Water is discharged from a 5-rn-deep lake into a finished concrete channel with a bottom slope of 0.004 through a sluice gate with a 0.7-m-high opening at the bottom. Shortly after supercritical uniform-flow conditions are established, the water undergoes a hydraulic jump. Determine the flow depth, velocity, and Froude number after the jump. Disregard the bottom slope when analyzing the hydraulic jump.
The flow depth after hydraulic jump.
The velocity after hydraulic jump.
The Froude number after hydraulic jump.
Answer to Problem 144P
The flow depth after hydraulic jump is
The velocity after hydraulic jump is
The Froude number after hydraulic jump is
Explanation of Solution
Given information:
The depth of the lack is
The below figure represent the depths of flow.
Figure-(1)
Write the expression of depth ratio.
Here, the depth of lack is
Write the expression of discharge.
Here, the coefficient of discharge is
Write the expression of flow rate in the form of manning equation.
Here, the cross section are is
Write the expression of hydraulic radius.
Here, the flow depth is
Substitute
Write the expression of flow velocity when undergo a hydraulic jump.
Write the expression of Froude number when undergo a hydraulic jump.
Write the expression of flow depth after hydraulic jump.
Write the expression of velocity after hydraulic jump.
Write the expression of Froude number after hydraulic jump.
Calculation:
Substitute
Refer Figure 13.46 "Discharge coefficient for drowned and free discharge from underflow gates" to find the value of
Consider width is
Substitute
Refer table 13.1 "Mean values of the manning coefficient
Consider the cross section area of the wall is
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The flow depth after hydraulic jump is
The velocity after hydraulic jump is
The Froude number after hydraulic jump is
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Chapter 13 Solutions
Fluid Mechanics: Fundamentals and Applications
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