Explanation Given information: The flow is steady, two-dimensional and incompressible and flow is from right to left when ψ increases in z-direction. Write the expression for stream function for velocity u -component. u = − ∂ ψ ∂ z ...... (I) Here, velocity component is u , stream function is ψ and position coordinate is z . Write the expression for stream function for velocity w -component. w = ∂ ψ ∂ x ...... (II) Here, velocity component is w and position coordinate is x . Write the expression for continuity equation. ∂ u ∂ x + ∂ w ∂ z = 0 ......(III) Calculation: Substitute ∂ ψ ∂ x for w and − ∂ ψ ∂ z for u in Equation (III)

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ISBN: 2810022150991

Author: CENGEL

Publisher: MCG

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Fluid Kinematics

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 120P

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The stream function.

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Chapter 9, Problem 119P

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9-94: Repeat Prob. 9–93, but let the inner cylinder be stationary and the outer cylinder rotate at angular velocity ?o. Generate an exact solution for u?(r) using the step-by-step procedure discussed in this chapter. I have done 9-93 and know it is on here already but here is the problem statement for it: 9-93: An incompressible Newtonian liquid is confined between two concentric circularcylinders of infinite length— a solid inner cylinder of radius Ri and a hollow, stationaryouter cylinder of radius Ro (Fig. P9–93; the z-axis is out ofthe page). The inner cylinder rotates at angular velocity ?i .The flow is steady, laminar, and two-dimensional in ther? -plane. The flow is also rotationally symmetric, meaningthat nothing is a function of coordinate ? (u? and P arefunctions of radius r only). The flow is also circular,meaning that velocity component ur = 0 everywhere.Generate an exact expression for velocity component u? asa function of radius r and the other parameters in theproblem.…

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An incompressible Newtonian liquid is confined between two concentric circular cylinders of infinite length— a solid inner cylinder of radius Ri and a hollow, stationary outer cylinder of radius Ro. The inner cylinder rotates at angular velocity ?i. The flow is steady, laminar, and two-dimensional in the r?-plane. The flow is also rotationally symmetric, meaning that nothing is a function of coordinate ? (u? and P are functions of radius r only). The flow is also circular, meaning that velocity component ur = 0 everywhere. Generate an exact expression for velocity component u? as a function of radius r and the other parameters in the problem. You may ignore gravity.

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The stream function.

Solution Summary: The author writes the expression for stream function for velocity u -component and for continuity equation.

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