Chapter 14 | 739

COOL

WATER

WARM

WATER

AIR

35 °C

100 kg/s

100 kg/s

System

boundary

4

1

3

2

1 atm

20 °C

f 1 = 60%

30 °C

f 2 = 100%

V 1

Makeup

water

22 °C

·

FIGURE 14–34

Schematic for Example 14–9.

Properties The enthalpy of saturated liquid water is 92.28 kJ/kg at 22°C

and 146.64 kJ/kg at 35°C (Table A–4). From the psychrometric chart,

h 1 42.2 kJ/kg dry air h 2 100.0 kJ/kg dry air

v 1 0.0087 kg H 2 O/kg dry air v 2 0.0273 kg H 2 O/kg dry air

v 1 0.842 m^3 /kg dry air

Analysis We take the entire cooling towerto be the system, which is shown

schematically in Fig. 14–34. We note that the mass flow rate of liquid water

decreases by an amount equal to the amount of water that vaporizes in the

tower during the cooling process. The water lost through evaporation must be

made up later in the cycle to maintain steady operation.

(a) Applying the mass and energy balances on the cooling tower gives

Dry air mass balance:

Water mass balance:

or

Energy balance:

or

Solving for m·agives

Substituting,

Then the volume flow rate of air into the cooling tower becomes

(b) The mass flow rate of the required makeup water is determined from

Discussion Note that over 98 percent of the cooling water is saved and

recirculated in this case.

m#makeupm#a^1 v 2 
v 12  1 96.9 kg>s 21 0.0273
0.0087 2 1.80 kg/s

V

#

1 m

#

av 1 ^1 96.9 kg>s^21 0.842 m

(^3) >kg 2 81.6 m 3
/s
m

a
1 100 kg>s 231 146.64
92.28 2 kJ>kg 4
31 100.0
42.2 2 kJ>kg 4
31 0.0273
0.0087 21 92.28 2 kJ>kg 4
96.9 kg>s
m

a
m# 31 h 3
h 42
1 h 2
h 12
1 v 2
v 12 h 4
m

3 h 3 m

a^1 h 2
h 12 ^1 m

3
m

makeup^2 h 4
ainm

ha
out
m

hSm

a 1 h 1 m

3 h 3 m

a 2 h 2 m

4 h 4
m

3
m

4 m

a^1 v 2
v 12 m

makeup^
m

3 m

a 1 v 1 m

4 m

a 2 v 2
m

a 1 m

a 2 m

a^
SUMMARY
In this chapter we discussed the air–water-vapor mixture,
which is the most commonly encountered gas–vapor mixture
in practice. The air in the atmosphere normally contains some
water vapor, and it is referred to as atmospheric air. By con-
trast, air that contains no water vapor is called dry air. In the
temperature range encountered in air-conditioning applica-
tions, both the dry air and the water vapor can be treated as
ideal gases. The enthalpy change of dry air during a process
can be determined from
The atmospheric air can be treated as an ideal-gas mixture
whose pressure is the sum of the partial pressure of dry air Pa
and that of the water vapor Pv,
PPaPv
¢hdry aircp ¢T 1 1.005 kJ>kg#°C 2 ¢T