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Unformatted text preview: ME 309 Fall 2008 Section 2 (Merkle) Homework # 24 Due Mon 27 Oct 2008 Problem 241 . Water at 300 K flows from a higher reservoir to a lower one through a 10 mm diameter cast iron pipe that is 50 m in length. The average velocity is measured to be 10 m/ s. The entrance to the pipe is a squareedged entrance. The exit is a sudden expansion. Estimate the height of the free surface of the upper reservoir. Take α = 1 throughout. Solution: Given: density, viscosity, pipe diameter, pipe length, pipe type, and entrance and exit characteristics; Assumptions: incompressible flow, mechanical energy equation holds, alpha = 1. Find : Flow rate Analysis: Apply mechanical energy equation: pump m l h h h gz U p gz U p Δ + = + + + + ∑ ∑ 2 2 2 2 2 1 2 1 1 1 2 2 α ρ α ρ No pumping, last term drops out. Density: 998 kg/m 3 μ = 0.001 N.s/m 2 Cast iron pipe, ε = 0.26 mm Table 8.1, p330. Minor losses: Squareedged entrance K ent = 0.5 (Table 8.2, p334, or from AR= 0 on Fig. 8.15) Sudden exit (area ratio 0 from Fig. 8.15) a K exit = 1.0 Apply mechanical energy equation from free surface in upper reservoir to pipe inlet: (Note: It’s okay to apply mechanical energy equation from surface to surface at the outset—I’ve done it in increments to be sure things are clear.) (No losses in this region; velocity at surface is zero: 2 1 2 1...
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 Spring '08
 MERKLE
 Fluid Dynamics, Kinetic Energy, Orders of magnitude, pipe inlet, mechanical energy equation

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