Explanation Given information: The air flow rate is equal to 3000 m 3 / h a 1 = a 3 = 20 c m a 2 = a 4 = 12 c m The efficiency of the blower is equal to 75 % The pressure difference can be given as, Δ P = ρ V 2 2 ( f L D ) In above equation, Δ P - Pressure difference ρ - Density of air V - Velocity of the flow f - Friction factor L - Length of the pipe D - Hydraulic Diameter Calculation: Assume the air at 20 ° C will have, ρ = 1.2 k g / m 3 μ = 1.8 × 10 − 5 k g / m s First of all, The flow rate is equal to, Q = 3000 m 3 / h 3600 = 0.833 m 3 / s Calculate the velocity of section 1 & 3, V 1 & 3 = Q A = 0.833 m 3 / s ( 0.2 m ) 2 = 20.825 m / s Calculate the velocity of section 2 & 4, V 2 & 4 = Q A = 0.833 m 3 / s ( 0.12 m ) 2 = 57.847 m / s Calculate the Reynolds’s number for section 1 & 3, Re 1 & 3 = ( ρ V d ) μ = ( 1.2 k g / m 3 ) ( 20.825 m / s ) ( 0.2 m ) 1.8 × 10 − 5 k g / m s = 277666.67 Calculate the Reynolds’s number for section 2 & 4, Re 2 & 4 = ( ρ V d ) μ = ( 1.2 k g / m 3 ) ( 57.847 m / s ) ( 0.12 m ) 1.8 × 10 − 5 k g / m s = 462776 Calculate the roughness ratio for section 1 & 3, ε d = 0

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 6, Problem 6.117P

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