# Fluid Dynamics, Buoyancy problem

1. Sep 22, 2008

### latitude

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 $$\rho$$air = $$\rho$$^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
$$\rho$$o = $$\rho$$fluid(g)h
B = $$\rho$$[(g)V
$$\rho$$[ = m/v

mg < $$\rho$$(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 = $$\rho$$(g)V
(400)(9.81) = B = $$\rho$$(g)V

But this doesn't seem to make sense to me??

2. Sep 22, 2008

### Sakha

You need to determine whats the $$\rho$$ 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.

3. Sep 22, 2008

### latitude

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?

4. Sep 22, 2008

### Sakha

Just plug in the z, which would be 8000m, and e is a known constant, just like pi.