Consider uniform water flow in a wide channel made of unfinished concrete laid on a slope of 0.0022. Now water flows over a 15-cm-high bump. If the flow over the bump is exactly critical (Fr = 1), determine the flow rate and the flow depth over the bump per m width.
The flow rate.
The flow depth over the bump per
Answer to Problem 119P
The flow rate is
The flow depth is
Explanation of Solution
Given information:
The slope of the wide channel made of unfinished concrete is
The flow is steady and uniform, the channel is sufficiently wide so that the end effects are negligible, the frictional effects during the flow over the bump are negligible bottom slope is constant, roughness coefficient is constant along the channel, the width of the water channel is assumed to be
Write the expression for the flow rate for which the hydraulic radius is equal to the flow depth from the manning equation.
Here, the manning coefficient for an open channel of unfinished concrete is
Write the expression for the critical depth corresponding to the flow rate.
Here, the water flow rate through the channel per meter width is
Write the expression for the average flow velocity.
Write the expression for the specific energy before the bump.
Here, the average flow velocity is
Write the expression for the critical specific energy.
As, the critical specific energy is equal to the specific energy after the bump because the critical depth corresponding to the flow rate is equal to the depth of the flow after the bump.
Here, the critical depth of the flow is
Write the expression for the specific energy on the bump.
Here, the height of the bump is
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
By hit and trial method.
Substitute
Substitute
Conclusion:
The flow rate is
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Chapter 13 Solutions
Fluid Mechanics Fundamentals And Applications
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