Explanation Given information: The value of upper streamline function is 4.35 m 2 / s , the average velocity is 11.5 m / s and the final value of stream function is 2.03 m 2 / s . Write the expression for the total volume flow rate per unit width through upper branch. V ˙ W = ψ 1 − ψ 3 ............ (I) Here, the upper line stream function is ψ 1 , the stream function of third pipe is ψ 3 , the total volume flow rate per unit width through upper branch is V ˙ W . Write the expression for the cross- sectional area of the duct. A = W h ............ (II) Here, the cross- sectional area of the duct is A , the width of the duct is W and the height of the duct is h . Write the expression for the volume flow rate. V ˙ = V A ............ (III) Here, the average velocity is V and the volume flow rate is V ˙ . Calculation: Substitute W h for A in Equation (IV). V ˙ = V W h V ˙ W = V h ............. (V) Substitute 4.35 m 2 / s for ψ 1 and 2

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Chapter 9, Problem 62P

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The height of the duct in cm.

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The height of the duct in cm .

Solution Summary: The author explains the value of the upper streamline function, the average velocity, and the final value for the stream function.

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The height of the duct in cm.

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