Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 15 - Fluids and Elasticity - Exercises and Problems - Page 439: 69

Answer

$1.3\;\rm L$

Work Step by Step

The piston is applying a volume stress on the water. And we know that the volume strain of water due to a pressure is given by $$\dfrac{\Delta V}{V_i}=\dfrac{-P}{B}$$ So, the number of liters of water that come out to atmospheric pressure after the safety plug on the top flies off is given by $\Delta V$. $\Delta V$ is the amount that comes out to neutralize the pressure between the vessel and the atmospheric pressure. $$\Delta V=\dfrac{-P}{B}V_i$$ Plugging the given (see table 15.3 for Bulk modulus) of water; $$\Delta V=\dfrac{-2000\times 10^3}{0.2\times 10^{10}}(1.3)=\bf -0.0013\;\rm m^3$$ $$\Delta V = -0.0013\times 1000=\color{red}{\bf -1.3}\;\rm L$$
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