Concept explainers
The expression for stream function.
The plot some streamlines of the flow.
Answer to Problem 63EP
The expression for the stream function is
The following figure represents the streamlines of the flow.
Explanation of Solution
Given information:
The incompressible flow filed for which the velocity
Write the expression for the velocity along
Here, the stream function along
Write the expression for the velocity along
Here, the stream function along
Write the expression for quadric stream function.
Here, the stream function is
Calculation:
Substitute
Integrate Equation (IV) with respect to
Here, the constant is
Substitute
Differentiate Equation (V) with respect to
Substitute
Substitute
Here, the constant is
Substitute
Substitute
Substitute
Substitute
Solve Equation (XII) by taking positive sign.
Solve Equation (XII) by taking negative sign.
The following table shows that the value of stream function with respect to value of
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Plot the streamlines on y x plane by using Equation (XII) and the range of
Figure-
The Figure
Conclusion:
The expression for the stream function is
The following figure represents the streamlines of the flow.
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Chapter 9 Solutions
Fluid Mechanics: Fundamentals and Applications
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