SPX - Cooling Tower Performance Basic Theory and Practice (CTII-01A)
SPX - Cooling Tower Performance Basic Theory and Practice (CTII-01A)
SPX - Cooling Tower Performance Basic Theory and Practice (CTII-01A)
Including this loss of heat through evaporation, the total heat balance
between air and water, expressed as a differential equation, is:
G = mass flow of dry air through the cooling tower — lb/min Heat Load = gpm x R x 81⁄3 = Btu/min (2)
h1 = enthalpy (total heat content) of entering air — Btu/Ib of dry
air Where:
h2 = enthalpy of leaving air — Btu/Ib of dry air gpm = water flow rate through process and over tower — gal/min
R = “range” = the difference between the hot and cold water
temperatures — °F (see Figure 3)
Within the water stream, the rate of heat loss would appear to be
81⁄3 = pounds per gallon of water
L (t1 – t2), where:
Load
Heat Load = L x R
measured, and a glance at Figure 2 (psychrometric chart)
shows that lines of constant wet-bulb are parallel to lines of
constant enthalpy, whereas lines of constant dry-bulb have no
Cold Water °F
L lb/min of water fixed relationship to enthalpy. Therefore wet-bulb temperature is
Approach
the air parameter needed to properly size a cooling tower and its
°F
Wet Bulb °F
Effects of Variables
FIGURE 3
Although several parameters are defined in Figure 3, each of which
will affect the size of a cooling tower, understanding their effect
Note from formula (2) that heat load establishes only a required
is simplified if one thinks only in terms of 1) heat load, 2) range,
temperature differential in the process water and is unconcerned
3) approach and 4) wet-bulb temperature. If three of these
with the actual hot and cold-water temperatures themselves.
parameters are held constant, changing the fourth will affect the
Therefore, the mere indication of a heat load is meaningless to the
cooling tower size as follows:
application engineer attempting to properly size a cooling tower.
More information of a specific nature is required. 1 C
ooling tower size varies directly and linearly with heat load.
See Figure 4.
Optimum operation of a process usually occurs within a relatively
narrow band of flow rates and cold-water temperatures, which ooling tower size varies inversely with range. See Figure 5.
2 C
establishes two of the parameters required to size a cooling Two primary factors account for this. First; increasing the range
tower — gpm and cold-water temperature. The heat load — Figure 3 — also increases the ITD (driving force) between
developed by the process establishes a third parameter — hot- the incoming hot-water temperature and the entering wet-bulb
water temperature coming to the cooling tower. For example, let’s temperature. Second, increasing the range (at a constant heat
assume that a process developing a heat load of 125,000 Btu/min load) requires that the water flow rate be decreased — formula
performs best if supplied with 1,000 gpm of water at 85°F. With a (2) — which reduces the static pressure opposing the flow of air.
slight transformation of formula (2) we can determine the water
temperature elevation through the process as: 3 C
ooling tower size varies inversely with approach. A longer
approach requires a smaller cooing tower. See Figure 6.
125,000
R= = 15°F Conversely, a smaller approach requires an increasingly larger
1,000 x 81⁄3
cooling tower and, at 5°F approach, the effect upon the cooling
tower size begins to become asymptotic. For that reason, it is
Therefore, the hot water temperature coming to the cooling tower not customary in the cooling tower industry to guarantee any
would be 85°F + 15°F = 100°F. approach less than 5°F.
Constants:
6 Heat Load
Constants: Approach
1.3 Wet Bulb
Range
5 Approach
Wet-bulb 1.2
Tower Size Factor
4 1.1
Tower Size Factor
3 1.0 Dec
reas
ing
.9 gpm
2
.8
1
.7
.6
1 2 3 4 5 6 60 80 100 120 140 160 180 200
Range Variance —%
Heat Load Factor
FIGURE 4 FIGURE 5
2.5
Constants: 2.0
Heat Load Constants:
2.0 Heat Load
Tower Size Factor
Range
1.0
1.0
.05 0.5
5 10 15 20 25 30 55 60 65 70 75 80
Approach — °F Wet-Bulb (°F) (Example)
FIGURE 6 FIGURE 7
4 C
ooling tower size varies inversely with wet-bulb temperature. • T
he air’s moisture content increased from 72 grains to 163
When heat load, range, and approach values are fixed, reducing grains (7000 grains = 1 lb). These 91 grains of moisture (0.013
the design wet-bulb temperature increases the size of the lb of water) were evaporated from the water at a latent heat
cooling tower — see Figure 7. This is because most of the of vaporization of about 1000 Btu/Ib. This means that about
heat transfer in a cooling tower occurs by virtue of evaporation 13 of the 15 Btus removed from the water (about 86% of the
(which extracts approximately 1000 Btus for every pound of total) occurred by virtue of evaporation. (The latent heat of
water evaporated), and air’s ability to absorb moisture reduces vaporization of water varies with temperature, from about 1075
with temperature. Btu/Ib at 32°F to 970 Btu/Ib at 212°F. Actual values at specific
temperatures are tabulated in various thermodynamics manuals.)
• T
otal heat content (enthalpy) increased from 30.1 Btus to 45.1
Btus. This enthalpy increase of 15 Btus was gained from the
water. Therefore, one pound of water was reduced in temperature
by the required amount of 15°F (85-70) — see page 1.
In the interest of technological progress, all products are subject to design and/or material change without notice ISSUED 10/2012 CTII-01A
COPYRIGHT © 2013 SPX Corporation