Problem $2$:

Consider a and axial compressor with tip radius of $0\mathrm{.}3$ m $.$ Air enters the stage axially $($no rotation$)$ at $140\frac{m}{s}$ with a total temperature of $230C$ and a total pressure of $390$ kPa $.$ The design limit of relative Mach number at the tip is $0\mathrm{.}82$ and the allowable air deflection angle is $15$ while the stage efficiency is $85\%.$ Assume the compressor is operating at deign condition with work done factor of $0\mathrm{.}87$ with $Cp=1\mathrm{.}02k\frac{J}{k}gK,R=0\mathrm{.}287k\frac{J}{k}gK$ and $=1\mathrm{.}38,$ find:

a$)$ The maximum rotational speed of the rotor and blade angles at leading ant trailing edges.

b$)$ The maximum pressure ratio.

c$)$ The degree of reaction.

d$)$ Consider free vortex mode at rotor exit, find the design angles and degree of reaction at the hub for hub to tip ratio of $0\mathrm{.}8.$

e$)$ The required power input to the stage.

f$)$ If the relative Mach number limit at the tip is increased to $0\mathrm{.}83$ what will be to total pressure ratio and the required power input.

For all problems draw the blade cross section using NACA $4$ digit airfoil generator and the velocity triangles.