Problem 5.36 - Problem*5.36[Difficulty 3 U h y x Given...

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Problem *5.36 [Difficulty: 3] U x y h Given: Linear velocity profile Find: Stream function ψ ; y coordinate for half of flow Solution: Basic equations: u y ψ v x ψ and we have uU y h v0 Assumption: Incompressible flow; flow in x-y plane Check for incompressible x u y v 0 x U y h 0 y 0 0 Hence x u y v 0 Flow is INCOMPRESSIBLE Hence y h y ψ ψ xy () y U y h d Uy 2 2h fx and x ψ ψ x 0 d gy Comparing these () 0 and 2 The stream function is
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