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

The conservation of energy principle (Eq. 17–31) requires that the stagna-

tion enthalpy remain constant across the shock; h 01 
h 02. For ideal gases

h
h(T), and thus

(17–34)

That is, the stagnation temperature of an ideal gas also remains constant

across the shock. Note, however, that the stagnation pressure decreases

across the shock because of the irreversibilities, while the thermodynamic

temperature rises drastically because of the conversion of kinetic energy

into enthalpy due to a large drop in fluid velocity (see Fig. 17–32).

We now develop relations between various properties before and after the

shock for an ideal gas with constant specific heats. A relation for the ratio of

the thermodynamic temperatures T 2 /T 1 is obtained by applying Eq. 17–18

twice:

Dividing the first equation by the second one and noting that T 01 
T 02 ,we

have

(17–35)

From the ideal-gas equation of state,

Substituting these into the conservation of mass relation r 1 V 1 
r 2 V 2 and

noting that Ma 
V/cand , we have

(17–36)

T 2

T 1

P 2 V 2

P 1 V 1

P 2 Ma 2 c 2

P 1 Ma 1 c 1

P 2 Ma 22 T 2

P 1 Ma 12 T 1

a

P 2

P 1

b

2

a

Ma 2

Ma 1

b

2

c
 1 kRT

r 1 

P 1

RT 1

¬and¬r 2

P 2

RT 2

T 2

T 1

1 Ma^211 k 1 2> 2

1 Ma^221 k 1 2> 2

T 01

T 1

 1 a

k 1

2

bMa^21 ¬and¬

T 02

T 2

 1 a

k 1

2

bMa^22

T 01 
T 02

Chapter 17 | 847

Ma = 1

0

s

SHOCK

WA

VE

Subsonic flow

h

h

a

h 01

1

1

2

2

= h 02

h 01 h 02

P^02

P^01

b Ma = 1

V

2

2

2

(^2)
(Ma < 1)
Supersonic flow
h (Ma^ > 1)
1
ss
V^2
1
2
Fanno line
Rayleigh line FIGURE 17–31
The h-sdiagram for flow across a
normal shock.
Normal
shock
P
P 0
V
Ma
T
T 0
r
s
increases
decreases
decreases
decreases
increases
remains constant
increases
increases
FIGURE 17–32
Variation of flow properties across a
normal shock.
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