# physics

A room has a volume of 164 m3. An air-conditioning 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.

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1. 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.

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posted by drwls

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