Problem 6.110 - Problem 6.110 Given: Velocity potential...

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Problem 6.110 [Difficulty: 2] Given: Velocity potential Find: Show flow is incompressible; Stream function Solution: Basic equations: Irrotationality because φ exists u y ψ = v x ψ = u x φ = v y φ = Incompressibility x u y v + 0 = We have φ xy , ()x 5 10 x 3 y 2 5x y 4 + x 2 y 2 + = uxy , () x φ , = , ( ) 30 x 2 y 2 4 2x + 5y 4 = vxy , y φ , = , ( ) 20 x 3 y 20 x y 3 2y = Hence x , y , + 0 = Hence flow is INCOMPRESSIBLE Hence u y ψ = so ψ , y , df x + = 10 x 2 y 3 4
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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