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

Converging–Diverging Nozzles

When we think of nozzles, we ordinarily think of flow passages whose

cross-sectional area decreases in the flow direction. However, the highest

velocity to which a fluid can be accelerated in a converging nozzle is limited

to the sonic velocity (Ma 
1), which occurs at the exit plane (throat) of the

nozzle. Accelerating a fluid to supersonic velocities (Ma 1) can be accom-

plished only by attaching a diverging flow section to the subsonic nozzle at

the throat. The resulting combined flow section is a converging–diverging

nozzle, which is standard equipment in supersonic aircraft and rocket propul-

sion (Fig. 17–26).

Forcing a fluid through a converging–diverging nozzle is no guarantee

that the fluid will be accelerated to a supersonic velocity. In fact, the fluid

may find itself decelerating in the diverging section instead of accelerating

if the back pressure is not in the right range. The state of the nozzle flow is

determined by the overall pressure ratio Pb/P 0. Therefore, for given inlet

conditions, the flow through a converging–diverging nozzle is governed by

the back pressure Pb, as will be explained.

Chapter 17 | 841

Solution Nitrogen gas enters a converging nozzle. The properties at the

nozzle exit are to be determined.

Assumptions 1 Nitrogen is an ideal gas with k
1.4. 2 Flow through the

nozzle is steady, one-dimensional, and isentropic.

Analysis The schematic of the duct is shown in Fig. 17–25. For isentropic

flow through a duct, the area ratio A/A* (the flow area over the area of the

throat where Ma 
 1) is also listed in Table A–32. At the initial Mach

number of Ma 1 
0.3, we read

With a 20 percent reduction in flow area, A 2 
0.8A 1 , and

For this value of A 2 /A* from Table A–32, we read

Here we chose the subsonic Mach number for the calculated A 2 /A* instead

of the supersonic one because the duct is converging in the flow direction

and the initial flow is subsonic. Since the stagnation properties are constant

for isentropic flow, we can write

which are the temperature and pressure at the desired location.

Discussion Note that the temperature and pressure drop as the fluid accel-

erates in a converging nozzle.

P 2

P 1

P 2 >P 0

P 1 >P 0

S P 2 
P 1 a

P 2 >P 0

P 1 >P 0

b
 1 100 kPa2a

0.8993

0.9395

b
95.7 kPa

T 2

T 1

T 2 >T 0

T 1 >T 0

S T 2 
T 1 a

T 2 >T 0

T 1 >T 0

b
 1 400 K2a

0.9701

0.9823

b
395 K

T 2

T 0

0.9701

P 2

P 0

0.8993 Ma 2 
0.391

A 2

A*

A 2

A 1

A 1

A*

 1 0.8 21 2.0351 2 
1.6281

A 1

A*

2.0351

T 1

T 0

0.9823¬

P 1

P 0

0.9395

A 1

P 1 = 100 kPa

T 1 = 400 K

Ma 1 = 0.3

P 2

T 2

Ma 2

N 2

Nozzle

A 2 = 0.8A 1

FIGURE 17–25

Schematic for Example 17–6 (not to

scale).

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