Question

A turbojet aircraft flies with a velocity of 800 ft/s at an altitude where the air is at 10 psia and 20 F. The compressor has a pressure ratio of 8, and the temperature of the gases at the turbine inlet is 2200 F. Utilizing the air-standard assumptions, determine (a) the temperature and pressure of the gases at every point of the cycle, (b) the velocity of the gases at the nozzle exit

Answer 1

a) The temperature and pressure of the gases at every point of the cycle are

T = 38.23 K

P = 2.91 kpa

Respectively

b) The velocity V of the gasses at the nozzle exit = 3590 m/s

Explanation: Please find the attached files for the solutions

Answer 2

Pressure = 115.6 psia

Step-by-step explanation:

Given:

v=800ft/s

Air temperature = 10 psia

Air pressure = 20F

Compression pressure ratio = 8

temperature at turbine inlet = 2200F

Conversion:

1 Btu =775.5 ft lbf,
`g_(c)` = 32.2 lbm.ft/lbf.s², 1Btu/lbm=25037ft²/s²

Air standard assumptions:

`c_(p)`= 0.0240Btu/lbm.°R, R = 53.34ft.lbf/lbm.°R = 1717.5ft²/s².°R 0.0686Btu/lbm.°R

k= 1.4

Energy balance:

`h_(1) + (v_(1) ^(2) )/(2) = h_(a) + (v_(a) ^(2) )/(2)\\`

As enthalpy exerts more influence than the kinetic energy inside the engine, kinetic energy of the fluid inside the engine is negligible

hence
`v_(a) ^(2) = 0`

`h_(1) + (v_(1) ^(2) )/(2) = h_(a) \\h_(1) -h_(a) = - (v_(1) ^(2) )/(2) \\ c_(p) (T_(1) -T_(a))= - (v_(1) ^(2) )/(2) \\(T_(1) -T_(a)) = - (v_(1) ^(2) )/(2c_(p) )\\ T_(a)=T_(1) + (v_(1) ^(2) )/(2c_(p) )`

`T_(1)` = 20+460 = 480°R

`T_(a) =480+ ((800)(800)/(2(0.240)(25037)`= 533.25°R

Pressure at the inlet of compressor at isentropic condition

`P_(a ) =P_(1)((T_(a) )/(T_(1) )) ^(k/(k-1))`

`P_(a)` =
`(10)((533.25)/(480)) ^(1.4/(1.4-1))`= 14.45 psia

`P_(2)= 8P_(a) = 8(14.45) = 115.6 psia`