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: 57

Answer

The water speed in each pipe is 3.5 m/s

Work Step by Step

We can find the volume flow rate of the water as: $flow~rate = \frac{V}{t}$ $flow~rate = \frac{(3.0\times 10^6~L)(\frac{1~m^3}{1000~L})}{60~s}$ $flow~rate = 50~m^3/s$ Note that the volume flow rate in each pipe is $25~m^3/s$. The volume flow rate is the water speed times the cross-sectional area of the pipe. We can find the water speed in each pipe as: $flow~rate = v~A = 25~m^3/s$ $v = \frac{25~m^3/s}{\pi~r^2}$ $v = \frac{25~m^3/s}{(\pi)(1.5~m)^2}$ $v = 3.5~m/s$ The water speed in each pipe is 3.5 m/s.
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