physics
posted by RC .
A room has a volume of 164 m3. An airconditioning system is to replace the air in this room every 26.8 minutes, using ducts that have a square cross section. Assuming that air can be treated as an incompressible fluid, find the length of a side of the square if the air speed within the ducts is (a) 3.00 m/s and (b) 8.00 m/s.

Required volume flow rate:
164m^3/(26.8*60 s) = 0.102 m^3/s
That equals (Area)*(Velocity).
For a square duct, Area = a^2.
a is the side length of the square.
a = sqrt(0.102/V)
Plug in the numbers.
Solve for a.