a) In the usual notations show that the expression for the degree of reaction of a repeating turbine stage is : C. R = (tan B3 - tan B) 2U [6 marks] b) An axial flow turbine stage is designed in this way to supply 6 MW to a compressor with a rotational speed of 7500 r.p.m, transmission losses being negligible. Blading with R = 0.55 and a loading coefficient of y =1.70 for a flow coefficient >=1.30 has been identified. 1- Calculate the mean blade speed and the mean blade radius if the mass flow rate through the stage is 80 kg/s; [3 marks] 2- Determine all the gas angles at the mean radius, and draw the nozzle (stator) and rotor blades, together with the velocity triangles; [9 Marks] 3- Calculate the torque in the shaft; [3 marks] 4- Write down the main assumptions that are being made in arriving at free-vortex design of the axial flow turbines and compressors. [4 marks]