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Roof withstanding a storm

  1. Jan 22, 2007 #1
    1. The problem statement, all variables and given/known data
    Someone is putting a small shed in their backyard. The roof is not nailed down so gravity alone is holding it down. The wind suddenly flows across the top of the roogf at 20 m/s. The air inside the shed is 1.01 x 10^15 Pa, the normal atmospheric pressure. The roof has an area of 16m^2 and a mass of 250 kg. Density of air is 1.29 kg/m^3. Will the roof fly off?


    2. Relevant equations



    3. The attempt at a solution

    The answer is that the roof will fly off.

    In order for this to be true, pressure inside plus gravity must be greater than pressure outside.

    Pushing down I have Pressure_up = 1.01 x 10^5 Pa.

    I know that Pressure_down = mg/A + P_wind

    I know this must be less than 1.01 x 10^5

    However, what is the formula for Pressure_wind? I know the faster the wind, the smaller the pressure. I know formulas such as p + .5*density*v^2 + density*g*y, but it seems like a higher velocity would yield a higher pressure with this formula. It shouldn't be that way. What am I doing wrong?
     
  2. jcsd
  3. Jan 22, 2007 #2

    AlephZero

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    What is "p + .5*density*v^2 + density*g*y" equal to?

    If you use the equation correctly, you will find higher velocity does give lower pressure.
     
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