HW_23_Soln - ME 309 Fall 2008 Section 2(Merkle Homework 23...

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ME 309 Fall 2008 Section 2 (Merkle) Homework # 23 Due Fri 24 Oct 2008 Problem 23-1 . Water flows through a horizontal, 10- mm smooth tube with a flow rate of 0.060 kg/s . Assuming that the flow is fully developed, calculate the average velocity, the Reynolds number, the approximate maximum velocity, the friction factor, the pressure drop for a 50 m length of pipe and the pumping power in watts needed to maintain the flow. Take the density of water as 995 kg.m 3 and the viscosity as 0.003 ns/m 2 . Solution: Given: mass flow rate, density, viscosity, pipe diameter, pipe length; Assumptions: incompressible, no body forces, fully developed Find : Reynolds number, average velocity, maximum velocity, friction factor, pressure drop for a 50 m length and pumping power Analysis: Average velocity : s m D m A m U / 768 . 0 010 . 995 06 . 0 4 4 2 2 = = = = π ρπ ρ & & Reynolds number : 2550 10 3 010 . 0 768 . 0 995 Re 3 = × = = - μ ρ D U (Flow is turbulent). Maximum velocity : (use power law profile) ( )( ) 2 max 2 1 2 1 n n n U u + + = with n = 7: 22 . 1 7 7 2 15 8 max = = U u . Thus, s m u / 940 . 0 max = Friction factor : From the Blasius correlation: 0445 . 0
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