A steam turbine is driving a centrifugal water pump. Due to high water demand (summer operation), there will be a tendency for the pump to exceed its rated capacity at certain times of the day. What will happen to the turbine if the pump rated capacity is exceeded say by 25%?

 

What will happen to the steam turbine depends on what control/protection systems are installed. Unless the steam turbine is oversized with respect to the pump, a 25% overload is by far something not acceptable.

To reply to your question, if the steam turbine is equipped with a governing system (and I presume that the inlet steam valves are designed to run the steam turbine at no more than 10% overload), then when you try to load the steam turbine with 25% oveload, the steam turbine will simply slow down (energy out is more than energy in) until the trip speed is reached.

If on the other hand, the steam inlet conditions are modified to allow the steam turbine to run on overload conditions of up to 25% overload, then definitely the steam turbine will not last long. In the short term, you risk tripping due to high exhaust pressure/temperature. In the long run, you will wear out the steam turbine internals fast.

If you have already managed to run the steam turbine with a 25% overload, either you have an oversized steam turbine (with respect to the pump)without knowing or you have operated the steam turbine well off design conditions.