[fixup34]

How large a diameter of a Helium balloon must I have to just lift a 10 lb weight?

[ebaines]

About 2.6 meters. Here's how to estimate this:

The volume of air you need to displace with the helium baloon can be calculated from the difference between the density of air and the density of helium, both at atmospherice pressureand 0 degrees C:

Density of air - see: Density of air - Wikipedia, the free encyclopedia
1.29 kg/m^3

Density of helium - see: Helium - Wikipedia, the free encyclopedia 0.1786 g/L, or 0.1786 Kg/m^3.

The lifting power of the baloon is determined by the difference in weight of the helium in the baloon versus the air it displaces. So the volume of He you need to lift 10 Kg is:

V = 10 kg / (1.29 - 0.1786 Kg/m^3) = 9 m^3 of He.

To calculate the diameter of the baloon that is 9 cubic meters in volume, use:

V = 4/3 pi R^3 = 1/6 pi D^3.

Or D = (6 * V/pi)^1/3. Plug and chug:

D = (6* 9/3.14) ^ 1/3 = 2.6 m.

This assumes that the weight of the baloon material itself is included in the 10 Kg, and that the inflation pressure of the He is 1 atmosphere. If you have to increase the pressure in the baloon in order for it to maintain its shape, then there is more weight of He and the baloon's lifting power is decreased.