The eye of a centrifugal compressor has a hub - tip radius ratio of 0.4, a maximum relative flow Mach number of 0.9, and an absolute flow that is uniform and completely axial. Determine the optimum speed of rotation for the condition of maximum mass flow given that the mass flow rate is 4.536 kg/s. Also, determine the outside diameter of the eye and the ratio of axial velocity blade speed at the eye tip. Figure 7.12 may be used to assist the calculations.