Concept explainers
A sluice gate with free outflow is used to control the discharge rate of water through a channel Determine the flow rate per unit width when the gate is raised to yield a gap of 50 cm and the upstream flow depth is measured to be 2.8 m. Also determine the flow depth and the velocity downstream.
The flow rate per unit width.
The flow depth.
The velocity for downstream.
Answer to Problem 140P
The flow rate per unit width is
The flow depth is
The velocity for downstream is
Explanation of Solution
Given Information:
The height for the sluice gate is
Write the expression for the flow depth.
Here, the height of the sluice gate is
Write the expression for the discharge rate.
Here, the discharge coefficient is
Write the expression for the cross- sectional area at upstream.
Write the expression for the cross -sectional area at downstream.
Write the expression for the upstream velocity of the fluid.
Write the expression for the downstream velocity of the fluid.
Write the expression for the upstream specific energy.
Write the expression for the downstream specific energy.
Calculation:
Substitute
Refer to Figure 13.44 "Discharge coefficient for the drowned and free discharge from underflow gates" to obtain the coefficient of the discharge as
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Since, the specific energy at downstream is equal the specific stream at upward stream hence
Substitute
Substitute
Substitute
Conclusion:
The flow rate per unit width is
The flow depth is
The velocity for downstream is
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Chapter 13 Solutions
Fluid Mechanics: Fundamentals and Applications
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