Problem 4.157 - Problem 4.157[Difficulty 2 Given Mass...

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Problem 4.157 [Difficulty: 2] Given: Mass moving betweem two jets Find: Time st slow to 2.5 m/s; plot position; rest position; explain 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 The given data is ρ 999 kg m 3 = M5 k g = V2 0 m s = U 0 10 m s = U 2.5 m s = A 100 mm 2 = Then a rf M u 1 ρ VU () A [] u 2 ρ + A + u 3 m 3 + = where a rf dU dt = u 1 = u 2 + = and u 3 0 = Hence dU dt M ρ A 2 + 2 + = 4 ρ A V U = Separating and integrating dU U 4 ρ A V M dt = or ln U ( ) ln U 0 4 ρ A V M t = UU 0 e 4 ρ A V M t = (1) Solving for t t M 4 ρ V A
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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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