Problem 4.82 - Problem 4.82 [Difficulty: 2] CS y x Given:...

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Problem 4.82 [Difficulty: 2] R x y x CS c d Given: Water flow through orifice plate Find: Force to hold plate 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 ρ V 2 2 A 2 V 1 2 A 1 + = From continuity QV 1 A 1 = V 2 A 2 = so V 1 Q A 1 = 20 ft 3 s 4 π 1 3 ft 2 × = 229 ft s = and V 2 V 1 A 1 A 2 = V 1 D d 2 = 229 ft s 4 1.5 2 × = 1628 ft s = NOTE: problem has an error: Flow rate should be 2 ft 3 /s not 20 ft 3 /s! We will provide answers to both Hence R x 200 lbf in 2 π 4in 2 4 × 1.94 slug ft 3 1628 ft s 2 π 1.5 in 2 4 × 229 ft s
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