Problem 6.108 - Problem 6.108 [Difficulty: 2] Given: Stream...

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Problem 6.108 [Difficulty: 2] Given: Stream function Find: Velocity field; Show flow is irrotational; Velocity potential Solution: Basic equations: Incompressibility because ψ exists u y ψ = v x ψ = u x φ = v y φ = Irrotationality x v y u 0 = We have ψ xy , ()x 6 15 x 4 y 2 15 x 2 y 4 + y 6 = 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 = x , y , 0 = Hence flow is IRROTATIONAL Hence u x φ = so φ , x , d fy +
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