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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.

  • physics -

    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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