However, let's make a few assumptions. Perhaps this is a steam driven pump. A pump governor could be a mechanical device where the centripedal force moves a weight outward with mechanical linkage to reduct the steam flow. Perhaps the self operated regulator is a valve that uses force on the diaphragm. These can be pressure reduction to maintain the downstream pressure or pressure relieving to limit the inlet pressure.
A pump governor traditionally is a valve, very much like a remote-sensing regulator, installed on the steam line to a turbine-driven pump. The valve is actuated by sensing the outlet pressure of the pump. If the pump is making pressure greater than setpoint, the sensing line allows the pump outlet pressure into the diaphragm case of the governor and the pressure forces the valve to move toward closed until the setpoint is restored. Conversely if the pressure downstram of the pump is below setpoint, the pressure in the diaphragm is overcome by spring foce on the other side of the diaphragm, the valve opens a bit and lets more steam through to spin the turbine faster, making more pressure.
So this would be straight proportional control, and for every flowrate there would be a slightly different pressure associated.
Now in the modern world we would put a pressure transmitter on the pump discharge, run the signal thru a PID controller, outputting to an air-operated control valve on the steam line to the turbine. With a properly tuned loop, then the pressure would be dead-nuts on all the time AND your instrument techs would be dealing with familiar equipemnt...it's just a pressure control loop when it's piped up this way.
