(adsbygoogle = window.adsbygoogle || []).push({}); 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??

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# Homework Help: Fluid Dynamics, Buoyancy problem

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