In steam, gas and hydroelectric power plants, the device that drives the electric generator is the turbine. As the fluid passes through the turbine, work is done against the blades which are attached to the shaft. As a result, the shaft rotates and the turbine produces work.

Two adiabatic steady$-$state $($process takes place isentropically$)$ steam turbines are operating in parallel and have efficiency of $x$ as shown in the figure. The streams exiting from the turbines are blended in an adiabatic process to obtain saturated vapor in a mixing tank. Calculate the mass flow rates of inlet streams of steam passing through turbines so that the total power output of the turbines is $Y.$

Notes:

Clearly show all assumptions you make and show all individual steps for partial credits.

Exiting streams $3$ and $4$ may not be superheated steam!

Enthalpy change should be modified to actual enthalpy change after finding the actual work by using the reversible work and efficiency.

Use only the steam tables given in Smith&Van Ness&Abbott

Efficiency $($X$)$ is $83\%$ and The power output $($Y$)14900$ kW$.$