Problem 6.110

# 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 x y , ( ) x 5 10 x 3 y 2 5 x y 4 + x 2 y 2 + = u x y , ( ) x φ x y , ( ) = u x y , ( ) 30 x 2 y 2 5 x 4 2 x + 5 y 4 = v x y , ( ) y φ x y , ( ) = v x y , ( ) 20 x 3 y 20 x y 3 2 y = Hence x u x y , ( ) y v x y , ( ) + 0 = Hence flow is INCOMPRESSIBLE Hence u y ψ = so ψ x y , ( ) y u x y
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