Problem 5.25 - Problem*5.25[Difficulty 2 Given Velocity...

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Problem *5.25 [Difficulty: 2] i h y U V ˆ Given: Velocity field for viscometric flow of Example 5.7: Find: (a) Stream function (b) Locate streamline that divides flow rate equally Solution: The flow is incompressible, so the stream function may be derived x v y u Governing Equations: (Definition of stream function) Integrating the velocity will result in the stream function: ψ y u d f x ( ) y U y h d f x ( ) U y 2 2 h f x ( ) Let ψ = 0 at y = 0, so f(x) = 0: ψ U y 2 2 h The stream function is a maximum value at y = h:
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