Explanation Write the expression the energy balance equation for the horizontal pipe. p 1 γ + V 1 2 2 g + z 1 = p 2 γ + V 2 2 2 g + z 2 + h L (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 and the head loss is h L . Rearrange the equation (I) in terms of pressure drop. ( p 1 γ − p 2 γ ) = + V 2 2 2 g + z 2 − V 1 2 2 g − z 1 + h L ( p 1 − p 2 ρ g ) = ( V 2 2 2 g − V 1 2 2 g ) + ( z 2 − z 1 ) + h L ( p 1 − p 2 ) = ρ g [ ( V 2 2 2 g − V 1 2 2 g ) + ( z 2 − z 1 ) + h L ] Δ p = ρ g [ ( V 2 2 2 g − V 1 2 2 g ) + ( z 2 − z 1 ) + h L ] (II) Consider the steady state system so the velocity remains constant throughout the pipe. V 1 = V 2 = V (III) The given pipe line horizontal so the change in datum height ( z 2 − z 1 ) is zero. ( z 2 − z 1 ) = 0 (IV) Substitute equation (III) and(IV) in equation (II) and simplify. Δ p = ρ g [ ( 0 ) + ( 0 ) + f l v 2 2 g D ] Δ p = [ 0 + 0 + ρ f l v 2 2 D ] Δ p = ρ f l v 2 2 D (V) Write the expression for the area of the duct. A = w × h (VI) Here, width of the duct is w and height of the duct is h . Write the expression for the perimeter of the duct. P = 2 ( w + h ) (VII) Write the expression for the velocity using continuity equation. Write the relation for the hydraulic diameter. D h = 4 A P (VIII) Here, Area of duct is A and Perimeter of duct is P Write the expression for the velocity using continuity equation. V = Q A (IX) Here, discharge is Q . Write the equation for Reynolds number. Re = ρ V D μ (X) Here, the Reynolds number is Re , the velocity of the fluid is V and the dynamics viscosity of fluid is μ . Conclusion: Substitute 12 in. for w and 6 in. for h in equation (VI). A = 12 in . × 6 in . =72 in . 2 × ( 1 ft 12 in

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 62P

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The pressure drop in the duct.

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Chapter 8.4, Problem 61P

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

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