Problem 4.172 - Problem 4.172 [Difficulty: 4] y x CS (moves...

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Problem 4.172 [Difficulty: 4] CS (moves at speed U) c d F f R y y x Given: Water jet striking moving vane Find: Plot of terminal speed versus turning angle; angle to overcome static friction Solution: Basic equations: Momentum flux in x and y directions Assumptions: 1) Incompressible flow 2) Atmospheric pressure in jet 3) Uniform flow 4) Jet relative velocity is constant Then F f Ma rfx u 1 ρ V 1 A 1 () u 2 ρ V 2 A 2 + = VU ρ A [] ( ) cos θ ρ A + = a rfx ρ 2 A 1 cos θ F f M = (1) Also R y Mg v 1 ρ V 1 A 1 v 2 ρ V 2 A 2 + = 0V U ( ) sin θ ρ A + = R y ρ 2 A sin θ + = At terminal speed a rfx = 0 and F f = μ k R y . Hence in Eq 1 0 ρ t 2 A 1 cos θ μ k ρ t 2 A sin θ + M = ρ t 2 A 1 cos θ μ k sin θ M μ k g = or t μ k M g ρ A 1 cos θ μ k sin θ = U t V μ k M g ρ A 1 cos θ μ k sin θ = The terminal speed as a function of angle is plotted below; it can be generated in Excel
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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Problem 4.172 - Problem 4.172 [Difficulty: 4] y x CS (moves...

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