
Concept explainers
The flow rate through the channel and the equivalent manning's coefficient.

Answer to Problem 54P
The flow rate is
Explanation of Solution
Given Information:
The figure below shows the cross -section of the channel.
Figure-(1)
The bottom slope of the channel is
Write the expression for flow rate.
Here, the manning's coefficient for channel 1 is
Write the expression for area of channel 1.
Here, the area of section a is
Write the expression to calculate the area of channel a.
Here, the breadth of section a is
Write the expression to calculate the area of channel b.
Here, the breadth of section b is
Write the expression to calculate the area of channel c.
Here, the breadth of section c is
Write the expression to calculate the area of channel d.
Here, the breadth of section d is
Write the expression to calculate the perimeter of the concrete channel.
Write the expression to calculate the perimeter of the light brush channel.
Here, the breadth of the light brush channel is
Write the expression to calculate the total perimeter.
Write the expression to calculate the equivalent hydraulic radius.
Write the expression to calculate the area of light brush channel.
Write the expression for total area.
Write the expression for hydraulic radius for channel 1.
Write the expression for the hydraulic radius for channel 2.
Write the expression for equivalent flow rate.
Here, the equivalent manning's coefficient is
Calculation:
Substitute
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Refer to the Table (13.1), "Mean values of Manning coefficient for water flow open channels" to obtain the value of
Substitute
Substitute
Conclusion:
The flow rate is
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Chapter 13 Solutions
Fluid Mechanics: Fundamentals and Applications
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