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

84 | Thermodynamics

Generator

=

= 0.75 × 0.97

= 0.73

Turbine

turbine–gen

turbine= 0.75 generator= 0.97

turbine generator

hh

hhh

FIGURE 2–59

The overall efficiency of a
turbine–generator is the product of the
efficiency of the turbine and the
efficiency of the generator, and
represents the fraction of the
mechanical energy of the fluid
converted to electric energy.

Turbine Generator

1862 kW

m = 5000 kg/s

h = 50 m

·

Lake

hgenerator= 0.95

FIGURE 2–60

Schematic for Example 2–16.

and

Generator: (2–48)

A pump is usually packaged together with its motor, and a turbine with its

generator. Therefore, we are usually interested in the combinedor overall

efficiencyof pump–motor and turbine–generator combinations (Fig. 2–59),

which are defined as

(2–49)

and

(2–50)

All the efficiencies just defined range between 0 and 100 percent. The

lower limit of 0 percent corresponds to the conversion of the entire mechani-

cal or electric energy input to thermal energy, and the device in this case

functions like a resistance heater. The upper limit of 100 percent corresponds

to the case of perfect conversion with no friction or other irreversibilities,

and thus no conversion of mechanical or electric energy to thermal energy.

EXAMPLE 2–16 Performance of a Hydraulic Turbine–Generator

The water in a large lake is to be used to generate electricity by the installa-

tion of a hydraulic turbine–generator at a location where the depth of the

water is 50 m (Fig. 2–60). Water is to be supplied at a rate of 5000 kg/s. If

the electric power generated is measured to be 1862 kW and the generator

efficiency is 95 percent, determine (a) the overall efficiency of the turbine–

generator, (b) the mechanical efficiency of the turbine, and (c) the shaft

power supplied by the turbine to the generator.

Solution A hydraulic turbine–generator is to generate electricity from the

water of a lake. The overall efficiency, the turbine efficiency, and the turbine

shaft power are to be determined.

Assumptions 1 The elevation of the lake remains constant. 2 The mechani-

cal energy of water at the turbine exit is negligible.

Properties The density of water can be taken to be r
1000 kg/m^3.

Analysis (a) We take the bottom of the lake as the reference level for conve-

nience. Then kinetic and potential energies of water are zero, and the

change in its mechanical energy per unit mass becomes

0.491 kJ>kg

emech,inemech,out

P

r

 0 
gh
 1 9.81 m>s^221 50 m2a

1 kJ>kg

1000 m^2 >s^2

b

hturbinegen
hturbinehgenerator

W

#

elect,out

W

#

turbine,e

W

#

elect,out

0 ¢E

#

mech,fluid

hpumpmotor
hpumphmotor

W

#

pump,u

W

#

elect,in

¢E

#

mech,fluid

W

#

elect,in

hgenerator

Electric power output

Mechanical power input

W

#

elect,out

W

#

shaft,in