I think about a rotating torus (simplified tire) filled with ideal gas. Mass of gas is $m$ and molar mass is $M$. Pressure in non rotating torus is $p_0$. Temperature is constant $T$. Inner radius of torus is $r$ and outer radius is $R$.
Then the cylinder begins to rotate with angular velocity $\omega$
How can I derive difference of pressures near the wall between inner wall and outer wall? Do I need more data (for a simple model)?
If someone knows how to make it numerically, It would be also interesting for me.
I would also appreciate if someone could tell which book should I read to know more about solving such problems.