Explanation Given information: The constant angular velocity is ω , the gravitational constant is g , the height of the U tube is h , and the length is L . The figure below shows the schematic diagram for the U tube. Figure-(1) Write the expression for the pressure difference by applying the Bernoulli’s equation between point 1 and 2. P 1 ρ g + V 1 2 2 g + z 1 = P 2 ρ g + V 2 2 2 g + z 2 P 1 ρ g + ( ω r 1 ) 2 2 g + z 1 = P 2 ρ g + ( ω r 2 ) 2 2 g + z 2 z 1 − z 2 = P 2 − P 1 ρ g + ( ω r 2 ) 2 − ( ω r 1 ) 2 2 g 0 = P 2 − P 1 ρ g + ( ω r 2 ) 2 − ( ω r 1 ) 2 2 g Δ P ρ g = ( ω r 2 ) 2 − ( ω r 1 ) 2 2 g ...... (I) Here, the change in the pressure is Δ P , the velocity of the liquid is V , and the density of the liquid is ρ . Write the expression for the pressure at point 1. P 1 = ρ g ( h + h 2 ) ...... (II) Write the expression for the pressure at point 2. P 2 = ρ g ( h 2 ) ...... (III) Write the expression for the change in pressure. Δ P = P 2 − P 1 ...... (IV) Calculation: Substitute ρ g ( h + h 2 ) for P 1 and ρ g ( h 2 ) for P 2 in Equation (IV)

Fluid Mechanics Fundamentals And Applications

3rd Edition

ISBN: 9780073380322

Author: Yunus Cengel, John Cimbala

Publisher: MCGRAW-HILL HIGHER EDUCATION

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Chapter 3, Problem 134P

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The relation for the angular velocity in terms of g, h and l.

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Chapter 3, Problem 133P

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The relation for the angular velocity in terms of g , h and l .

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