Consider a double-sided centrifugal compressor with the following design parameters:

Outlet diameter of impeller: 50 cm
Speed, N: 270 rev/s
Mass flow rate, m : 16.0 kg/s
Inlet stagnation temperature, T01: 288 K
Inlet stagnation pressure, p01: 1.01 bar
Isentropic eciency of impeller only,c : 0.9
Radial gap of vaneless space: 4.0 cm
Axial depth of vaneless space: 5.0 cm
Slip factor, σ: 0.9
Power input factor, : 1.04

Calculate the following:

1) The stagnation pressure, p02 and stagnation temperature, T02 at the outlet of the impeller, assuming no pre-whirl (i.e., Cw 1 = 0).

2) Show that the radial outlet velocity at the impeller tip is about 96 m/s and hence find the Mach number and air leaving angle at the impeller tip. Neglect the thickness of the impeller disk when calculating areas.

3) Assuming isentropic diffusion in vaneless space, find the correct angle of the leading edges of the diffuser vanes, and also find the Mach number at this radius.