In an aircraft jet engine at takeoff, the combustion products expand adiabatically in the exhaust nozzle. At entrance to the nozzle, the pressure is

0.180MPa

and the temperature is

1200K

. The kinetic energy of the gas entering the nozzle is very much smaller than the kinetic energy of the gas leaving the nozzle.\ The specific heat of the exhaust gas varies with temperature approximately as follows:\

c_(p)=0.959+1.16\\\\times 10^(-4)T+3.65\\\\times 10^(-8)T^(2),

\ in which the units of

c_(p)

are

k(J)/(k)g*K

and

T

is the temperature in

K

. The molecular weight of the exhaust gas is 30 .\ Supposing the expansion to be frictionless (reversible) as well as adiabatic, show how the exhaust velocity and pressure will depend on the exhaust temperature for a series of values: 1100,1000 , and

900K

. At each temperature determine also the speed of sound

\\\\sqrt(\\\\gamma RT)

.

4. In an aircraft jet engine at takeoff, the combustion products expand adiabatically in the exhaust nozzle. At entrance to the nozzle, the pressure is 0.180MPa and the temperature is 1200K. The kinetic energy of the gas entering the nozzle is very much smaller than the kinetic energy of the gas leaving the nozzle. The specific heat of the exhaust gas varies with temperature approximately as follows: cp=0.959+1.16104T+3.65108T2, in which the units of cp are kJ/kgK and T is the temperature in K. The molecular weight of the exhaust gas is 30 . Supposing the expansion to be frictionless (reversible) as well as adiabatic, show how the exhaust velocity and pressure will depend on the exhaust temperature for a series of values: 1100,1000 , and 900K. At each temperature determine also the speed of sound RT