homework4_solns - Homework 4 Fluid Mechanics CE 3502 Fall,...

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Homework 4 Fluid Mechanics CE 3502 Fall, 2008 Due: November 6 5:30 in lab section drop box. FOR FULL CREDIT FOR EACH PROBLEM IN THIS ASSIGNMENT: SHOW ALL OF YOUR WORK; define all variables; justify all statements (1) For this siphon shown on the right, the elevations at A, B, C, and D are 30 m, 31 m, 28 m, and 27 m, respectively. The head loss between the inlet and point B is three quarters of the velocity head, and the head loss in the pipe itself between point B and the end of the pipe is one-half of the velocity head. For these conditions, what is the discharge and what is the pressure at point B? The pipe diameter = 0.25m. Assume laminar flow, so that α = 2.0. Find: v B and p B Solution: Start with energy conservation from A to C L T 2 C C C P 2 A A A h h g 2 v z p h g 2 v z p + + α + + γ = + α + + γ (1) atm C A p p p = = , so 0 p p C A = ; m 2 z z C A = ; 0 h , h T P = ; g 2 v 2 4 9 g 2 v g 2 v 2 1 g 2 v 4 3 h h h 2 B 2 B 2 B 2 B ESPANSION PIPE , L L = α + α + α = + = Use this information in equation (1): () s / m 95 . 2 9 / s / m 81 . 9 * m 8 v g 4 v 9 m 2 2 B 2 B = = = Or, if loss due to the sudden expansion into the reservoir is neglected g 2 v 2 4 5 g 2 v 2 1 g 2 v 4 3 h h 2 B 2 B 2 B PIPE , L L = α + α = = Use this information in equation (1): () s / m 96 . 3 5 / s / m 81 . 9 * m 8 v g 4 v 5 m 2 2 B 2 B = = = Now solve for energy conservation from A to B L T 2 B B B P 2 A A A h h g 2 v z p h g 2 v z p + + α + + γ = + α + + γ (2) GAGE , B GAGE , B GAGE , A p 0 p p = ; m 1 z z B A = ; 0 h , h T P = ; g 2 v 4 3 h h 2 B PIPE , L L α = = Use this information in equation (2):
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homework4_solns - Homework 4 Fluid Mechanics CE 3502 Fall,...

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