Problem 4.90 - Problem 4.90 [Difficulty: 2] y x Ry Rx CS...

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Problem 4.90 [Difficulty: 2] R x CS R y y x Given: Data on nozzle assembly Find: Reaction force Solution: Basic equation: Momentum flux in x and y directions Assumptions: 1) Steady flow 2) Incompressible flow CV 3) Uniform flow For x momentum R x V 2 cos θ () ρ V 2 A 2 = ρ V 2 2 π D 2 2 4 cos θ = From continuity A 1 V 1 A 2 V 2 = V 2 V 1 A 1 A 2 = V 1 D 1 D 2 2 = V 2 2 m s 7.5 2.5 2 × = V 2 18 m s = Hence R x 1000 kg m 3 18 m s 2 × π 4 × 0.025 m 2 × cos 30 deg × Ns 2 kg m × = R x 138 N = For y momentum R y p 1 A 1 W ρ Vol g V 1 ρ V 1 A 1 V 2 sin θ ρ V 2 A 2 = R y p 1 π D 1 2 4 W + ρ Vol g + ρπ 4 V 1 2 D 1 2 V 2 2 D 2 2 sin θ + = where W 4.5 kg 9.81 × m s
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