Problem 5.41 - Problem 5.41[Difficulty 3 Given x component...

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Problem 5.41 [Difficulty: 3] Given: x component of velocity field Find: Simplest y component for incompressible flow; Acceleration of particle at (1,3) Solution: Basic equations u y ψ v x ψ We are given uxy ()A x 5 10 x 3 y 2 5x y 4  Hence for incompressible flow ψ xy () y u d y Ax 5 10 x 3 y 2 y 4 d 5 y 10 3 x 3 y 3 5 fx vxy x ψ x y x 5 y 10 3 x 3 y 3 5 A 4 y 10 x 2 y 3 y 5 Fx Hence A 4 y 10 x 2 y 3 y 5 where F(x) is an arbitrary function of x The simplest is A 4 y 10 x 2 y 3 y 5 For this flow a x u x u v y u a x 5 10 x 3 y 2 y 4 x 5 10 x 3
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