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If wind blows at 39 m/s over a house,

  1. Dec 12, 2011 #1
    what is the net force on the roof if its area is 320 m^2 and is flat?

    I don't even know where to start.
     
  2. jcsd
  3. Dec 12, 2011 #2
    What class are you taking?
     
  4. Dec 12, 2011 #3
    physics 1

    i think i have to use bernoulli's formula but i don't know how
     
  5. Dec 12, 2011 #4

    ehild

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    What does Bernouilli's principle state?

    ehild
     
  6. Dec 15, 2011 #5
    1/2ρv12 + p1 = 1/2ρv22 + p2
     
  7. Dec 16, 2011 #6

    ehild

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    Correct. If you look at the equation you see that the pressure is smaller when the speed of the air is greater. The speed of air is zero below the roof in the building, v1=0 and the pressure below the roof is just the usual p1=1 atm. The wind blows over the roof, its speed is v2=39 m/s. p2 =p1 - 1/2 (rho) v22.
    The pressure means the force exerted to unit surface. The air inside the building exerts F1=p1A upward force to the flat roof of area A. The air outside exerts p2A downward force to the roof. What is the net force then?

    ehild
     
  8. Dec 18, 2011 #7
    This is the answer I'm supposed to get

    3.1×10^5

    or 310000

    Let me try it the way you said

    Since V1 = 0 the first term goes away

    P1 = 1/2 ρ 39^2 + P2

    (1.225 = density of air)

    101325 - 1/2 * 1.225 * 1521 = P2

    101325 - 931.6125 = 100393.3875

    100393.3875 * A = Fnet

    100393.3875 * 320 = 32125884

    Not right. :surprised

    What am I doing wrong?
     
  9. Dec 18, 2011 #8

    Dick

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    For one thing you should really put units on stuff. For another thing you are only calculating the force on the roof exerted by the air outside the house. There's another force exerted on the roof by the air inside the house that isn't moving. They are in opposite directions.
     
  10. Dec 18, 2011 #9

    ehild

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    You calculated the force of the blowing air, but you need the net force. Read my previous post.

    ehild
     
  11. Dec 18, 2011 #10
    Oh, okay. Got it now. The problem with this question is that it doesn't give you the value for air density, so even a slight difference in the value you chose will make a difference in the big numbers. With the 1.225 I used above I was getting ~290000 then I used 1.29 and got the ~310000 I needed.

    Thanks!
     
  12. Dec 18, 2011 #11

    ehild

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    You get more accurate result if you express the force symbolically and pug in the data at the end. The net force is
    F=PA-P2A=(P1-P2)A=[P1-(P1-1/2 ρv2)]A=(1/2 ρv2)A
    No need to calculate the pressure.
    The density of air depends quite much on the temperature and hight above sea level.
    It should have been given in the problem.

    ehild
     
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