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

stagnation pressure, stagnation density, etc.). The stagnation state and the

stagnation properties are indicated by the subscript 0.

The stagnation state is called the isentropic stagnation statewhen the

stagnation process is reversible as well as adiabatic (i.e., isentropic). The

entropy of a fluid remains constant during an isentropic stagnation process.

The actual (irreversible) and isentropic stagnation processes are shown on

the h-sdiagram in Fig. 17–4. Notice that the stagnation enthalpy of the fluid

(and the stagnation temperature if the fluid is an ideal gas) is the same for

both cases. However, the actual stagnation pressure is lower than the isen-

tropic stagnation pressure since entropy increases during the actual stagna-

tion process as a result of fluid friction. The stagnation processes are often

approximated to be isentropic, and the isentropic stagnation properties are

simply referred to as stagnation properties.

When the fluid is approximated as an ideal gaswith constant specific

heats, its enthalpy can be replaced by cpTand Eq. 17–1 can be expressed as

or

(17–4)

Here T 0 is called the stagnation(or total) temperature,and it represents

the temperature an ideal gas attains when it is brought to rest adiabatically.

The term V^2 /2cpcorresponds to the temperature rise during such a process

and is called the dynamic temperature.For example, the dynamic temper-

ature of air flowing at 100 m/s is (100 m/s)^2 /(2 1.005 kJ/kg ·K) 
5.0 K.

Therefore, when air at 300 K and 100 m/s is brought to rest adiabatically (at

the tip of a temperature probe, for example), its temperature rises to the

stagnation value of 305 K (Fig. 17–5). Note that for low-speed flows, the

stagnation and static (or ordinary) temperatures are practically the same.

But for high-speed flows, the temperature measured by a stationary probe

placed in the fluid (the stagnation temperature) may be significantly higher

than the static temperature of the fluid.

The pressure a fluid attains when brought to rest isentropically is called

the stagnation pressureP 0. For ideal gases with constant specific heats,P 0

is related to the static pressure of the fluid by

(17–5)

By noting that r
1/vand using the isentropic relation , the

ratio of the stagnation density to static density can be expressed as

(17–6)

When stagnation enthalpies are used, there is no need to refer explicitly to

kinetic energy. Then the energy balance for a single-stream,

steady-flow device can be expressed as

qinwin 1 h 01 gz 12 
qoutwout 1 h 02 gz 22 (17–7)

E

#

in
E

#

out

r 0

r

a

T 0

T

b

1 >1k 12

Pvk
P 0 v 0 k

P 0

P

a

T 0

T

b

k>1k 12

T 0 
T

V^2

2 cp

cpT 0 
cpT

V^2

2

Chapter 17 | 825

FIGURE 17–3

Kinetic energy is converted to

enthalpy during a stagnation process.

© Reprinted with special permission of King

Features Syndicate.

s

Actual state

h

Isentropic

stagnation

state

P^0

P^0 ,act

Actual

stagnation

state

h

V^2

0

h

P

2

FIGURE 17–4

The actual state, actual stagnation

state, and isentropic stagnation state

of a fluid on an h-sdiagram.

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