modeling buoyancy of a gas envelope in the atmosphere 1

[JoeFrickinFriday]

Greetings -

My background: I have a Ph.D. in mechanical engineering, so I'm well-versed in fluid mechanics, thermodynamics, and all that jazz.

I was recently involved in an online discussion regarding the extraction of mechanical work from the buoyancy of a hydrogen balloon. I took a stab at modeling atmospheric buoyancy, but I'm pretty sure I came up short.

Suppose a vessel is filled with hydrogen gas. It will be buoyant in the atmosphere, provided that the hydrogen is not compressed to the point that it's actually more dense than the surrounding atmosphere. This may happen if the vessel is rigid, or even elastic (such as a weather balloon).

In the case of a rigid vessel, the buoyancy varies as a function of altitude. The work done by the buoyant force can be calculated; if the vessel is allowed to rise (from sea level) to extreme heights (>100 km), the mechanical work done by the buoyant force is equal to the volume of the vessel times the sea-level atmospheric pressure. This can easily be shown in an Excel spreadsheet containing a model of atmospheric properties versus altitude: you can calculate the buoyancy at any altitude, the incremental buoyant work done over each step of altitude, and integrate up to any desired height.

Suppose instead that the vessel is NOT of fixed volume, and is not even elastic. Instead, suppose the vessel is an untensed gas envelope, like one of those super-high altitude balloons. At sea level it's only partially filled, leaving lots of room for expansion. With no tension in the vessel material, the hydrogen inside is allowed to expand so that it's always at ambient pressure. In this situation, how does the buoyancy of the balloon vary with altitude?

 

[ione]

Uuh, I have re-read my post: where was my head set? Probably at such an height oxygen was too scarce . Thanks Zeke