Explanation Given information: The total available pumping power is equal to 8000 h p The total length is 2147 m i l e s The power of the pump can be defined as below, P o w e r = ρ g Q h f In above equation, ρ - Density of the fluid Q - Volumetric flow rate h p - Head loss The head loss is defined as, h f = V 2 2 g ( f L D ) In above equation, V - Velocity of the flow f - Friction factor L - Length D - Diameter Assume, that the crude oil at 40 ° C will have, ρ = 1.67 s l u g / f t 3 μ = 1.11 × 10 − 4 s l u g / ( f t . s ) Calculation: Convert, 8000 h p = 4400000 l b f . f t / s 2147 m i l e s = 1.1336 × 10 7 f t To find the flow rate, P = ρ g Q h f Substitute for head loss, P = ρ Q V 2 2 ( f L D ) Assume, f = 0.015 In above equation, substitute for flow rate, P = ρ π D V 3 8 ( f L ) Find the velocity from above equation, P = ρ π D V 3 8 ( f L ) 4400000 l b f . f t / s = π ( 1.67 s l u g / f t 3 ) ( 3 f t ) V 3 8 ( 0.015 ) ( 1.1336 × 10 7 f t ) V = 2.36 f t / s Find the Reynolds’s number, Re = ρ V D μ = ( 1.67 s l u g / f t 3 ) ( 2

8th Edition

ISBN: 9780073398273

Author: Frank M. White

Publisher: McGraw-Hill Education

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Chapter 6, Problem 6.48P

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The flow rate in barrels per minute.

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Chapter 6 Solutions

Fluid Mechanics

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