a) To determine The minimum required height when losses are neglected. Explanation Write the expression for the energy balance equation for the given system including the major and minor losses. p 1 γ + V 1 2 2 g + z 1 = p 2 γ + V 2 2 2 g + z 2 + ∑ K L V 2 2 2 g + f l V 2 2 g (I) Here, the pressure at point 1 is p 1 , the velocity at point 1 is V 1 , the elevation at point 1 is z 1 , the pressure at point 2 is p 2 , the velocity at point 2 is V 2 , the elevation at point 2 is z 2 , loss coefficient is K L , friction factor is f , and length of the pipe is l . Write the expression to calculate the area of pipe. A = π 4 D 2 (II) Here, the diameter of pipe is D . Write the expression for the velocity using continuity equation. V = Q A (III) Here, discharge is Q . Write the equation for Reynolds number. Re = V D ν (IV) Here, the Reynolds number is Re , the velocity of the fluid is V and the kinematic viscosity of fluid is ν . Rewrite the equation (II) by neglecting the minor loss. h = p 2 γ + ( 1 + f l D ) V 2 2 g − 16 (V) Conclusion: Refer figure (1), Calculate the datum height of the section (1). z 1 = ( 10 + h + 6 ) = 16 + h ft Substitute 0 for p 1 , 0 for V 1 , 0 for Z 2 , and ( 16 + h ) ft for z 1 in equation (I). 0 + 0 + ( 16 + h ) = p 2 γ + V 2 2 g + f l D V 2 2 g + ∑ K L V 2 2 g h = p 2 γ + ( 1 + f l D + ∑ K L ) V 2 2 g − 16 (VI) Substitute 6 in. for D in equation (II). A = π 4 ( 6 in . ) 2 A = π 4 ( 6 in . × 1 ft 12 in . ) 2 = 0 .19635 ft 2 Substitute 1 ft 3 /s for Q and 0 .19635 ft 2 for A in equation (III) V = 1 ft 3 /s 0 b) To determine The minimum required height when losses are considered.

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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Applied Fluid Mechanics

A fluid is a substance that is continuously deformed by the application of shear stress. The rate of deformation of a fluid depends on its viscosity. The fluid tries to flow when it interacts with some other system.

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Chapter 8.5, Problem 66P

To determine

The minimum required height when losses are neglected.

To determine

The minimum required height when losses are considered.

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

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