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

17–5 ■ SHOCK WAVES AND EXPANSION WAVES

We have seen that sound waves are caused by infinitesimally small pressure

disturbances, and they travel through a medium at the speed of sound. We

have also seen that for some back pressure values, abrupt changes in fluid

properties occur in a very thin section of a converging–diverging nozzle

under supersonic flow conditions, creating a shock wave.It is of interest to

study the conditions under which shock waves develop and how they affect

the flow.

Normal Shocks

First we consider shock waves that occur in a plane normal to the direction

of flow, called normal shock waves.The flow process through the shock

wave is highly irreversible and cannotbe approximated as being isentropic.

Next we follow the footsteps of Pierre Lapace (1749–1827), G. F. Bern-

hard Riemann (1826–1866), William Rankine (1820–1872), Pierre Henry

Hugoniot (1851–1887), Lord Rayleigh (1842–1919), and G. I. Taylor

Chapter 17 | 845

(b) Since the flow is isentropic, the properties at the exit plane can also be

calculated by using data from Table A–32. For Ma 
2 we read

Thus,

and

The nozzle exit velocity could also be determined from Ve
Maece, where ce

is the speed of sound at the exit conditions:

(c) Since the flow is steady, the mass flow rate of the fluid is the same at all

sections of the nozzle. Thus it may be calculated by using properties at any

cross section of the nozzle. Using the properties at the throat, we find that

the mass flow rate is

Discussion Note that this is the highest possible mass flow rate that can

flow through this nozzle for the specified inlet conditions.

m

#


r*A*V*
 1 2.761 kg>m^32120  10 ^4 m^221 517.5 m>s 2 
2.86 kg/s

845.2 m>s

Ve
Maece
Mae 2 kRTe
 2

B

1 1.4 21 0.287 kJ>kg#K 21 444.5 K2a

1000 m^2 >s^2

1 kJ>kg

b

Ve
Mae*c*
 1 1.6330 21 517.5 m>s 2 
845.1 m/s

Ae
1.6875A*
 1 1.6875 21 20 cm^22 
33.75 cm^2

re
0.2300r 0 
 1 0.2300 21 4.355 kg>m^32 
1.002 kg/m^3

Te
0.5556T 0 
 1 0.5556 21 800 K 2 
444.5 K

Pe
0.1278P 0 
 1 0.1278 21 10 MPa 2 
0.1278 MPa

Pe

P 0

0.1278

Te

T 0

0.5556

re

r 0

0.2300 Ma*t
1.6330

Ae

A*

1.6875

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