Explanation Given data: The diameter of narrow end is 1.0 mm , the volume flow rate of narrow end is 0.020 L s , temperature at narrow end is 20 ° C , diameter of wide end is 4.0 mm , length of narrow end is 1.0 m , and length of wide end is 1.0 m . Formula used: Write the expression for Poiseuille’s equation of viscous fluid Δ p = 8 η L Q π R 4 (1) Here, η is coefficient of viscosity, L is length, Q is flow rate, and R is radius. Refer to Table 13.3 in the textbook for the viscosities of fluids. From Table 13.3, the coefficient of viscosity of water at 20 ° C is 1.0 × 10 − 3 Pa ⋅ s . Consider the fluid is not an ideal fluid and has viscosity, since fluid is dependent on temperature and lengths of tubes. The gauge pressure at point P is equal to the pressure difference between pressures at point P and atmospheric pressure at narrowed open end. And hence the gauge pressure is as same as the pressure difference between the point P and open end of tube. The tube has same volume flow rate and lengths for two ends. Find the inner radius of narrowed open end ( R 1 ) . R 1 = 1.0 mm 2 = 0.5 mm = 0.0005 m { ∵ 1 mm = 0.001 mm } Find the inner radius of tube ( R 2 ) . R 2 = 4.0 mm 2 = 2.0 mm = 0.002 m { ∵ 1 mm = 0.001 mm } Write the expression for total pressure difference between point P and open end of tube ( Δ p ) . Δ p = Δ p 1 + Δ p 2 (2) Modify the equation (1) for narrowed open end. Δ p 1 = 8 η L Q π R 1 4 Here, R 1 is radius of narrowed open end. Modify the equation (1) for wide end. Δ p 2 = 8 η L Q π R 2 4 Here, R 2 is radius of narrowed wide end. Substitute 8 η L Q π R 1 4 for Δ p 1 and 8 η L Q π R 2 4 for Δ p 2 , Δ p = 8 η L Q π R 1 4 + 8 η L Q π R 2 4 = 8 η L Q π ( 1 R 1 4 + 1 R 2 4 ) Substitute 1

3rd Edition

ISBN: 9780321989246

Author: Knight

Publisher: PEARSON CO

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Variation of pressure

From the equation of pressure, pressure is directly proportional to the applied force.

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Chapter 13, Problem 65GP

To determine

The gauge pressure at point P.

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Chapter 13, Problem 64GP

Chapter 13, Problem 66GP

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Chapter 13 Solutions

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The gauge pressure at point P.

Solution Summary: The author analyzes Poiseuille's equation of viscosity of fluids. The gauge pressure is equal to the pressure difference between pressures at point P and atmospheric pressure at narrowed open end.

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The gauge pressure at point P.

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Chapter 13 Solutions