Pumping fluid against a centrifugal force
I am in need of some assistance regarding a theoratical problem I have. It goes something like this:
Imagine a vertically placed axle, rotating at a constant angular velocity (omega). From the middle of this axle extends an arm and on the edge of that arm is a unit containing (amongst other things) an oil pump. The purpose of this oil pump is to pump the oil from the unit to the centre of the rotating axle (against the centrifugal force). Say that the exit pressure of the pump is 25 bar, how do I calculate the pressure drop along the oil canal in the arm (assuming zero friction in the pipe itself)? Ultimately, I would like to know the pressure reading at the centre of the rotating axle, where the centrifugal force is equal to zero.
At first, I thought I could use Bernoulli's equation for incompressible flow, but it doesn't appear to be working for me, as I get a higher pressure reading at the centre of the axle, than at the exit of the pump.