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

Isentropic efficiencies are defined differently for different devices since
each device is set up to perform different tasks. Next we define the isen-
tropic efficiencies of turbines, compressors, and nozzles by comparing the
actual performance of these devices to their performance under isentropic
conditions for the same inlet state and exit pressure.

Isentropic Efficiency of Turbines

For a turbine under steady operation, the inlet state of the working fluid and
the exhaust pressure are fixed. Therefore, the ideal process for an adiabatic
turbine is an isentropic process between the inlet state and the exhaust pres-
sure. The desired output of a turbine is the work produced, and the isen-
tropic efficiency of a turbineis defined as the ratio of the actual work
output of the turbine to the work output that would be achieved if the
process between the inlet state and the exit pressure were isentropic:

(7–60)

Usually the changes in kinetic and potential energies associated with a fluid
stream flowing through a turbine are small relative to the change in enthalpy
and can be neglected. Then the work output of an adiabatic turbine simply
becomes the change in enthalpy, and Eq. 7–60 becomes

(7–61)

where h 2 aand h 2 sare the enthalpy values at the exit state for actual and
isentropic processes, respectively (Fig. 7–49).
The value of hTgreatly depends on the design of the individual compo-
nents that make up the turbine. Well-designed, large turbines have isentropic
efficiencies above 90 percent. For small turbines, however, it may drop even
below 70 percent. The value of the isentropic efficiency of a turbine is
determined by measuring the actual work output of the turbine and by cal-
culating the isentropic work output for the measured inlet conditions and the
exit pressure. This value can then be used conveniently in the design of
power plants.

hT

h 1 h 2 a

h 1 h 2 s

hT

Actual turbine work

Isentropic turbine work



wa

ws

Chapter 7 | 371

h

s

1

h 2 s

h 2 a

h 1

2 s

2 a

P 2

P 1

Inlet state

Actual process

Isentropic process

Exit

pressure

s 2 s = s 1

wa w

s

FIGURE 7–49

The h-sdiagram for the actual and

isentropic processes of an adiabatic

turbine.

EXAMPLE 7–14 Isentropic Efficiency of a Steam Turbine

Steam enters an adiabatic turbine steadily at 3 MPa and 400°C and leaves at

50 kPa and 100°C. If the power output of the turbine is 2 MW, determine (a)

the isentropic efficiency of the turbine and (b) the mass flow rate of the

steam flowing through the turbine.

Solution Steam flows steadily in a turbine between inlet and exit states. For

a specified power output, the isentropic efficiency and the mass flow rate are

to be determined.

Assumptions 1 Steady operating conditions exist. 2 The changes in kinetic

and potential energies are negligible.