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Homework Help: Velocity of air moving past a duct.

  1. Apr 20, 2013 #1
    1. The problem statement, all variables and given/known data
    A hospital room has dimensions 8m by 9m by 3.25m tall. A round duct of diameter 12cm is used to supply air to the room. If the air in the room is to be exchanged 6 times every hour, how fast must the air move through the duct?

    3. The attempt at a solution

    OK, I want to use this equation
    I'm using
    A = area of duct
    V = velocity of duct.
    The lower case letters represent the room.
    AV = av
    We want V.
    So we get V = (av)/(V)
    Now looking that the equation I don't have given information for the velocity of the air in the room (v). So , v = L/T where L = length and T = time.
    So putting this back in we get

    V = aL / VT
    aL is just volume so
    V = Volume of room / VT
    Now from the problem they give us the period is 6 cycles per hour.
    So T = 1/f
    Then , (1hr/6cycles) (360 seconds) = 60 seconds ( I question this conversion because my answer seems high.)

    Plugging all the values in we get.
    V = ( 8m x 9m x 3.25m) / (Pi(0.06)^2 )(60 seconds))
    So I got V = 334.8 m/s this seems totally wrong. Because of how fast it is.
    What did I do wrong? Maybe 3.34 m/s seems more reasonable.

    Please help me find my error.
  2. jcsd
  3. Apr 20, 2013 #2

    Andrew Mason

    User Avatar
    Science Advisor
    Homework Helper

    There are 3600 seconds in an hour. So each cycle would be 600 seconds, not 60.

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