A hydro$-$storage plant has a generator$-$motor efficiency of $92\%,$ turbine mechanical efficiency

of $83\mathrm{.}5\%$ and a pump mechanical efficiency of $75\%.$ The average elevation between the upper

pool and lower is $98$ m $,$ the volume flowrate in the penstock is $26\mathrm{.}5\frac{m^3}{s}$ and the length and

diameter of the penstock are $125$ m and $1\mathrm{.}8$ m respectively. The rated power output of the plant

is $24,000kW,$ with a plant use factor of $72\%,$ serving for a $1\mathrm{.}5-$hour peak load. The leakage loss

at the penstock is $33\frac{m^3}{m}in$ and the daily evaporation loss at the upper pool is negligible. Solve

the following.

a$)$ Head loss at the penstock when working as a turbine $(f=0\mathrm{.}02),$ m

b$)$ The overall turbine efficiency, $\%$

c$)$ Head loss at the penstock when working as a pump $(f=0\mathrm{.}02),m$

d$)$ Electrical power to pump back the water to the upper pool for $1\mathrm{.}75$ hrs$.,$ kW

e$)$ Conversion Efficiency, $\%$