An axial-flow turbine stage is to be designed for free-vortex conditions at exit from the nozzle row and for zero swirl at exit from the rotor. The gas entering the stage has a stagnation temperature of 1000 K, the mass flow rate is 32 kg/s, the root and tip diameters are 0.56 m and 0.76 m, respectively, and the rotor speed is 8000 rev/min. At the rotor tip, the stage reaction is 50% and the axial velocity is constant at 183 m/s. The velocity of the gas entering the stage is equal to that leaving. Determine

a. the maximum velocity leaving the nozzles;

b. the maximum absolute Mach number in the stage;

c. the root section reaction;

d. the power output of the stage;

e. the stagnation and static temperatures at stage exit