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Problem 4.61 - Problem 4.61 Given Data on flow through a...

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Problem 4.61 [Difficulty: 3] Given: Data on flow through a bend Find: Find net momentum flux Solution: 0 = CS A d V r r ρ Basic equations Momentum fluxes: mf x = mf y = Assumptions: 1) Steady flow 2) Incompressible flow Evaluating mass flux at 1, 2 and 3 0 h 1 y V 1 y ( ) w d V 2 w h 2 + V 3 w h 3 + 0 = or V 3 h 3 0 h 1 y V 1 y ( ) d V 2 h 2 = 0 h 1 y V 1max y h 1 d V 2 h 2 = V 1max h 1 h 1 2 2 V 2 h 2 = Hence V 1max 2 h 1 V 3 h 3 V 2 h 2 + ( ) = Using given data V 1max 3.8 m s = For the x momentum, evaluating at 1, 2 and 3 mf x 0 h 1 y V 1 y ( ) ρ V 1 y ( ) w d V 3 cos θ ( ) ρ V 3 h 3 w + = mf x 0 h 1 y V 1max y h 1 2 ρ w d V 3 2 ρ h 3 cos θ ( ) w + = V 1max 2 h 1 2 h 1 3 3 ρ w V 3
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