$7\mathrm{.}78.$ A hydropower installation is to be located where the downstream water$-$surface elevation is $100m$ below the water$-$surface elevation in the reservoir. The $2\mathrm{.}0m-$diameter concrete$-$lined penstock is $500m$ long and has an estimated roughness height of $15mm.$ When the flow rate through the system is $20\frac{m^3}{s},$ the combined head loss in the turbine and draft tube is $5\mathrm{.}0m,$ and the average velocity in the tailrace is $0\mathrm{.}80\frac{m}{s}.$

Estimate the power that can be extracted from the system.