Problem 4.77 - Problem 4.77[Difficulty 2 y x CS Rx Given...

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Problem 4.77 [Difficulty: 2] R x y x CS c d Given: Water flow through elbow Find: Force to hold elbow Solution: Basic equation: Momentum flux in x direction for the elbow Assumptions: 1) Steady flow 2) Incompressible flow 3) Uniform flow Hence R x p 1g A 1 + p 2g A 2 + V 1 ρ V 1 A 1 () V 2 ρ V 2 A 2 = R x p 1g A 1 p 2g A 2 ρ V 1 2 A 1 V 2 2 A 2 + = From continuity V 2 A 2 V 1 A 1 = so V 2 V 1 A 1 A 2 = V 1 D 1 D 2 2 = V 2 0.8 m s 0.2 0.04 2 = V 2 20 m s = Hence R x 350 10 3 × N m 2 π 0.2 m 2 4 × 75 10 3 × N m 2 π 0.04 m 2 4 ×
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