5.2. Derive an expression for the degree of reaction of an axial compressor stage in terms of the flow angles relative to the rotor and the flow coefficient. Data obtained from early cascade tests suggested that the limit of efficient working of an axial-flow compressor stage occurred when (i) a relative Mach number of 0.7 onto the rotor is reached; (ii) the flow coefficient is 0.5; (iii) the relative flow angle at rotor outlet is 30 deg measured from the axial direction; (iv) the stage reaction is 50%. Find the limiting stagnation temperature rise which would be obtained in the first stage of an axial compressor working under the above conditions and compressing air at an inlet stagnation temperature of 289 K. Assume the axial velocity is constant across the stage.