Essential University Physics: Volume 1 (4th Edition)

Published by Pearson
ISBN 10: 0-134-98855-8
ISBN 13: 978-0-13498-855-9

Chapter 15 - Exercises and Problems - Page 290: 38

Answer

15 m/s

Work Step by Step

Please see the attached image first. Here we use the Bernoulli's equation, $P+\frac{1}{2}\rho V^{2}+\rho gy = constant$ Where $P- Pressure$, $\frac{1}{2}\rho V^{2}-Kinetic\space energy\space per\space unit \space volume$, $\rho gy- Gravitational \space potential \space energy \space per\space unit \space volume.$ Let's plug known values into this equation. $P_{1}+0+\rho gh=P_{2}+\frac{1}{2}\rho V_{hole}^{2}+0$ $\frac{2(P_{1}-P_{2})+2\rho gh}{\rho}=V_{hole}^{2}$ ; Let's plug known values into this equation. $\frac{2(186\times10^{3}-10^{5})N/m^{2}+2\times10^{3}kg/m^{3}\times9.8\space m/s\times2.68\space m}{1000\space kg/m^{3}}=V_{hole}^{2}$ $V_{hole}=15 m/s$
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