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

872 | Thermodynamics

(b) The velocity of sound and the Mach numbers at the throat and the exit

of the nozzle are determined by replacing differential quantities with

differences,

The velocity of sound at the throat is determined by evaluating the specific

volume at st
7.1292 kJ/kg · K and at pressures of 1.115 and 1.065 MPa

(Pt 25 kPa):

The Mach number at the throat is determined from Eq. 17–12 to be

Thus, the flow at the throat is sonic, as expected. The slight deviation of

the Mach number from unity is due to replacing the derivatives by

differences.

The velocity of sound and the Mach number at the nozzle exit are deter-

mined by evaluating the specific volume at s 2 
7.2019 kJ/kg · K and at

pressures of 325 and 275 kPa (P 2

 25 kPa):

and

Thus the flow of steam at the nozzle exit is supersonic.

Ma

V

c

929.8 m>s

515.4 m>s

1.804

c


B

1325  2752 kPa

11 >0.63596 1 >0.72245 2 kg>m^3

a

1000 m^2 >s^2

1 kPa#m^3 >kg

b
515.4 m>s

Ma

V

c

585.8 m>s

584.6 m>s

1.002

c


B

11115  10652 kPa

11 >0.23776 1 >0.24633 2 kg>m^3

a

1000 m^2 >s^2

1 kPa#m^3 >kg

b
584.6 m>s

c
a

0 P

0 r

b

1 > 2

s

c

¢P

¢ 11 >v 2

d

1 > 2

s

SUMMARY

In this chapter the effects of compressibility on gas flow are

examined. When dealing with compressible flow, it is conve-

nient to combine the enthalpy and the kinetic energy of the

fluid into a single term called stagnation(or total) enthalpy

h 0 , defined as

The properties of a fluid at the stagnation state are called

stagnation propertiesand are indicated by the subscript zero.

The stagnation temperatureof an ideal gas with constant spe-

cific heats is

which represents the temperature an ideal gas would attain if

it is brought to rest adiabatically. The stagnation properties of

an ideal gas are related to the static properties of the fluid by

T 0 
T

V^2

2 cp

h 0 
h

V^2

2

The speed at which an infinitesimally small pressure wave

travels through a medium is the speed of sound. For an ideal

gas it is expressed as

The Mach numberis the ratio of the actual velocity of the

fluid to the speed of sound at the same state:

The flow is called sonicwhen Ma 
1,subsonicwhen Ma 1,

supersonicwhen Ma 1,hypersonicwhen Ma 1, and

transonicwhen Ma 
1.

Ma

V

c

c


B

a

0 P

0 r

b

s

 2 kRT

P 0

P

a

T 0

T

b

k>1k 12

¬and¬

r 0

r

a

T 0

T

b

1 >1k 12

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