An aircraft is flying at Mach 095 at an altitude where the p

An aircraft is flying at Mach 0.95 at an altitude where the pressure is 30 kPa and the temperature is -50 C. The diffuser at the intake to the engine decreases the Mach number to 0.3 at the inlet of the engine. Find the pressure and temperature at the inlet of the engine.

Solution

M1 = 0.95, p1 = 30 kPa, T1 = -50 oC = 223 K and M2 = 0.3

At M1 = 0.95: T₀/T₁ = 1.181 and p₀/p₁ = 1.787 and

At M2 = 0.3: T₀/T₂ = 1.018 and p₀/p₂ = 1.064

The pressure and temperature at the inlet to the engine are:

p₂₌(p₀/p₁)*(p₂/p₀)*p₁₌ (1.787/1)*(1/1.064)*(30)=50.39kPa

T_{2 =} (T0/T1)*(T2/T0)*T1 = (1.181/1)*(1/1.081)*(223)= 258.7K= -14.29^{0 C}