Rotating Cylinder - Understanding Gas Pressure and Density

[Johnsson]

Hi,

I have a cylindrical container of gas that is rotating about the axis (of symmetry).
I'm trying to understand and calculate what is happening to the atmosphere inside.

Obviously, as the cylinder accelerates up to speed, the gas will also accelerate and eventually get to the same speed as the container (I have baffles to help this) and the gas will be more compressed/dense against the inside surface and less dense at the axis.

I'm wanting to get some idea of the pressure and density of the air at various points (inside surface and axis).
I can't use standard formulas that relate to a constant gravity/density (Pres.=Density x g x height) due to the fact that the artificial gravity/centripetal force created by the rotation is not constant across the radius of the cylinder and therefore the density also changes.The two scenarios I am looking at are -

1) a sealed cylinder i.e. fixed volume of gas - Is there any effect on the calculation if the rotational speed is such that the axis is under vacuum?

2) a cylinder with a hole at the axis i.e. gas can flow into cylinder as it accelerates up to speed. - I guess we can assume that gas pressure at the axis is constant at 1 atmosphere (ambient)

rough parameters I'm working with are
Cylinder volume - 1 litre
Cylinder radius - 0.05m
Rot speed - 2000 rpm
Air is at standard room temp and pressure

 

[Johnsson]

how about if I substitute F=mw^2r into the P=dgh formula.

P=dmw^2r^2

Can I use this for gas pressure calculation in this case.

Please not this is not a hypothetical question or an academic problem but rather a scenario in our work environment.