Centrifugal Compressors' Thrust Load Calculation & Direction of force

It is not quite as simple as this, but the basic idea is to calculate the areas that various pressures act on. The sum of these pressures on each stage impeller minus the balance piston thrust is the total net thrust. By the way it is usually about 70 to 80% of the calculated value in multistage pumps (due to the fluid revolving in that area behind the vanes). and I would guess something similar for compressors. If you have the design calculations for the thrust bearing these thrusts will be available to you there.

This diagram is from a pump manual but the principle is the same. Assume that the discharge pressure acts across the area of the back shroud and that the suction pressure acts on the area of the suction eye. (This is not true in that the impeller is spinning as is the fluid so the pressure is not equal across the whole area.) You also need to subtract the area of the shaft.

The balance piston is just the area times the pressure on one side minus the area times the pressure on the other. The balance line will drop the pressure probably to first stage seal chamber pressure or similar area, so that the seals at either end of the compressor see roughly the same pressure which is close to suction pressure.