEN CHANNEL FLOW (ENGLISH)
2.15.1 PROBLEM 1 Evaluation of Correction Factors α and β
Calculate the correction factors α and β for a cross-section given the discharge measurement
during the peak flood event for the year. From Table 2.8, the following values are obtained:
Q
=
5,370 cfs
1,485 ft2
A
=
W
=
163 ft
21,070 ft4/sec2
=
Vi∆Qi
85,500 ft5/sec3
Vi 2∆Qi
=
coefficient G of 3.27. If the value of D65 is used for ks, then for yo = 12.8 ft (the maximum depth)
y0
12.8
(304.8) ≅ 8,700
=
0.45
ks
and for yo = 1.1 ft (the smallest non-zero depth)
y0
1.1
(304.8) ≅ 750
=
0.45
ks
2.79
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