Explanation Given information: The volume flow rate per unit width through the circle having a radius ( r ) is ∨ ˙ L . The source of the line is at the origin. The stream function which is along the x direction in positive direction is 0 . Here, the width is L and the volume flow rate is ∨ ˙ . The x axis and the y axis are dividing the circle in 4 equal parts which are given below. Positive x axis ( θ = 0 ) and positive y axis ( θ = 90 ° ) . Positive y axis ( θ = 90 ° ) and negative x axis ( θ = 180 ° ) . Negative x axis ( θ = 180 ° ) and negative y axis ( θ = 270 ° ) . Negative y axis ( θ = 270 ° ) and positive x axis ( θ = 0 ) . The volume flow rate is divided equally between them. Hence, the volume flow rate between positive y axis and positive x axis equals to the quarter of the total flow rate ( 1 4 ∨ ˙ L ) . This volume flow rate per unit width in between two stream lines becomes equal to the difference in the values for the two stream lines. Write the expression for the difference in values of two streamlines. ψ ( θ = 90 ° ) − ψ x ( θ = 0 ) = 1 4 ∨ ˙ L ........... (I) Here, the stream function along the positive y axis is ψ ( θ = 90 ° ) . The volume flow rate in between the negative x axis and positive x axis is equal to the half of the total volume flow rate which is given as ( 1 2 ∨ ˙ L )

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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The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid stat…

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Chapter 9, Problem 73P

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The value of the ψ along positive y axis where θ=90°.

The value of the ψ along negative x axis where θ=180°.

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Chapter 9, Problem 72P

Chapter 9, Problem 74P

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The value of the ψ along positive y axis where θ = 90 ° . The value of the ψ along negative x axis where θ = 180 ° .

Solution Summary: The author compares the value of the psi along positive and negative x axis, and the volume flow rate per unit width through the circle having a radius.

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The value of the ψ along positive y axis where θ=90°.

The value of the ψ along negative x axis where θ=180°.

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Chapter 9 Solutions

The value of the ψ along positive y axis where θ = 90 ° . The value of the ψ along negative x axis where θ = 180 ° .

Solution Summary: The author compares the value of the psi along positive and negative x axis, and the volume flow rate per unit width through the circle having a radius.

Concept explainers

Videos

The value of the ψ along positive y axis where θ=90°. The value of the ψ along negative x axis where θ=180°.

Want to see the full answer?

Chapter 9 Solutions

The value of the ψ along positive y axis where θ=90°.

The value of the ψ along negative x axis where θ=180°.