Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 10 - Fluids - Problems - Page 287: 41

Answer

The speed of the air flow in the air duct is 4.4 m/s

Work Step by Step

We can use the room dimensions to find the volume flow rate as: $flow~rate = \frac{V}{t}$ $flow~rate = \frac{(8.2~m)(5.0~m)(3.5~m)}{(12~min)(60~s/min)}$ $flow~rate = 0.20~m^3/s$ The volume flow rate in the air duct is the air speed times the cross-sectional area of the air duct. $flow~rate = v~A = 0.20~m^3/s$ $v~\pi ~r^2 = 0.20~m^3/s$ $v = \frac{0.20~m^3/s}{\pi~r^2}$ $v = \frac{0.20~m^3/s}{(\pi)(0.12~m)^2}$ $v = 4.4~m/s$ The speed of the air flow in the air duct is 4.4 m/s.
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