Explanation Write the expression for the major head loss when the flow is turbulent ( h L ) T . ( h L ) T = f T l v 2 2 g D (I) Here, friction factor for turbulent flow is f T , length of the pipe is l , and diameter of the pipe is D . Write the expression for the major head loss when the flow is laminar ( h L ) L . ( h L ) L = f L l v 2 2 g D (II) Divide the equation (I) by equation (II). ( h L ) T ( h L ) L = f T l v 2 2 g D f L l v 2 2 g D ( h L ) T ( h L ) L = f T f L (III) Here, friction factor for turbulent flow is f T , length of the pipe is l , and diameter of the pipe is D . Write the expression to calculate the area of pipe. A = π 4 D 2 (IV) Here, the diameter of pipe is D . Write the expression for the flow rate using the continuity equation. Q = A V V = Q A (V) Here, the flow rate is Q , area of cross section of pipe is A , and velocity of pipe at point is V . Write the equation for Reynolds number. Re = V D ν (VI) Here, the Reynolds number is Re , the velocity of the fluid is V and the kinematic viscosity of fluid is ν . Write the expression for the friction factor for laminar flow. f L = 64 Re (VII) Here, Reynolds number is Re . Conclusion: Substitute 40 mm for D in equation (IV). A = π 4 ( 40 mm ) 2 A = π 4 ( 40 mm × 1 m 1000 mm ) 2 = 1.257 × 10 − 3 m 2 Substitute 0.001 m 3 /s for Q and 1.257 × 10 − 3 m 2 for A in equation (V)

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 43P

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The ratio of head loss for the actual turbulent flow compared to that if it were laminar flow.

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Chapter 8.4, Problem 42P

Chapter 8.4, Problem 44P

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

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