$(25pts)$ Water $(=998k\frac{g}{m^3})$ flows from a higher reservoir to a lower reservoir. There is a turbinegenerator system in between which provides $45$ kW of electrical power. Reservoirs are very large and they are open to atmosphere. The free surface of the upper reservoir is $105$ m higher than that of the lower reservoir. If the flow rate of water is measured to be $0\mathrm{.}05\frac{m^3}{s},$ determine the efficiency of the turbine$-$generator system. An engineer proposed to double the flow rate in order to increase the electrical power output. Knowing that the losses in the turbine$-$generator system are going to be proportional to the square of the flow rate, how much will the efficiency of the system be affected for this case? Mechanical Engineering