Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 14 - Fluids and Elasticity - Exercises and Problems: 26

Answer

It would take 6.8 minutes to fill the pool.

Work Step by Step

We can find the volume flow rate of the water in the hose. The volume flow rate is the water speed times the cross-sectional area of the hose as: $flow~rate = v~A$ $flow~rate = v~\pi~r^2$ $flow~rate = (3.0~m/s)(\pi)(0.0125~m)^2$ $flow~rate = 1.47\times 10^{-3}~m^3/s$ We can convert the volume flow rate to units of liters as: $flow~rate = (1.47\times 10^{-3}~m^3/s)(\frac{1000~L}{1~m^3})$ $flow~rate = 1.47~L/s$ We can find the time it takes to fill the pool as: $t = \frac{volume}{flow~rate}$ $t = \frac{600~L}{1.47~L/s}$ $t = 408~s = 6.8~min$ It would take 6.8 minutes to fill the pool.
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