Explanation Given data: Volume of the glycerol is 7.2 m 3 , Viscosity of the glycerol is 0.934 Pa ⋅ s , Pressure at the input end is 8.6 × 10 5 Pa , Length of the pipe is 15 m, and Time in which glycerol is pumped through the pipe 55 minutes. Formula used: Write the expression for Poiseuille’s law. Q = π R 4 ( P 2 − P 1 ) 8 η L (1) Here, Q is the volume flow rate, R is the radius, P 1 , P 2 is the pressure at the input and output end, L is the length, and η is the viscosity. Explanation: The value of atmospheric pressure is 1.013 × 10 5 Pa . The output end of the pipe is exposed to the atmospheric pressure hence pressure at the output is atmospheric pressure. The volume flow rate can be determined by finding the ratio of the volume of glycerol to the total time elapsed that is, Q = V t (2) Rearrange equation (1) to solve for R . π R 4 ( P 2 − P 1 ) = Q 8 η L R 4 = Q 8 η L π ( P 2 − P 1 ) R = Q 8 η L π ( P 2 − P 1 ) 4 (3) Substitute equation (2) in equation (3), R = V 8 η L π ( P 2 − P 1 ) t 4 (4) Consider the conversion factor for min to s

10th Edition

ISBN: 9781118836880

Author: John D. Cutnell, Kenneth W. Johnson

Publisher: WILEY

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Chapter 11, Problem 92AP

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The radius of the pipe.

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Chapter 11 Solutions

Physics, Volume One: Chapters 1-17

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