Q5. The inlet of a centrifugal compressor is fitted with free-vortex guide vanes to provide a positive prewhirl of 30° at the shroud. The inlet hub-shroud radius ratio is 0.4 and a requirement of the design is that the relative inlet Mach number, M₁. 11,rel, does not exceed 0.9. The air mass flow is 1 kg/s, the stagnation pressure and temperature are 101.3 kPa and 288 K. For air take R = 287 J/(kgK) and k = 1.4. Assuming optimum conditions at the shroud, determine (i) the rotational speed of the impeller; (ii) the inlet static density downstream of the guide vanes at the shroud and the axial velocity; (iii) the inducer tip diameter and velocity.