Answer
$\eta_{turbine-generator}=0.76$
$\eta_{turbine}=0.80$
$W_{t}=1962kW$
Work Step by Step
Here we are working with potential energy, so the energy that have the fluid and enters to the turbine is:
$W_{in}=mgh=5000\frac{kg}{s}*9.81\frac{m}{s^2}*50m=2452.5kW$
Since the electric power generation is $1862kW$, the overall efficiency of the turbine-generator is:
$\eta_{turbine-generator}=\frac{W_{out}}{W_{in}}=\frac{1862kW}{2452.5kW}=0.76$
The efficiency of the turbine is:
$\eta_{turbine}=\frac{0.76}{0.95}=0.80$
And the shaft power sypplied by the turbine to the generator is:
$W_{t}=2452.5kW*0.80=1962kW$
