Concept explainers
Repeat Prob. 13-142 for a velocity of 3.2 ms after the hydraulic jump.
The flow rate of water through the gate per meter width.
The flow depth
The energy dissipation ratio of the jump.
Answer to Problem 143P
The flow rate of water through the gate per meter width is
The flow depth
The energy dissipation ratio of the jump is
Explanation of Solution
Given information:
Water is flowing through a sluice gate, the velocity of water before reaching the gate is
The flow is considered per meter width so
The figure below shows the flow.
Figure-(1)
Write the expression for the cross sectional area at
Here, the width is
Write the expression for the cross sectional area at
Here, the velocity at section
Write the expression for the conservation of mass.
Here, the velocity at section (3) is
Write the expression for the Froude number at section
Here, the acceleration due to gravity is
Write the expression for the flow depth.
Write the expression for the conservation of mass.
The flow depth at section (2) is
Write the expression for the Froude number at section
Write the expression for the head loss during jumping.
Here, the velocity at section (2) is
Write the expression for the specific energy before the jump.
Write the expression for the dissipation ratio.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Here Froude number is greater than
Substitute
Substitute
Substitute
Conclusion:
The flow rate of water through the gate per meter width is
The flow depth
The energy dissipation ratio of the jump is
Want to see more full solutions like this?
Chapter 13 Solutions
Fluid Mechanics: Fundamentals and Applications