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I need to find the gas pressure required to make a balloon take a given volume, knowing the gas densities and atmospheric pressure. Is there a typical law/correlation that can be used to approximate it ?

I imagine the main factors are the parameters of the surface (elasticity, which probably is a non-linear function of volume), but maybe I am wrong

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A balloon is comprised of surface patches that expand with hydrostatic pressure and taken on a certain shape. If the material shape and properties are known, the direct problem of finding out what shape it takes at a given pressure and thus the volume is straight forward. The inverse problem; however, isn't. In this case one would normally model the volume vs pressure numerically and then invert to give the pressure.

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