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

The ratio of the stagnation to static pressure is obtained by substituting
Eq. 17–18 into Eq. 17–5:

(17–19)

The ratio of the stagnation to static density is obtained by substituting
Eq. 17–18 into Eq. 17–6:

(17–20)

Numerical values of T/T 0 ,P/P 0 , and r/r 0 are listed versus the Mach number
in Table A–32 for k
1.4, which are very useful for practical compressible
flow calculations involving air.
The properties of a fluid at a location where the Mach number is unity (the
throat) are called critical properties,and the ratios in Eqs. (17–18) through
(17–20) are called critical ratios(Fig. 17–18). It is common practice in the
analysis of compressible flow to let the superscript asterisk (*) represent the
critical values. Setting Ma
1 in Eqs. 17–18 through 17–20 yields

(17–21)

(17–22)

(17–23)

These ratios are evaluated for various values of kand are listed in Table
17–2. The critical properties of compressible flow should not be confused
with the properties of substances at the critical point (such as the critical
temperature Tcand critical pressure Pc).

r*

r 0

a

2

k 1

b

1 >1k 12

P*

P 0

a

2

k 1

b

k>1k 12

T*

T 0

2

k 1

r 0

r

c 1 a

k 1

2

bMa^2 d

1 >1k 12

P 0

P

c 1 a

k 1

2

bMa^2 d

k>1k 12

Chapter 17 | 835

Subsonic

nozzle

Supersonic

nozzle

T*, P*, r*

Tt

P

r r

t

t

To

P

r

o

o

T *

P *

*

(if Mat = 1)

(Mat = 1)

Throat

Throat

FIGURE 17–18

When Mat
1, the properties at the

nozzle throat become the critical

properties.

TABLE 17–2

The critical-pressure, critical-temperature, and critical-density ratios for

isentropic flow of some ideal gases

Superheated Hot products Monatomic

steam, of combustion, Air, gases,

k
1.3 k
1.33 k
1.4 k
1.667

0.5457 0.5404 0.5283 0.4871

0.8696 0.8584 0.8333 0.7499

0.6276 0.6295 0.6340 0.6495

r*

r 0

T*

T 0

P*

P 0