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

Isentropic Efficiencies of Compressors and Pumps

The isentropic efficiency of a compressoris defined as the ratio of the
work input required to raise the pressure of a gas to a specified value in an
isentropic manner to the actual work input:

(7–62)

Notice that the isentropic compressor efficiency is defined with the isen-
tropic work input in the numeratorinstead of in the denominator. This is
because wsis a smaller quantity than wa, and this definition prevents hC
from becoming greater than 100 percent, which would falsely imply that the
actual compressors performed better than the isentropic ones. Also notice
that the inlet conditions and the exit pressure of the gas are the same for
both the actual and the isentropic compressor.
When the changes in kinetic and potential energies of the gas being com-
pressed are negligible, the work input to an adiabatic compressor becomes
equal to the change in enthalpy, and Eq. 7–62 for this case becomes

(7–63)

where h 2 aand h 2 sare the enthalpy values at the exit state for actual and
isentropic compression processes, respectively, as illustrated in Fig. 7–51.
Again, the value of hCgreatly depends on the design of the compressor.
Well-designed compressors have isentropic efficiencies that range from 80
to 90 percent.
When the changes in potential and kinetic energies of a liquid are negligi-
ble, the isentropic efficiency of a pump is defined similarly as

(7–64)

When no attempt is made to cool the gas as it is compressed, the actual
compression process is nearly adiabatic and the reversible adiabatic (i.e.,
isentropic) process serves well as the ideal process. However, sometimes
compressors are cooled intentionally by utilizing fins or a water jacket
placed around the casing to reduce the work input requirements (Fig. 7–52).
In this case, the isentropic process is not suitable as the model process since
the device is no longer adiabatic and the isentropic compressor efficiency
defined above is meaningless. A realistic model process for compressors
that are intentionally cooled during the compression process is the
reversible isothermal process. Then we can conveniently define an isother-
mal efficiency for such cases by comparing the actual process to a
reversible isothermal one:

(7–65)

where wtand waare the required work inputs to the compressor for the
reversible isothermal and actual cases, respectively.

hC

wt

wa

hP

ws

wa



v 1 P 2 P 12

h 2 ah 1

hC

h 2 sh 1

h 2 ah 1

hC

Isentropic compressor work

Actual compressor work



ws

wa

Chapter 7 | 373

h 2 s

h

s

1

h 1

h 2 a

2 s

2 a

P 2

P 1

Inlet

state

s 2 s = s 1

wa

Exit

pressure

ws

Actual

process

Isentropic

process

FIGURE 7–51

The h-sdiagram of the actual and

isentropic processes of an adiabatic

compressor.

Air

COMPRESSOR

Cooling

water

FIGURE 7–52

Compressors are sometimes

intentionally cooled to minimize the

work input.