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.