The front of an airplane jet engine is a DIFFUSER, Calculate the pressure and temperature produced by a jet engine Solution At inlet, P1=14.7 psi = 101.35 kpa ; T1 =80 F = 299.82 K; V1 = 409 miles/hr=182.84 m/s V2=60 ft/sec = 18.29 m/s mass flow rate is constant rho1*A1*V1 = rho2*A2*V2 rho = P/(R_a*T) where P is pressure, R_a is gas constant, T is temperature. rho1 = 101.35*1000/(287*299.82) = 1.178 kg/m^3 and A2 = 0.9*A1 hence 1.178*A1*182.84 = rho2*0.9*A1*18.29 rho2 = 13.08 kg/m^3 from energy conservation h+v^2/2 = constant h1+V1^2/2 = h2+V2^2/2 Cp*(T2-T1) = (V1^2-V2^2)/2 = 182.84^2/2 - 18.29^2/2 1005*(T2-T1) = 16547.97 T2 = 316.28 K rho2 = P2/R_a*T2 = 13.08 P2 = 287*316.28*13.08 = 1187.32 kpa or T2 = 109.63 F P2 = 172.2 psi .

1. The front of an airplane jet engine is a DIFFUSER, Calculate the pressure and temperature
produced by a jet engine
Solution
At inlet, P1=14.7 psi = 101.35 kpa ; T1 =80 F = 299.82 K; V1 = 409 miles/hr=182.84 m/s
V2=60 ft/sec = 18.29 m/s
mass flow rate is constant
rho1*A1*V1 = rho2*A2*V2
rho = P/(R_a*T) where P is pressure, R_a is gas constant, T is temperature.
rho1 = 101.35*1000/(287*299.82) = 1.178 kg/m^3
and A2 = 0.9*A1
hence
1.178*A1*182.84 = rho2*0.9*A1*18.29
rho2 = 13.08 kg/m^3
from energy conservation
h+v^2/2 = constant
h1+V1^2/2 = h2+V2^2/2
Cp*(T2-T1) = (V1^2-V2^2)/2 = 182.84^2/2 - 18.29^2/2
1005*(T2-T1) = 16547.97

2. T2 = 316.28 K
rho2 = P2/R_a*T2 = 13.08
P2 = 287*316.28*13.08 = 1187.32 kpa
or
T2 = 109.63 F
P2 = 172.2 psi