Problem $2($D&H Problem $7\mathrm{.}2)$

The air entering the impeller of a centrifugal compressor has an absolute axial velocity of $100\frac{m}{s}.$ At rotor exit the relative air angle measured from the radial direction is $26{36}^{\text{'}},$ the radial component of velocity is $120\frac{m}{s},$ and the tip speed of the radial vanes is $500\frac{m}{s}.$ Determine the power required to drive the compressor when the air flow rate is $2\mathrm{.}5k\frac{g}{s}$ and the mechanical efficiency is $95\%.$ If the radius ratio of the impeller eye is $0\mathrm{.}3,$ calculate a suitable inlet diameter assuming the inlet flow is incompressible. Determine the overall total pressure ratio of the compressor when the total$-$to$-$total efficiency is $80\%,$ assuming the

velocity at exit from the diffuser is negligible. Answers: a$)579$kW b$)169$ mm c$)50\mathrm{.}0$