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 0.56m and 0.76 m respectively, and the rotor speed is 8000 rev/min. At the rotor tip the stage reaction is 50% 206 Fluid Mechanics, Thermodynamics of Turbomachinery and the axial velocity is constant at 183 m/s. The velocity of the gas entering the stage is equal to that leaving.

Determine

(i) the maximum velocity leaving the nozzles;

(ii) the maximum absolute Mach number in the stage;

(iii) the root section reaction;

(iv) the power output of the stage;

(v) the stagnation and static temperatures at stage exit.

(Take R = 0.287 kJ/(kg°C) and Cp = 1.147 kJ/(kg°C).)