The first stage of an axial compressor is designed on free vortex princi- ples, with no inlet guide vanes. The rotational speed is 6000 rev/min and the stagnation temperature rise is 20 K. The hub-tip ratio is 0.60, the work done factor is 0.93 and the isentropic efficiency of the stage is 0.89. Assuming an inlet velocity of 140 m/s and ambient conditions of 1.01 bar and 288 K, calculate (i) the tip radius and corresponding rotor air angles ẞ1 and 2, if the Mach number relative to the tip is limited to 0.95, (ii) the mass flow entering the stage, (iii) the stage stagnation pressure ratio and power input, and (iv) the rotor air angles at the root section. Take R = 0.287 kJ/kg K, Cp = 1.005 kJ/kg K and y = 1.4.