We have a pump that circulates a very cold heat transfer media through the evaporator of a refrigeration machine and out to the users. The pump was mis-specified and has a much higher differential head than is required. The result is that we have to throttle the discharge valve to prevent the pump from running out on its curve and shutting the motor down on high current. We can't replace the impeller to match the process requirements so we will eventually replace the pump. The refrigeration capacity is tight and this "wasted" energy started me thinking about how much heat is being added to the system by the pump.
I understand that the inefficient power of the pump is directly converted to heat (1 minus fractional pump efficiency times the calculated hydraulic horsepower). I also understand that the frictional pressure drop in the piping and equipment downstream of the pump will be converted to heat. But now we are converting the pressure drop across the discharge valve directly into heat by the difference between the calculated hydraulic HP based on the head and flow upstream of the throttled discharge valve and the head and flow downstream of the valve. This is correct, right? My question is how much more heat is the pump adding to the system? I have read that the entire hydraulic HP of the pump will be eventually converted into heat but I don't understand that. It seems that the head required to pump the heat transfer media from the elevation of the pump discharge to the elevation of the users would be useful work and would not be converted into heat.
The differential head for any pump needs to be based on the system pressure drop plus the elevation of the highest user. But what if the highest elevation user requires only a small fraction of the total flow? Will all the energy imparted to the larger "low elevation flow" get immediately converted to heat somewhere downstream of the pump? Can someone please help me to understand?