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Problem 5.29 - Problem*5.29[Difficulty 3 Given Velocity...

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Problem *5.29 [Difficulty: 3] Given: Velocity field Find: Whether it's 1D, 2D or 3D flow; Incompressible or not; Stream function ψ Solution: Basic equation: x ρ u () y ρ v z ρ w t ρ 0 u z ψ w x ψ Assumption: Incompressible flow; flow in x-z plane (v = 0) Velocity field is a function of x and z only, so is 2D Check for incompressible x u z w 0 x z3x 2 z 2  6x z z xx 2 3z 2 6 x z Hence x u z w 0 Flow is INCOMPRESSIBLE Hence uz 3 x 2 z 2 z ψ ψ xz z 2 z 2 d 3 2 x 2 z 2 1 4 z 4 fx and wxx 2 2 x ψ ψ x 2 2
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