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Fluid Mechanics; Lift Force on a Roof; Bernoulli's Equation

  1. Sep 24, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to find the net force acting on a flat squared roof with area A while the wind is blowing outside at some velocity, [tex]v_1[/tex].

    2. Relevant equations

    Bernoulli's Equation:
    [tex]P_1+\frac{1}{2}\rho v_1^2+\rho gy_1= P_2+\frac{1}{2}\rho v_2^2+\rho gy_2[/tex]


    3. The attempt at a solution

    The roof is flat, so the air pushing up from the inside is at the same depth as the air pushing down on the outside, so [tex]y_1=y_2[/tex]. I'm also assuming that the velocity of the air inside the house is zero, [tex]v_2=0[/tex]. So I can rearrange Bernoulli's equation:

    [tex]P_2-P_1=\frac{1}{2}\rho v_1^2[/tex]

    I think that the net force should be:

    [tex]\Sigma F=(P_2-P_1)A-Mg=\frac{1}{2}\rho v_1^2A-Mg[/tex]

    M is the mass of the roof. The problem is that I cannot find the mass, nor is it given. I"m told the that the roof is has an area of 225m and the wind is 100 mph. I convert the airspeed to meters-per-second, which is about 44.70 m/s. I can plug these numbers in, along with the known density of air, but it doesn't do any good if I don't know M.
     
    Last edited: Sep 24, 2011
  2. jcsd
  3. Sep 24, 2011 #2

    ehild

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    That roof does not float in the air, but is supported by the walls. I am sure the problem means the net force from air.


    ehild
     
  4. Sep 24, 2011 #3
    lol, yeah that's probably true for most roofs.

    It turns out that my first instinct was correct, I just need to find the net force from air as you say. When I first made the calculation I obtained a number slightly greater than the value given in the back of the book, it turns out that the density of air is either 1.29 kg/m^3 or 1.20 kg/m^3 depending on varying conditions, I was using the former.
     
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