To determine The power that the pump supplies to the oil if the head losses are negligible. Explanation Write the expression of specific weight of the mercury. γ Hg = S G Hg γ Water (I) Here, the specific gravity of the mercury is S G Hg and the specific weight of the water is γ Water . Write the expression of specific weight of the oil. γ oil = S G oil γ Water (II) Here, the specific gravity of the mercury is S G Hg and the specific weight of the water is γ Water . Write the expression of area at point 1 . A 1 = π 4 d 1 2 (III) Here, the diameter at point 1 is d 1 . Write the expression of area at point 2 . A 2 = π 4 d 2 2 (IV) Here, the diameter at point 2 is d 2 . Write the expression of flow rate of oil. Q = A 1 V 1 (V) Here, the velocity at point 1 is V 1 . Write the expression of flow rate of oil. Q = A 2 V 2 (VI) Here, the velocity at point 2 is V 2 . Write the expression of manometer equation. p 1 + γ oil H + ( 3 ft ) γ Hg = p 2 + ( 3 ft + H + h ) γ oil γ oil ( p 1 γ oil + H + ( 3 ft ) γ Hg γ oil ) = γ oil ( p 2 γ oil + ( 3 ft + H + h ) γ oil γ oil ) ( p 1 γ oil + H + ( 3 ft ) γ Hg γ oil ) = ( p 2 γ oil + ( 3 ft + H + h ) γ oil γ oil ) p 2 γ oil = p 1 γ oil + H + ( 3 ft ) γ Hg γ oil − ( 3 ft + H + h ) γ oil γ oil (VII) Here, the pressure at point 2 is p 2 , the pressure at point 1 is p 1 , the difference of datum head is h and the head is H . Write the expression of mechanical energy equation at point 1 and 2 of manometer. p 1 γ oil + V 1 2 2 g + z 1 + h p − h L = p 2 γ oil + V 2 2 2 g + z 2 (VIII) Here, the datum head at inlet is z 1 , the datum at exit is z 2 , the pump head is h p and the head loss is h L . Substitute p 1 γ oil + H + ( 3 ft ) γ Hg γ oil − ( 3 ft + H + h ) γ oil γ oil for p 2 γ oil in Equation (VIII). p 1 γ oil + V 1 2 2 g + z 1 + h p − h L = p 1 γ oil + H + ( 3 ft ) γ Hg γ oil − ( 3 ft + H + h ) γ oil γ oil + V 2 2 2 g + z 2 V 1 2 2 g + z 1 + h p − h L = H + ( 3 ft ) γ Hg γ oil − 3 ft − H − h + V 2 2 2 g + z 2 V 1 2 2 g + h p − h L + z 1 − z 2 = ( 3 ft ) γ Hg γ oil − 3 ft − h + V 2 2 2 g h p = V 2 2 2 g − V 1 2 2 g + ( 3 ft ) γ Hg γ oil − 3 ft − h − ( z 1 − z 2 ) + h L

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 5.3, Problem 106P

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The power that the pump supplies to the oil if the head losses are negligible.

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Chapter 5.3, Problem 105P

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Chapter 5 Solutions

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

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