Determine Power required to drive the compressor

Question

The first axial-flow air compressor stage without inlet guide vanes is operating at a speed of 15000 r.p.m. in the atmospheric conditions of T₀ = 288 K, P_o = 1.01 bar. The rotor mean blade ring diameter is 0.34 m and hub to tip ratio is 0.5. Atmospheric air enters the stage with a velocity of 150 m/s. Consider constant axial velocity through the stage and take stage efficiency as 0.86, mechanical efficiency as 0.97, work done factor as 0.97, C_p = 1.005 kJ/kg/K and R = 0.287 kJ/kg/K. Sketching the axial compressor stage with velocity diagrams and labeling with most general notations used in practice, determine the following for attaining relative velocity ration across rotor (de Haller number) of 0.73 :

1. Mass flow rate in kg/s
2. Maximum Mach number at rotor blade at entry
3. Angles made by relative and absolute velocity at rotor entry and exit with axial direction
4. Power required to drive the compressor
5. Stage pressure ratio                                                                                                10+15