Question $01-$ Axial Flow Compressor

$1\mathrm{.}1$ The first stage of axial flow compressor is designed using free vortex theory. The rotational speed of the compressor is $60000$ rpm and stagnation temperature rise are $20$ K $.$ The hub to tip is $0\mathrm{.}6$ and work done factor is $0\mathrm{.}93.$ The stage has an isentropic efficiency of $0\mathrm{.}89.$ Assume inlet to be axial with velocity of $140\frac{m}{s},$ pressure $1\mathrm{.}01$ bar and temperature $288$ K $.$ If Mach number relative to tip is $0\mathrm{.}95.$

Determine

$1\mathrm{.}1\mathrm{.}1$ the blade angle at inlet $({}_1).$

$1\mathrm{.}1\mathrm{.}2$ the mass flow rate across the compressor stage.

$(5)$

$1\mathrm{.}1\mathrm{.}3$ the stage stagnation pressure ratio.

$1\mathrm{.}1\mathrm{.}4$ the rotor air angles at the root of the blade.

$1\mathrm{.}1\mathrm{.}5$ the power input of the compressor.

$20$