Explanation Given data: The speed of water is 1.4 m s . Formula used: Write the expression for Bernoulli’s equation relating the two points along the cylindrical pipe. p 2 + 1 2 ρ v 2 2 + ρ g y 2 = p 1 + 1 2 ρ v 1 2 + ρ g y 1 (1) Here, ρ is density of water, g is gravity, which is 9.80 m s 2 , p 1 is pressure at wide end of pipe, v 1 is speed at wide end of pipe, y 1 is height at wide end of pipe, p 2 is pressure at narrow end of pipe, v 2 is speed at narrow end of pipe, and y 2 is height narrow end of pipe. Write the expression for area of pipe ( A ) . A = 1 2 π D 2 (2) Here, r is radius. Refer to Table 13.1 in the textbook for the densities of fluids at 1 atm pressure. From table 13.1, the density of water is 1000 kg m 3 at pressure 1 atm. Consider water is an ideal fluid. The heights at two ends of pipe is same since it is horizontal, hence y 1 = y 2 . Write the expression for diameter of narrowed pipe ( D 2 ) . D 2 = D 1 2 Here, D 1 is diameter at wide end. Write the expression for pressure difference between wide and narrow ends of pipe ( Δ p ) . Δ p = p 1 − p 2 Substitute y 1 for y 2 in equation (1), p 2 + 1 2 ρ v 2 2 + ρ g y 1 = p 1 + 1 2 ρ v 1 2 + ρ g y 1 Re-arrange the expression. p 1 − p 2 = 1 2 ρ v 2 2 + ρ g y 1 − 1 2 ρ v 1 2 − ρ g y 1 p 1 − p 2 = 1 2 ρ ( v 2 2 − v 1 2 ) Substitute Δ p for p 2 − p 1 , Δ p = 1 2 ρ ( v 2 2 − v 1 2 ) (3) Write the expression for speed at point 2 by the use of continuity equation. v 2 = A 1 A 2 v 1 (4) Here, A 1 is area of pipe at wide end, and A 2 is area of pipe at the narrow end

College Physics: A Strategic Approach (3rd Edition)

3rd Edition

ISBN: 9780321879721

Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field

Publisher: PEARSON

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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 59GP

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The pressure difference between wide and narrow ends of the pipe.

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Chapter 13, Problem 58GP

Chapter 13, Problem 60GP

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Chapter 13 Solutions

College Physics: A Strategic Approach (3rd Edition)

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The pressure difference between wide and narrow ends of the pipe.

Solution Summary: The author explains that the pressure difference between wide and narrow ends of the pipe is 15 kPa.

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The pressure difference between wide and narrow ends of the pipe.

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Chapter 13 Solutions