local scour. There is to be no increase in water surface elevation upstream of the bridge at the
design discharge. The energy losses are expected to be small so they can be neglected.
At the bridge, the design flood discharge is 141.6 cms. The river is 30.48 m wide and has a uniform
flow depth of 3.05 m for the design discharge.
What is the maximum height of the structure that will not cause backwater at the
bridge at the design discharge?
The unit discharge (q) in the river at design flood discharge is:
Q
141.6
= 4.65 m3 / s / m
q =
=
W
30.48
The average velocity (V) is
Q
141.6
V =
=
= 1.52 m / s
A
92.96
The specific head (H) is
2
2
V + y = 1.52 + 3.05 = 3.17 m
H =
2g
19.62
As a first approximation assume no energy loss in the bridge reach. Then at the check dam, the
elevation of the total energy line is 3.17 m above the bed (Figure 2.43). At the dam:
Hmin + ∆Zmax = 3.17 m
Figure 2.43. Sketch of backwater curve over check dam.
That is, the dam can be built to a height of ∆Zmax which decreases the specific head at the dam to
Hmin. From Section 2.6.3 and Equation 2.147
3
Hmin = 2 yc
2.77
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