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Fluid Dynamics, Buoyancy problem

  1. Sep 22, 2008 #1
    1. The problem statement, all variables and given/known data
    How many cubic metres of helium are required to lift a balloon with a 400 kg payload to 8000 m? Assume balloon maintains constant volume, and density of the air decreases with altitude z according to the expression [tex]\rho[/tex]air = [tex]\rho[/tex]^e^-z/8000, where z is in metres and po = 1.25 kg/m^3 is the density of air at sea level.

    2. Relevant equations
    [tex]\rho[/tex]o = [tex]\rho[/tex]fluid(g)h
    B = [tex]\rho[/tex][(g)V
    [tex]\rho[/tex][ = m/v

    mg < [tex]\rho[/tex](g)V (Not sure if this is right?? But buoyancy should be stronger if it is to rise, correct?)

    I'm not sure how to go about this. I see I need to find volume, so I know the Buoyancy equation with be used, and I think I should find the Buoyancy-- so I assume I need to find the Buoyant force on the "payload" (whatever that is.) Since I don't know the payload's density or volume, I figure that probably
    mg = [tex]\rho[/tex](g)V
    (400)(9.81) = B = [tex]\rho[/tex](g)V

    But this doesn't seem to make sense to me??
  2. jcsd
  3. Sep 22, 2008 #2
    You need to determine whats the [tex]\rho[/tex] of air at 8000m to be able to find out the required buoyancy.
    I don't know if its requires, but take into consideration the weight of helium too.
  4. Sep 22, 2008 #3
    Ah :( So I have to use that bit with the e? I'm not really sure how :[ I'm assuming it's some kind of calculus thing...? Related rates, perhaps?
  5. Sep 22, 2008 #4
    Just plug in the z, which would be 8000m, and e is a known constant, just like pi.
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