Concept explainers
(a)
The dimension for the circular channel.
Answer to Problem 50P
The diameter of the circular channel is
The depth of the circular channel is
Explanation of Solution
Given Information:
The water flow rate is
Write the expression for the volume flow rate of the water.
Here, the manning coefficient is
Write the expression for the radius of the semicircle.
Here, the diameter of the semicircle is
Write the expression for the area of the circular channel.
Here, the diameter of the circle is
Write the expression for the perimeter of the circular channel.
Substitute
Write the expression for the flow depth of the circular channel.
Calculation:
Refer to table 13-1 "Mean values of the manning coefficient
Substitute
Substitute
Conclusion:
The diameter of the circular channel is
The depth of the circular channel is
(b)
The dimension for the rectangular channel.
Answer to Problem 50P
The dimension for the rectangular channel are-
The bottom breadth of the rectangular channel is
The depth of the rectangular channel is
Explanation of Solution
Given Information:
The water flow rate is
Write the expression for the area of the rectangular channel.
Here, the depth of the rectangular is
Write the expression for the flow depth of the rectangular channel.
Substitute
Write the expression for the perimeter of the rectangular channel.
Substitute
Substitute
Calculation:
Substitute
Substitute
Conclusion:
The bottom breath of the rectangular channel is
The depth of the rectangular channel is
(c)
The dimension for the trapezoidal channel.
Answer to Problem 50P
The bottom breath of the trapezoidal channel is
The depth of the trapezoidal channel is
Explanation of Solution
Given Information:
The water flow rate is
Write the expression for the area of the trapezoidal channel.
Here, the trapezoidal angle is
Write the expression for the flow depth of the trapezoidal channel.
Write the expression for the inclined height of the trapezoidal section.
Write the expression for the perimeter of the trapezoidal channel.
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
The bottom breath of the trapezoidal channel is
The depth of the trapezoidal channel is
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Chapter 13 Solutions
FLUID MECHANICS CONNECT ACCESS
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