a) To determine The flow rate of turbine when head losses are negligible. Explanation Write the expression for the energy balance equation between the reservoir and diffuser outlet. p 1 γ + V 1 2 2 g + z 1 = p 2 γ + V 2 2 2 g + z 2 + f l V 2 2 g + h T (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 , friction factor is f , length of the pipe is l , acceleration due to gravity is g , diameter of the pipe is D , and the turbine head loss is h T . Section (1) and (2) is open to atmosphere so the pressure at section (1) and (2) is zero. p 1 = p 2 = 0 Section (1) is reservoir so the velocity of the section is negligible. V 1 = 0 Datum is considered from the datum level so z 2 = 0 . Use the prescribed statement in equation (I) and simplify, z 1 = V 2 2 2 g + f l V 2 2 g D + h T (II) Write the continuity equation. Q = A V 2 Q = π 4 ( D 2 ) × V 2 (III) Write the expression for the loss in the turbine. h T = P γ Q h T = P γ ( A V 2 ) h T = P γ ( π 4 D 2 × V 2 ) (IV) Conclusion: Substitute 400 kW for P , 9.81 × 10 3 N/m 3 for γ , 1 m for D in equation (III). h T = 400 kW ( 9.81 × 10 3 N/m 3 ) ( π 4 ( 1 m ) 2 × V 2 ) = 400 kW × 1000 N ⋅ m s 1 kW ( 9 b) To determine The flow rate of turbine when head 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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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 85P

To determine

The flow rate of turbine when head losses are negligible.

To determine

The flow rate of turbine when head losses are considered.

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Chapter 8.5, Problem 83P

Chapter 8.5, Problem 86P

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