Problem # $2$

A radial inflow turbine develops $60$ kW power when running at $60000$ rpm $.$ The pressure ratio $(\frac{P_{01}}{P_3})$ of the turbine is $2\mathrm{.}0.$ The inlet total temperature is $1200$ K $.$ The rotor has an inlet tip diameter of $12$ cm and an exit tip diameter of $7\mathrm{.}5$ cm $.$ The hub$-$tip ratio at exit is $0\mathrm{.}3.$ The mass flow rate is $0\mathrm{.}35k\frac{g}{s}.$ The nozzle angle is $70$ and the rotor exit blade angle is $40.$ If the nozzle loss coefficient is $0\mathrm{.}07,$ determine the total$-$to$-$static efficiency of the turbine and the rotor loss coefficient.