1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Homework Helper

    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.

  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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook