Calculating Helium Balloon Volume for 500 kg Payload

AI Thread Summary
To calculate the volume of a helium balloon needed to lift a 500 kg payload, the buoyancy force must equal the weight of the payload plus the weight of the helium. The equation V(1.29) = 500000 + V(0.178) is used, where V is the volume, and the densities of air and helium are incorporated. After solving, the required volume is determined to be 450 m³. A subsequent discussion involves calculating the altitude at which a balloon with a diameter of 100 feet and a total weight of 16,000 pounds can fly, using buoyancy principles and various formulas provided. The complexity of the calculations and the number of formulas presented create confusion for participants in the discussion.
nsw
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I can't seem to figure this simple helium balloon problem out? I would really appreciate some help? Thanks!

Estimate the volume of a helium-filled balloon at STP if it is to lift a payload of 500 kg. The density of air is 1.29 kg/cubic meter and helium has a density of .178 kg/cubic meter.

I think you use a formula like force bouyancy equals density of air times volume times gravity? but not quite sure.
 
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let V : Volume
a= density of air
b= density of He

we have

Code:
 V*a=500*10[sup]3[/sup]+V*b
 
How are you supposed to solve this equation with two unknowns?
 
only V is unknown
 
How do you solve

V(1.29)= 500000+V(0.178)

and is this really your answer?
 
Originally posted by nsw
How do you solve

V(1.29)= 500000+V(0.178)

and is this really your answer?

sorry the units of density are in Kg/m^3 so the equation will be

(1.29-0.178)V=500

V=450 m3
 
Where does the 500 come from?
 
isn't it the weight of the payload
 
Oh Yah! Thanks a Bunch!
 
  • #10
New problem

The values:
Balloon diameter : 100 feet
Balloon weight : 10,000 pounds
Payload weight : 6,000 pounds
Lifting gas : Helium
Air density at ground level : .0625 lbs/cubic foot
Temperature is constant

At what altitude does the balloon fly?

So far I've got:
h = alpha [0.862 - (16,000 lbs/ mass of air)]

I'm not even sure what the variables are, I was given 47 different formulas to determine the answer to this question, none of which are helping whatsoever.
 
Last edited:
  • #11
footos66 said:
The values:
Balloon diameter : 100 feet
Balloon weight : 10,000 pounds
Payload weight : 6,000 pounds
Lifting gas : Helium
Air density at ground level : .0625 lbs/cubic foot
Temperature is constant

At what altitude does the balloon fly?

So far I've got:
h = alpha [0.862 - (16,000 lbs/ mass of air)]

I'm not even sure what the variables are, I was given 47 different formulas to determine the answer to this question, none of which are helping whatsoever.
use bouyancy formula.
 
  • #12
Which is:

mass of air (at Height, h) = [mass of payload+mass of balloon+mass of lifting gas]

is that the right one?
 
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