Explanation Given information: The velocity field of the flow u r is U ∞ ( 1 − R 2 r 2 ) cos θ and u θ is U ∞ ( 1 + R 2 r 2 ) sin θ . Write the expression for the continuity equation. 1 r ∂ ( r u r ) ∂ r + 1 r ∂ ( u θ ) ∂ θ = 0 ........... (I) Here, component of the velocity is u r and component of the velocity is u θ . Substitute U ∞ ( 1 − R 2 r 2 ) cos θ for u r and U ∞ ( 1 + R 2 r 2 ) sin θ for u θ in the Equation (I). 1 r ∂ ( r ( U ∞ ( 1 − R 2 r 2 ) cos θ ) ) ∂ r + 1 r ∂ ( U ∞ ( 1 + R 2 r 2 ) sin θ ) ∂ θ = 0 U ∞ cos θ r ∂ ∂ r ( r − R 2 r ) + U ∞ r ( 1 + R 2 r 2 ) ∂ ∂ θ ( sin θ ) = 0 1 r U ∞ ( 1 + R 2 r 2

Fluid Mechanics: Fundamentals and Applications

4th Edition

ISBN: 9781259877827

Author: CENGEL

Publisher: MCG

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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 42P

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Whether velocity field satisfies the continuity equation.

The stream function corresponding to the velocity field.

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Chapter 9, Problem 41P

Chapter 9, Problem 44P

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Whether velocity field satisfies the continuity equation. The stream function corresponding to the velocity field.

Solution Summary: The author explains how the velocity field satisfies the continuity equation. The stream function is psi =U_infty.