[Caleb Sykes]

A cylindrical tank is filled with air with pressure p at temperature T. It has length l and radius r. There is no air flow into or out of the tank. The cylinder is then rotated in a circle such that one of the faces of the cylinder is at all times pointing directly toward the point of rotation and the other is facing away. The distance from the point of rotation to the near face is R >> r. The tank is rotated with angular velocity ω.

What is the pressure inside of the tank at any distance d perpendicular to the near face?

I know it sounds like a question from my physics textbook that I am trying to trick everyone into giving me an answer to, but I promise it is FRC related. I know that the pressure near the outside face will be greater than the pressure on the inside face, but I have no idea how one would go about calculating this.

EDIT: Assume that the rotation is happening in a horizontal plane so that gravity has no appreciable effect. I am only looking for the pressure as a function of distance from the near face, I don't care about the miniscule height differences due to gravity. I also don't believe that the value of r should change anything, but I included it anyway.