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

Isentropic Efficiency of Nozzles

Nozzles are essentially adiabatic devices and are used to accelerate a fluid.
Therefore, the isentropic process serves as a suitable model for nozzles. The
isentropic efficiency of a nozzleis defined as the ratio of the actual kinetic
energy of the fluid at the nozzle exit to the kinetic energy value at the exit of
an isentropic nozzle for the same inlet state and exit pressure. That is,

(7–66)

Note that the exit pressure is the same for both the actual and isentropic
processes, but the exit state is different.
Nozzles involve no work interactions, and the fluid experiences little or
no change in its potential energy as it flows through the device. If, in addi-
tion, the inlet velocity of the fluid is small relative to the exit velocity, the
energy balance for this steady-flow device reduces to

Then the isentropic efficiency of the nozzle can be expressed in terms of
enthalpies as

(7–67)

where h 2 aand h 2 sare the enthalpy values at the nozzle exit for the actual
and isentropic processes, respectively (Fig. 7–54). Isentropic efficiencies of
nozzles are typically above 90 percent, and nozzle efficiencies above 95
percent are not uncommon.

hN

h 1 h 2 a

h 1 h 2 s

h 1 h 2 a

V 22 a¬¬

2

hN

Actual KE at nozzle exit

Isentropic KE at nozzle exit



V 22 a

V 22 s

Chapter 7 | 375

(b) The required power input to the compressor is determined from the energy

balance for steady-flow devices,

Discussion Notice that in determining the power input to the compressor, we

used h 2 ainstead of h 2 ssince h 2 ais the actual enthalpy of the air as it exits

the compressor. The quantity h 2 sis a hypothetical enthalpy value that the air

would have if the process were isentropic.

58.0 kW

 1 0.2 kg>s 231 575.03285.14 2 kJ>kg 4

W

#

a,inm

# 1 h

2 ah 12

m

#

h 1 
W

#

a,inm

#

h 2 a

E

#

inE

#

out^

EXAMPLE 7–16 Effect of Efficiency on Nozzle Exit Velocity

Air at 200 kPa and 950 K enters an adiabatic nozzle at low velocity and is

discharged at a pressure of 80 kPa. If the isentropic efficiency of the nozzle

is 92 percent, determine (a) the maximum possible exit velocity, (b) the exit

temperature, and (c) the actual exit velocity of the air. Assume constant

specific heats for air.

h 2 s

h

s

h^1

1

h 2 a

2 s^2 a

P 2

P 1

Inlet state

Actual process

Isentropic process

s 2 s = s 1

Exit

pressure

V^22 a

2

V^22 s

2

FIGURE 7–54

The h-sdiagram of the actual and

isentropic processes of an adiabatic

nozzle.