Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

remaining part of the energy released shows up as the kinetic energy of the
exhaust gases relative to a fixed point on the ground and as an increase in
the enthalpy of the gases leaving the engine.

Chapter 9 | 523

EXAMPLE 9–9 The Ideal Jet-Propulsion Cycle

A turbojet aircraft flies with a velocity of 850 ft/s at an altitude where the air is

at 5 psia and 40°F. The compressor has a pressure ratio of 10, and the tem-

perature of the gases at the turbine inlet is 2000°F. Air enters the compressor

at a rate of 100 lbm/s. Utilizing the cold-air-standard assumptions, determine

(a) the temperature and pressure of the gases at the turbine exit, (b) the veloc-

ity of the gases at the nozzle exit, and (c) the propulsive efficiency of the cycle.

Solution The operating conditions of a turbojet aircraft are specified. The

temperature and pressure at the turbine exit, the velocity of gases at the

nozzle exit, and the propulsive efficiency are to be determined.

Assumptions 1 Steady operating conditions exist. 2 The cold-air-standard

assumptions are applicable and thus air can be assumed to have constant

specific heats at room temperature (cp
0.240 Btu/lbm · °F and k
1.4).

3 Kinetic and potential energies are negligible, except at the diffuser inlet

and the nozzle exit. 4 The turbine work output is equal to the compressor

work input.

Analysis The T-sdiagram of the ideal jet propulsion cycle described is shown

in Fig. 9–50. We note that the components involved in the jet-propulsion

cycle are steady-flow devices.

(a) Before we can determine the temperature and pressure at the turbine

exit, we need to find the temperatures and pressures at other states:

Process 1-2(isentropic compression of an ideal gas in a diffuser): For con-

venience, we can assume that the aircraft is stationary and the air is moving

toward the aircraft at a velocity of V 1 
850 ft/s. Ideally, the air exits the

diffuser with a negligible velocity (V 2 
0):

Process 2-3(isentropic compression of an ideal gas in a compressor):

T 3 
T 2 a

P 3

P 2

b

1 k 1 2>k


 1 480 R 211021 1.4^1 2>1.4
927 R

P 3 
 1 rp 21 P 22 
 11021 8.0 psia 2 
80 psia 1 
 P 42

P 2 
P 1 a

T 2

T 1

b

k>1k 12


 1 5 psia2a

480 R

420 R

b

1.4>11.4 12


8.0 psia

480 R

420 R

1 850 ft>s 22

21 0.240 Btu>lbm#R 2

a

1 Btu>lbm

25,037 ft^2 >s^2

b

T 2 
T 1 

V^21

2 cp

0 
cp 1 T 2 T 12 

V 12

2

h 2 

V 22

2

h 1 

V^21

2

P = const.

P = const.

s

T, °F

qin

qout

6

5

4

3

2

2000

–40 1

FIGURE 9–50

T-sdiagram for the turbojet cycle

described in Example 9–9.

0

¡