Would not the speed of such an auxiliary drive steam turbine be a function of the load it is driving, and probably also the inertia of the rotating shaft system, all balanced by its governor control as set by demand control signal?
In the last two months you have probably tried it, but...
I have returned to my office at Monash University in Australia, and can now look up my notes.
At a pump conference in London, I found this empirical formular developed in the South African mining industry, and have changed it into SI units. It applies for water at up to 54 degC:
Efficiency =...