To determine The friction pressure loss per unit length Explanation Write the expression for the hydraulic diameter. D h = D 2 − D 1 (I) Here, outer diameter is D 2 and inner diameter is D 1 . Write the expression for the velocity using the continuity equation. V = 4 Q π ( D 2 2 − D 1 2 ) (II) Here, discharge is Q . Write the expression for the major head loss ( h L ) m a j o r . ( h L ) m a j o r = f l V 2 2 g D h (III) Here, friction factor is f , length of the pipe is l , velocity is v , acceleration due to gravity is g , and hydraulic diameter of the pipe is D h . Write the expression for the frictional pressure loss. Δ p l = ρ g h L (IV) Here, density of the fluid is ρ . Substitute equation (I) and (II) in equation (III). ( h L ) m a j o r = f l ( 4 Q π ( D 2 2 − D 1 2 ) ) 2 2 g ( D 2 − D 1 ) = 8 f l Q 2 π 2 g ( D 2 2 − D 1 2 ) 2 ( D 2 − D 1 ) (V) Substitute equation (V) in equation (IV). Δ p l = ρ g ( 8 f l Q 2 π 2 g ( D 2 2 − D 1 2 ) ( D 2 − D 1 ) ) Δ p l = ( 8 f l Q 2 × ρ π 2 ( D 2 2 − D 1 2 ) 2 ( D 2 − D 1 ) ) (VI) Write the equation for Reynolds number. Re = V D h ν (VII) Here, the Reynolds number is Re , the velocity of the fluid is V and the kinematic viscosity of fluid is ν . Substitute equation (I) and (II) in equation (VII). Re = ( 4 Q π ( D 2 2 − D 1 2 ) ) ( D 2 − D 1 ) ν = 4 Q ( D 2 − D 1 ) π ( D 2 2 − D 1 2 ) ν Re = 4 Q π ν ( D 2 + D 1 ) (VIII) Conclusion: Refer table B.1, “Physical properties of water” at a temperature of 20 ° C , ν = 1 .0×10 -6 m 2 /s Substitute 0 .01 m 3 /s for Q , 1 .0×10 -6 m 2 /s for ν , 4 cm for D 2 , and 2 cm for D 1 in equation (VIII). Re = 4 ( 0

Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

8th Edition

ISBN: 9781119080701

Author: Philip M. Gerhart, Andrew L. Gerhart, John I. Hochstein

Publisher: WILEY

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Chapter 8.4, Problem 63P

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The friction pressure loss per unit length

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Chapter 8.4, Problem 62P

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Munson, Young and Okiishi's Fundamentals of Fluid Mechanics, Binder Ready Version

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