-


work;

I wish to have some understanding of the atmospheric dynamics of a space habitat of a given size.


-

There are two equations you need. First, I'm sure you're familiar with the formula for centrifugal force, the surrogate for gravity in this situation: rw^2 is the equivalent of our "g" here on earth. But g is nearly constant throughout the earth's atmosphere, whereas rw^2
increases linearly across the radius of the cylinder.  

Translated into terms of energy: the potential energy of a particle on earth is given by mgh, but in your space cylinder there's a pseudo-potential that can be found by integrating rw^2 to give

-(1/2)mr^2w^2.

The second equation you need is less familiar: At a constant
temperature T, the density of molecules in a region where their energy is E is proportional to the Boltzmann factor exp(-E/kT). In this situation, I believe you can get away with using our pseudopotential formula for E, and substituting

    E = -(1/2)mr^2w^2

into the Boltzmann factor.

So the pressure as a function of radius within the cylinder is
proportional to

    exp((mr^2w^2)/(2kT))

where m is the mass of a molecule of gas and kT is the Boltzmann
constant times temperature.

For practical values of r and w, the difference in pressure from axis to rim of the cylinder is negligible. But if r and w are very large, you can use the above to predict pressure as a function of radius. (To actually get numbers out of the formula, you will need to normalize your values with an integral of the function exp((mr^2w^2)/(2kT)) over a finite range of radii; it looks like an un-doable integral, akin to the standard error function, but in fact there's a geometric factor of r in the integral that makes it easy.



-