Problem 4.139 - Problem 4.139 Given: Jet impacting a...

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Problem 4.139 [Difficulty: 4] Given: Jet impacting a splitter vane Find: Mass flow rate ratio; new speed U Solution: Apply momentum equation to inertial CV Assumptions: No pressure force; neglect water mass on vane; steady flow wrt vane; uniform flow; no change of speed wrt the vane Basic equation Given data V2 5 m s = A 7.85 10 5 m 2 = U1 0 m s = θ 30 deg = ρ 999 kg m 3 = For constant speed wrt the vane, the jet velocity at each location is VU For no vertical force, y momentum becomes 0v 1 m 1 () v 2 m 2 + v 3 m 3 + = where v i and m i are the vertical components of velocity and mass flow rates, respectively, at the inlet and exits, wrt the vane coordinates Hence 00 VU m 2 + ( ) sin θ m 3 = or m 2 m 3 sin θ = m 2 m 3 sin θ = 1 2 = Note that m 1 ρ A = m 1 1.18 kg s = and m 1 m 2 m 3 + = so m 1 m 3 sin θ m 3 + = m 3 m 1 1 1 sin θ + = m 3 m 1 2 3 = m 3 0.784 kg s = m 2 0.392 kg s
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