I have never seen this done. That does not mean it has never been done. I work in a large oil refinery. We have about 20 large pumps that use balance lines to control the thrust in conjunction with a balance piston or balance disk. There is an FAQ on balance pistons / balance disks that you should read. The balance piston counters the cumulative thrust of the impellers by imposing a pressure drop across the cross-sectional area of a piston. Area times pressure differential equals force. If you change the pressure on the low pressure side of the balance piston by installing an orifice, you will change the differential pressure across the balance piston which will change the thrust force it provides. But, this creates a new problem. As the clearance in the balance piston increases, the flow through the balance line increases. The pressure drop across the orifice increases. The back pressure on the balance piston increases which reduces the thrust contribution of the balance piston. So, if you are relying on an orifice to adjust the thrust, you may have to change the orifice diameter as the clearance increases. We would not want to do that. For our pumps, the balance piston is designed to adequately balance out the thrust with new clearances and to still adequately balance out the thrust if the clearances in the balance piston are doubled. Beyond that, the pump must be overhauled to restore the clearances.
Johnny Pellin