A turbofan jet engine operates at a flight speed of M a = 0.7 and the ambient conditions are T a = 300 K and p a = 1 atm. The axial fan has no stator ahead of  the rotor, and the average radius of the...

A turbofan jet engine operates at a flight speed of M_a
= 0.7 and the ambient conditions are T_a
= 300 K and p_a
= 1 atm. The axial fan has no stator ahead of  the rotor, and the average radius of the fan blade is r_av
= 0.7 m and it rotates at 3600 RPM [γ = 1.4, c_p
= 0.24, R = 286.78 (m/s)²/K].

(a) Assuming η = 1.0 and the inlet area ratio is A_a/A₂
= 0.63 (A₂
is ahead of the fan and A_a
is in the free stream), calculate the axial velocity ahead of the fan blade.

(b) If the pressure coefficient of the fan rotor blade is C_p
= 0.55, calculate the stagnation pressure ratio p₀₃/p_0a
for the fan (for simplicity, assume η_stage
= 1.0).