$(40$ points$)$ As shown in the picture, a hydraulic turbine$-$generator is generating $66$ kW of electric power while lake water at a rate of $0\mathrm{.}18\frac{m^3}{s}$ passing through it between two locations at the same pressure. Density of the lake water is $=1050k\frac{g}{m^3}.$ The elevation difference between locations $is50m.$ Diameters of the inlet and outlet pipes of the turbine are $20$ cm and $14$ cm $,$ respectively. If the the power on the shaft of the turbine is $72$ kW and efficiency of the turbine is $\%90,$ determine:

$($a$)$ the loss in pipes in kW $,$

$($b$)$ efficiency of the turbine$-$generator.