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

Example 17–9 illustrates that the stagnation pressure and velocity

decrease while the static pressure, temperature, density, and entropy

increase across the shock. The rise in the temperature of the fluid down-

stream of a shock wave is of major concern to the aerospace engineer

because it creates heat transfer problems on the leading edges of wings and

nose cones of space reentry vehicles and the recently proposed hypersonic

space planes. Overheating, in fact, led to the tragic loss of the space shuttle

Columbiain February of 2003 as it was reentering earth’s atmosphere.

Chapter 17 | 851

The fluid properties after the shock (denoted by subscript 2) are related

to those before the shock through the functions listed in Table A–33. For

Ma 1 
2.0, we read

Then the stagnation pressure P 02 , static pressure P 2 , static temperature T 2 ,

and static density r 2 after the shock are

(b) The entropy change across the shock is

Thus, the entropy of the air increases as it experiences a normal shock,

which is highly irreversible.

(c) The air velocity after the shock can be determined from V 2 
Ma 2 c 2 ,

where c 2 is the speed of sound at the exit conditions after the shock:

(d) The mass flow rate through a converging–diverging nozzle with sonic

conditions at the throat is not affected by the presence of shock waves in

the nozzle. Therefore, the mass flow rate in this case is the same as that

determined in Example 17–7:

Discussion This result can easily be verified by using property values at the

nozzle exit after the shock at all Mach numbers significantly greater than unity.

m

#


2.86 kg/s

317 m/s

 1 0.5774 2

B

1 1.4 21 0.287 kJ>kg#K 21 750 K2a

1000 m^2 >s^2

1 kJ>kg

b

V 2 
Ma 2 c 2 
Ma 22 kRT 2

0.0942 kJ/kg#K

1 1.005 kJ>kg#K 2 ln 1 1.6875 2  1 0.287 kJ>kg#K 2 ln 1 4.5000 2

s 2 s 1 
cp ln

T 2

T 1

R ln

P 2

P 1

r 2 
2.6667r 1 
 1 2.6667 21 1.002 kg>m^32 
2.67 kg/m^3

T 2 
1.6875T 1 
 1 1.6875 21 444.5 K 2 
750 K

P 2 
4.5000P 1 
 1 4.5000 21 0.1278 MPa 2 
0.575 MPa

P 02 
0.7209P 01 
 1 0.7209 21 1.0 MPa 2 
0.721 MPa

Ma 2
0.5774¬

P 02

P 01

0.7209¬

P 2

P 1

4.5000¬

T 2

T 1

1.6875¬

r 2

r 1

2.6667

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