Explanation Given that the diameter of the stream at the faucet is 0.960 cm , the volume of 125 cm 3 is filled by the stream in 16.3 s . Write the expression for the volume flow rate of the water. flow rate = Δ V Δ t (I) Here, Δ V is the volume of water transferred, and Δ t is the time duration. Write the expression for the flow rate in terms of area of the stream at the faucet. flow rate = A 1 v 1 (II) Here, A 1 is the cross sectional area of the stream at the faucet, and v 1 is the speed of flow at the faucet. Equate the right hand sides of equations (I) and (II). Δ V Δ t = A 1 v 1 (III) Write the expression for the cross sectional area of the faucet tap in terms of its diameter. A 1 = π d 1 2 4 (IV) Here, d 1 is the diameter of the faucet tap. Use equation (IV) in (III) and solve for v Δ V Δ t = ( π d 1 2 4 ) v 1 v 1 = 4 Δ V π d 1 2 Δ t (V) Consider a point as point 2 at 13.0 cm below the faucet. Write Bernaulli’s equation for the give flow. P 1 + 1 2 ρ v 1 2 + ρ g y 1 = P 2 + 1 2 ρ v 2 2 + ρ g y 2 (VI) Here, P 1 is the pressure at point 1, P 2 is the pressure at point 2, ρ is the density of water, y 1 is the position of point 1 and y 2 is the position of point 2. The pressure P 1 = P 2 , and which is equal to the atmospheric pressure ( P 0 ), thus, equation (VI) ca be solved for v 2 as, P 0 + 1 2 ρ v 1 2 + ρ g y 1 = P 0 + 1 2 ρ v 2 2 + ρ g y 2 1 2 ρ v 1 2 + ρ g ( y 1 − y 2 ) = 1 2 ρ v 2 2 v 2 = v 1 2 + 2 g ( y 1 − y 2 ) (VII) Write the continuity equation for the flow of water through points 1 and 2

Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)

9th Edition

ISBN: 9781305266292

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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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 14, Problem 43P

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The diameter of the stream 13.0 cm below the opening of the faucet.

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Chapter 14, Problem 42P

Chapter 14, Problem 44P

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Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)

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The diameter of the stream 13.0 cm below the opening of the faucet.

Solution Summary: The author analyzes the flow rate of the water at the faucet.

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The diameter of the stream 13.0 cm below the opening of the faucet.

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Chapter 14 Solutions