Problem 6.111 - Problem 6.111 Given: Velocity potential...

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Problem 6.111 [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 = φ xy , ()x 6 15 x 4 y 2 15 x 2 y 4 + y 6 = uxy , () x φ , = , ( ) 60 x 3 y 2 6x 5 30 x y 4 = vxy , y φ , = , ( ) 30 x 4 y 60 x 2 y 3 6y 5 + = Hence x , y , + 0 = Hence flow is INCOMPRESSIBLE Hence u y ψ = so ψ , y , df x + = 20 x 3 y 3
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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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