Explanation Given Information: The water flow rate is 0.6 m 3 / s and the bottom slope is 0.0015 . Write the expression for the area of the trapezoidal channel. A c = y ( b + y tan θ ) ...... (I) Here, the trapezoidal angle is θ , the depth of the trapezoidal is y and the bottom breath of the trapezoidal channel is b . Write the expression for the flow depth of the trapezoidal channel. y = 3 2 b ...... (II) Write the expression for the inclined height of the trapezoidal section. c = y sin θ ...... (III) Write the expression for the perimeter of the trapezoidal channel. P = b + 2 c ...... (IV) Write the expression for the radius of the semicircle. R h = A c P ...... (V) Here, the diameter of the semicircle is D . Write the expression for the volume flow rate of the water. Q = a n A c R h 2 / 3 S o 1 / 2 ...... (VI) Here, the manning coefficient is n , the constant is a , the hydraulic radius is R h , the bottom slope is S o and the cross sectional flow area is A c . Calculation: Substitute 60 ° for θ and 3 2 b for y in Equation (III). c = 3 2 b sin 60 ° = 3 2 b 3 2 = b Substitute 60 ° for θ and 3 2 b for y in Equation (I). A c = 3 2 b ( b + 3 2 b tan 60 ° ) = 3 2 b ( b + 3 2 b 3 ) = 3 3 4 b 2 Substitute b for c in Equation (IV)

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Author: CENGEL

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Chapter 13, Problem 159P

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The width of the channel for the best cross section.

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Chapter 13, Problem 158P

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Chapter 13 Solutions

FLUID MECHANICS FUNDAMENTALS+APPS

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The width of the channel for the best cross section.

Solution Summary: The author explains the width of the channel for the best cross section, and the bottom slope, which is 0.0015.

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Chapter 13 Solutions