Problem 6.107 - Problem 6.107 [Difficulty: 2] Given: Stream...

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Problem 6.107 [Difficulty: 2] Given: Stream function Find: Find A vs B if 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 , ()A x 3 Bxy 2 x 2 + y 2 () + = uxy , y ψ , = , B 2 y 2x y = vxy , x ψ , = , 3 A x 2 By 2 + = x , y , 2 x 3A B + = Hence flow is IRROTATIONAL if B3 A = Hence u x φ = so φ , x , d fy + = 2B
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