(a) Explanation Take point 1 to be the top of the storage tank and point 2 to be the point of small hole. Assume that the top of the tank is open to the atmosphere so that the pressure at both the points will be equal to atmospheric pressure. Write the Bernoulli’s equation. P 1 + 1 2 ρ v 1 2 + ρ g y 1 = P 2 + 1 2 ρ v 2 2 + ρ g y 2 (I) Here, P 1 is the pressure at the point 1, ρ is the density of the liquid, v 1 is the speed of the liquid at point 1, g is the acceleration due to gravity, y 1 is the height of the point 1 above the reference position, P 2 is the pressure at the point 2, v 2 is the speed of the liquid at point 2 and y 2 is the height of the point 2 above the reference position. Write the continuity equation of fluids. A 1 v 1 = A 2 v 2 (II) Here, A 1 is the area through which the liquid moves at point 1, v 1 is the speed of the liquid at point 1, A 2 is the area through which the liquid moves at point 2 and v 2 is the speed of the liquid at point 2. Since the area of the top of the tank is much greater than the area of the small hole, according to equation (II), v 1 < < v 2 . Assume v 1 = 0 and the position of the small hole to be y 2 = 0 m . Substitute P 0 for P 1 , P 2 , 0 m/s for v 1 and 0 m for y 2 in equation (I) and rearrange it for v 2 (b) To determine The diameter of the hole.

Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)

5th Edition

ISBN: 9781305586871

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 15, Problem 43P

(a)

To determine

The speed at which the water leaves the hole.

(b)

To determine

The diameter of the hole.

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Chapter 15, Problem 42P

Chapter 15, Problem 44P

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Principles of Physics: A Calculus-Based Text, Hybrid (with Enhanced WebAssign Printed Access Card)

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The speed at which the water leaves the hole.

Solution Summary: The author explains how the speed at which the water leaves the hole is 17.7m/s.

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Chapter 15 Solutions