Calculating Helium Balloon Volume for 500 kg Payload

[nsw]

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.

 

[himanshu121]

let V : Volume
a= density of air
b= density of He

we have

 V*a=500*10[sup]3[/sup]+V*b

 

[nsw]

How are you supposed to solve this equation with two unknowns?

 

[himanshu121]

only V is unknown

 

[nsw]

How do you solve

V(1.29)= 500000+V(0.178)

and is this really your answer?

 

[himanshu121]

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

 

[nsw]

Where does the 500 come from?

 

[himanshu121]

isn't it the weight of the payload

 

[nsw]

Oh Yah! Thanks a Bunch!

 

[footos66]

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.

 

[Chronos]

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.

 

[footos66]

Which is:

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

is that the right one?