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 . Consider the steady state system so the velocity remains constant throughout the pipe. V 1 = V 2 = V (II) The given pipe line horizontal so the change in datum height ( z 2 − z 1 ) is zero. ( z 2 − z 1 ) = 0 (III) Substitute equation (III) and(IV) in equation (II) and simplify. p 1 γ = p 2 γ + h L ( p 1 − p 2 ) γ = h L Δ p = γ h L (IV) Write the expression for the area of the duct. A = w × h (V) 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 ) (VI) Write the expression for the velocity using continuity equation. Write the relation for the hydraulic diameter. D h = 4 A P (VII) Here, Area of duct is A and Perimeter of duct is P Write the expression for the velocity using continuity equation. V = Q A (VIII) Here, discharge is Q . Write the equation for Reynolds number. Re = ρ V D μ (IX) Here, the Reynolds number is Re , the velocity of the fluid is V and the dynamics viscosity of fluid is μ . Write the expression for the major head loss. h L = f l v 2 2 g D (X) Here, friction factor is f and length of the pipe is l . Write the expression for the power lost due to friction. P = Δ p × Q (XI) Here, discharge of the water is Q . Conclusion: Substitute 1 ft. for w and 1.5 ft. for h in equation (V). A = 1 ft × 1 .5 ft = 1.5 ft 2 Substitute 1 ft. for w and 1.5 ft. for h in equation (VI). P = 2 ( 1 ft + 1 .5 ft ) = 5 ft Substitute 1.5 ft 2 for A and 5 ft for P in equation (VII). D h = 4 ( 1.5 ft 2 ) 5 ft = 1.2 ft Substitute 5000 ft 3 /min for Q and 1 .5 ft 2 for A in equation (VIII). V = 5000 ft 3 min 1 .5 ft 2 V = 5000 ft 3 min × 1 min 60 s 1 .5 ft 2 = 55

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

Ch. 8.1 - Prob. 1P Ch. 8.1 - Rainwater runoff from a parking lot flows through...Ch. 8.1 - Blue and yellow streams of paint at 60 °F (each...Ch. 8.1 - Air at 200 °F flows at standard atmospheric...Ch. 8.1 - To cool a given room it is necessary to supply 4...Ch. 8.1 - Prob. 6P Ch. 8.1 - Prob. 7P Ch. 8.1 - (See The Wide World of Fluids article titled...Ch. 8.2 - For fully developed laminar pipe flow in a...Ch. 8.2 - Prob. 10P

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