Explanation We need to use continuity equation, ∂ u ∂ x + ∂ v ∂ y = 0 On integrating the continuity equation for v, We have, ∫ 0 h ∂ v ∂ y dy = − ∫ 0 h ∂ u ∂ x dy On integrating the continuity equation again for v, v ( h ) − v ( 0 ) = − ∫ 0 h ∂ u ∂ x dy Here, this is the case of no-slip condition, The velocity component is zero at the top and bottom of the boundary. i.e., At y = 0, v = 0 also, At y = h, v = 0 The continuity equation for the velocity reduced to, ∫ 0 h ∂ u ∂ x dy = 0 Equation of Leibnitz theorem from the textbook chapter 4, We have, d dx ∫ a ( x ) b ( x ) G ( x,y

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259696534

Author: Yunus A. Cengel Dr., John M. Cimbala

Publisher: McGraw-Hill Education

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Chapter 10, Problem 31P

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Chapter 10, Problem 30P

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Fluid Mechanics: Fundamentals and Applications

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d dx ∫ 0 h udy = 0 .

Solution Summary: The author explains the continuity equation for v. The velocity component is zero at the top and bottom of the boundary.

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Chapter 10 Solutions