The upstream flow rate per unit width (q) is:
Q 141.6
q=
=
= 4.65 cfs / ft
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
1.52
H= V + y =
+ 3.05 = 3.17 m
2g
19.62
According to Section 2.6.2 the maximum unit discharge for a given specific head (specific head
equals to a constant) occurs at the critical depth yc where the Froude number is 1. From
Equation 2.149 the critical depth yc for this specific head is:
1/ 3
2
2 V2
qmax
2
c
yc =
= H=
g
2g
3
1/ 2
1/ 2
2 3
3
2
qmax = g H
= 9.81 x 3.17
= 9.63 m3 / s / m
3
3
Therefore, the width of the channel can be contracted until the unit discharge q is a maximum.
The minimum width (maximum constriction) is:
Q
141.6
=
=
= 14.70 m
W min
qmax
9.63
and the maximum constriction is 30.48 -14.70 = 15.8 m
This contraction causes the flow to go to critical. This results in an undulating hydraulic jump
downstream. Also, when energy losses are considered there will be some backwater at the
constriction.
2.14.5 PROBLEM 5 Maximum Water Surface Elevation Upstream of a Grade Control
Structure Without Backwater (Neglecting Energy Losses)
A low grade control structure (check dam) is to be placed across a stream downstream of a
highway bridge. The stream is degrading. The purpose of the check dam is to maintain the
elevation of the water surface at the bridge, cause deposition of bed material, protect the abutments
and piers from long term degradation and contraction scour and increase the elevation of the be for
2.76
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