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.

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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