Problem 6.105 - Problem 6.105[Difficulty 2 Given Stream...

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Problem 6.105 [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 = ψ x y , ( ) x 5 10 x 3 y 2 5 x y 4 + = u x y , ( ) y ψ x y , ( ) = u x y , ( ) 20 x y 3 20 x 3 y = v x y , ( ) x ψ x y , ( ) = v x y , ( ) 30 x 2 y 2 5 x 4 5 y 4 = x v x y , ( ) y u x y , ( ) 0 = Hence flow is IRROTATIONAL Hence u x φ
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