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bouyant force for this problem?
I'm looking to check my work for a problem I had in class.
What is the buoyancy force generated by a 30x10^6 ft^3 helium-filled, high-altitude balloon, assuming the air density at 120,000 feet is 1.27x10^-5 slug/ft^3 ? Archimedes's principle states that the buoyancy of a balloon is equal to the weight of the air displaced by the balloon.
So it looks like I'm given density and a volume, so I can calculate mass. I did and got 371. Is that correct? If not, can someone offer some help?
1 Answer
- SteveLv 78 years agoFavorite Answer
The buoyant force is equal to the mass of the displaced air - the mass of the helium all multiplied by the gravitational constant g. The resulting units are pounds force.
Fb = V*g*(ρa - ρh)
The density of He is about 4/29 the density of air under the same conditions of T & P; this gives
Fb = V*g*ρa*(1 - 4/29) = 30E6*32.2*1.27E-5*(1 - 4/29) = 10576 lbf
