For centrifugal pumps the lower the delivery is, the lower the efficiency and hence the greater the internal energy loss converted into heat.
The formula brought by Karassik et al. in the Pump Handbook (Mc Graw-Hill) for the temperature rise in the pump due to a combination of steady state compression of the liquid flowing from suction to discharge, mechanical and liquid friction losses, internal leakage and recycles, may be expressed as follows:
[Δ]t = h/(778.cp.e)
which is larger than the rise expected following the GPSA engineering data book.
When estimating the minimum flow rate that can be maintained continuously without sustaining damage, Sulzer advises to add both above estimated temperature rises, the one -as given by Karassik- being attributed to liquid throttling in the clearance of the axial thrust balancing devices.
The sum of both rises would represent the total rise behind the balancing system, and should be considered (says Sulzer) especially when liquids are pumped at close to their vaporizing pressure.