Concept explainers
The expression for the stream function.
Answer to Problem 64P
The stream function is
Explanation of Solution
Given information:
The velocity component in
Write the expression for velocity coordinates along
Write the expression for continuity equation for incompressible flow.
Here, the change in distance along
Write the expression for the radial velocity component along
Here, the partial derivative of the stream function with respect to the change in distance along
Write the expression for velocity coordinates along
Here, the partial derivative of the stream function with respect to the change in distance along
Calculation:
Substitute
Integrate Equation (II) with respect to
Here, the constant is
Substitute
Substitute
Substitute
Integrate Equation (VII) with respect to
Substitute
Differentiate Equation (X) with respect to
Here, the constant is
Equate Equation (XI) with Equation (V).
Integrate Equation (XII) with respect to
Here, the constant is
Substitute Equation (XIII) in Equation (IX).
Conclusion:
The stream function is
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Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
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