Problem 5.77 - Problem 5.77 Given: Stream function Find:...

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Problem 5.77 [Difficulty: 3] Given: Stream function Find: If the flow is incompressible and irrotational Solution: Basic equations: Incompressibility x u y v 0 Irrotationality x v y u 0 Note: The fact that ψ exists means the flow is incompressible, but we check anyway ψ xy ()x 6 15 x 4 y 2 15 x 2 y 4 y 6 Hence uxy () y ψ 60 x 2 y 3 30 x 4 y 6y 5 vxy x ψ 60 x 3 y 2 6x 5 30 x y 4 For incompressibility x 120 x y 3 120 x
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