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Solutions6 - Problem 5.5[2 Given x component of velocity...

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Problem 5.5 [2] Given: x component of velocity Find: y component for incompressible flow; Valid for unsteady? How many y components? Solution: Basic equation: x ρ u ( ) y ρ v ( ) + z ρ w ( ) + t ρ + 0 = Assumption: Incompressible flow; flow in x-y plane Hence x u y v + 0 = or y v x u = x x 3 3 x y 2 ( ) = 3 x 2 3 y 2 ( ) = Integrating v x y , ( ) y 3 x 2 3 y 2 ( ) d = 3 x 2 y y
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