Explanation Given information: Diameter of the pipe is equal to 12 i n The velocity of the flow is equal to 60 f t / s The fluid is glycerin at 20 ° C The length L = 40 f t The efficiency of the pump is 75 % The power of the pump can be defined as below, P o w e r = ρ g Q h f η In the above equation, ρ - Density of the fluid Q - Volumetric flow rate h p - Head loss η - Efficiency of the pump The head loss is defined as, h f = V 2 2 g ( f L D ) In the above equation, V - Velocity of the flow f - Friction factor L - Length D - Diameter The friction velocity u * is defined as, u ∗ = V ( f 8 ) 1 2 The sub layer thickness y is defined as, y = 5 μ ρ u * In above equation, μ - Dynamic viscosity ρ - Density The Reynolds’s number is defined as, Re = ρ V D μ Assume, that the glycerin at 20 ° C will have, ρ = 2.445 s l u g / f t 3 μ = 0.0313 s l u g / f t s Calculation: Calculate the Reynolds’s number, Re = ρ V D μ = ( 2.445 s l u g / f t 3 ) ( 60 f t / s ) ( 12 12 f t ) 0.0313 s l u g / f t s = 4686.9 Calculate the friction factor, 1 f 1 2 = 2.0 log ( Re f 1 2 ) − 0.8 = 2.0 log ( ( 4686.9 ) f 1 2 ) − 0.8 f = 0.0381 Calculate the friction velocity, u * = V ( f 8 ) 1 2 = 60 f t / s ( 0

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 6, Problem 6.51P

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The sub layer thickness in inches and the pumping horsepower.

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