Problem 4.151 - Problem 4.151 [Difficulty: 4] Given: Vaned...

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Problem 4.151 [Difficulty: 4] Given: Vaned cart being hit by jet Find: Jet speed to stop cart in 1s and 2 s; distance traveled Solution: Apply x momentum Assumptions: 1) All changes wrt CV 2) Incompressible flow 3) Atmospheric pressure in jet 4) Uniform flow 5) Constant jet area Given data ρ 999 kg m 3 = M5 k g = D3 5 m m = θ 60 deg = U 0 5 m s = A π 4 D 2 = A 962 mm 2 = Then a rf M u 1 ρ VU + () A [] u 2 ρ + A + = where a rf dU dt = u 1 + = and u 2 + cos θ = Hence dU dt M ρ + 2 A ρ + 2 A cos θ = ρ + 2 A 1 cos θ = or dU dt M ρ + 2 A 1 cos θ = (1) dV U + + 2 ρ 1 cos θ A M dt = Note that V is constant, so dU = d(V+U), separating variables Integrating from U 0 at t = 0 to U = 0 at t 1 V 1 0 + ρ 1 cos θ A M t = Solving for V U 0 VV U 0 + ρ 1 cos θ A t M = V 2 0 + MU 0 ρ 1 cos θ A t Hence V U 0 2 U 0 2 4 U 0 M ρ A 1 cos θ t + + =
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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 4.151 - Problem 4.151 [Difficulty: 4] Given: Vaned...

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