A centrifugal compressor has an axial inlet and the outlet b

A centrifugal compressor has an axial inlet and the outlet blades at an angle such that the tangential component of the exit velocity has a value equal to 0.9 times the blade speed. The outlet radius is 30 cm and the desired pressure ratio is 3.5. The inlet stagnation temperature is T_0 = 298K. If the total-to- total efficiency eta_u of compressor is 0.8, at what angular speed does it need to be operated? [C_p = 1005 J/kg.K. gamma = 1.4, Psi = 1]

Solution

Pressure ratio = { 1+ V^2* (eta)/( Cp T0)} ^(1.4/0.4) V = tangential flow velocity

3.5 = { 1+ 0.8*0.81*U^2/(1005*298)}^(1.4/0.4)

where U blade speed

obtain 1+21.6x10^-6 U*U = 1.43

Solve for U = 140.97 m/s

N = 60*140.97/(pi*D) = 4487 rpm