Explanation Given information: The fluid is water at 20 ° C The elevation difference is 60 m The length of the pipe is 360 m The diameter of the pipe is equal to 12 c m The power delivered by the pump is equal to 15000 W The energy equation can be write as, p 1 ρ g + V 1 2 2 g + z 1 = p 2 ρ g + V 2 2 2 g + z 2 + h f − h p By solving further, we get h p = Δ z + h f = Δ z + V 2 2 g ( f L D ) The Reynolds’s number is defined as, Re = ρ V D μ In above equation, μ - Dynamic viscosity ρ - Density The power delivered by the pump is equal to, P o w e r = ρ g Q h p Assume, the water at 20 ° C will have, ρ = 998 k g / m 3 μ = 0.001 k g / m s Calculation: Find a formula for the h p Assume, f = 0.02 h p = Δ z + h f = Δ z + V 2 2 g ( f L D ) h p = 60 m + V 2 2 ( 9.81 m / s 2 ) ( ( 0.02 ) 360 m 0.12 m ) h p = 60 m + 3.0581 V 2 Substitute the above equation below, P o w e r = ρ g Q h p 15000 W = ( 9790 N / m 3 ) ( V ( π ( 0.06 m ) 2 ) ) ( 60 m + 3.0581 V 2 ) V = 3.95 m / s Calculate the Reynolds’s number, Re = ρ V D μ = ( 998 k g / m 3 ) ( 3.95 m / s ) ( 0.12 m ) 0.001 k g / m s = 473052 Calculate the friction factor, 1 f 1 2 = 2

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 6, Problem 6.58P

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