Problem 5.7 - Problem 5.7[Difficulty 2 Given y component of...

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Problem 5.7 [Difficulty: 2] Given: y component of velocity Find: x component for incompressible flow; Simplest x components? Solution: Basic equation: x ρ u ( ) y ρ v ( ) z ρ w ( ) t ρ 0 Assumptions: Incompressible flow ( ρ is constant) Flow is only in the x-y plane Hence x u y v 0 or x u y v y A x y x 2 y 2 A x x 2 y 2 A x y 2 y Integrating u x y ( ) x A x 3 3 x y 2 d
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