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Chapter VI Cooling tower design
Lecturer: Chakkrit Umpuch
Department of Chemical Engineering
Faculty of Engineering
Ubon Rachathani University
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What you will learn in this chapter ishere.
5.1 Introduction to cooling tower
5.2 Vapor pressure of water and humidity
5.3 Cooling tower theory5.4 Cooling tower design
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5.1Introduction
Cooling tower is the heat rejection device, which extracts heat waste
to atmosphere through the cooling of water stream to a lowertemperature.
The make-up water source is used to replenish water lost to evaporation.
Hot water from heat exchangers is sent to the cooling tower. The water exits
the cooling tower and is sent back to the exchangers or to other units forfurther cooling.
Figure 1: Closed Loop Cooling Tower System
What is cooling tower?
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Types of Cooling Towers
Figure 2: Mechanical Draft Counterflow Tower Figure 3: Mechanical Draft Crossflow Tower
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5.2 Vapor Pressure of Water and Humicdity
Vapor Pressure ofWater
Pure water can exist in three different physical states: solid ice, liquid
and vapor. The physical state in which it exists depends on thepressure and temperature.
AB line is liquid and vapor coexist in
equilibrium.
AC line is ice and liquid coexist in
equilibrium.
AD line is ice and vapor coexist in
equilibrium.
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5.2 Vapor Pressure of Water and Humidity
Steam Table
For example: At 100C (212F) the vapor pressure of water is 101.3 kPa (1.0 atm).
At 65.6C (150F) the vapor pressure of water is 25.7 kPa (3.72 atm).
At 25.7kPa and 65.6C, water will boil.
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5.2 Vapor Pressure of Water and Humidity
Humidity and Humidity Chart
1. Definition of humidity
The humidity H of an air-water vapor mixture is defined as the kg of watervapor contained in 1 kg of dry air.
where
pAis partial pressure of water vapor in the air.
P is the total pressure (101.325 kPa, 1.0 atm abs, or 760mmHg)
Saturated air is air in which the water vapor is in equilibrium with liquid water at thegiven conditions of pressure and temperature. Hence, the saturation humidity Hs is
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(6.1)
(6.2)
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5.2 Vapor Pressure of Water and Humidity
Humidity and Humidity Chart
2. Percentage humidity
The percent humidity Hp is defined as 100 times the actual humidity H of the
air divided by the humidity Hs if the air were saturated at the same temperature andpressure.
3. Percentage relative humidity
The amount of saturation of an air-water vapor mixture is also given aspercentage relative humidity HRusing partial pressures.
Note that HR Hp:
(6.3)
(6.4)
(6.5)
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Ex 6.1 The air in a room is at 26.7C (80F) and a pressure of 101.325
kPa and contains water vapor with a partial pressure pA= 2.76 kPa.
Calculate the following.
(a) Humidity, H.
(b) Saturation humidity, Hs, and percentage humidity, Hp.(c) Percentage relative humidity, HR.
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Solution:
(a) From the steam tables at 26.7C, the vapor pressure of water is pAS = 3.50 kPa
(0.507 psia). Also, pA = 2.76 kPa and P = 101.3 kPa (14.7 psia). For part (a), using
eq. 6.1,
kgairkgH
pP
pH
A
A /001742.0
)6.273.101(97.28
)76.2(02.18
97.28
02.182
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Solution:
(b) From part (b), using eq. 6.2, the saturation humidity is
The percentage humidity, from eq. 6.3, is
For part (c), from eq. 4, the percentage relative humidity is
kgairkgHpP
pH
As
Ass /002226.0
)05.33.101(97.28
)05.3(02.18
97.28
02.182
%3.7802226.0
)01742.0(100100
s
PH
HH
%9.7805.3
)76.2(100100 As
As
ppH
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5.2 Vapor Pressure of Water and Humidity
Humidity and Humidity Chart
4. Dew point of an air-water vapor mixture
The temperature at which a given mixture of air and water vapor would be
saturated is called the dew-point temperature or simply the dew point.
For example,
At 26C (80F), the saturation vapor pressure of water is pAS= 3.5 kPa (0.507 psia).
Hence the dew point of a mixture containing water vapor having a partial pressure of3.50 kPa is 26.7C.
If an air-water vapor mixture is at 37.8C and contains water vapor of p A= 3.50 kPa,
the mixture would not be saturated.On cooling to 26.7C, the air would be saturated, i.e., at the dew point..
On further cooling, some water vapor would condense, since the partial pressure
cannot be greater than the saturation vapor pressure.
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5.2 Vapor Pressure of Water and Humidity
Humidity and Humidity Chart
5. Humid heat of an air-water vapor mixture
The humid heat csis the amount of heat in J (or kJ) required to raise thetemperature of 1 kg of dry plus the water vapor present by 1 K or 1C.
(SI)
(English)
6. Humid volume of an air-water vapor mixture
The humid volume v His the total volume in m3 of 1 kg of dry air plus the vapor
it contains at 101.325 kPa (1.0 atm) abs pressure and the given gas temperature.
Using the ideal gas law,
(6.5)
(6.4)
(6.7)
(6.6)
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5.2 Vapor Pressure of Water and Humidity
Humidity and Humidity Chart
7. Total enthalpy of an air-water vapor mixture.
The total enthalpy of 1 kg of air plus its water vapor is Hy J/kg or kJ/kg dry air.
(SI)
(English)
8. Humidity chart of air-water vapor mixtures.A convenient chart of the properties of air-water vapor mixtures at 1.0 atm abs
pressure is the humidity chart. In this figure the humidity H is plotted versus the actual
temperature of the air-water vapor mixture (dry bulb temperature).
(6.9)
(6.8)
(6.10
)
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5.2 Vapor Pressure of Water and Humidity
Humidity and Humidity Chart
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Ex 6.2Air entering a dryer has a temperature (dry bulb temperature) of60C (140F) and a dew point of 26.7C (80F). Using the humidity
chart, determine the actual humidity H, percentage humidity Hp, humidheat cs, and the humid volume vHin SI and English units.
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Solution:
The dew point of 26.7C is the temperature when the given mixture is at 100%saturation. Starting at 26.7C, Fig. of humidity chart and drawing a H = 0.0225 kg
H2O/kg dry air is read off the plot. This is the actual humidity of the air at 60C. Stated
in another way, if air at 60C and having a humidity H = 0.0225 is cooled, its dew point
will be 26.7C. In English units, H = 0.0225 lb H2O/lb dry air.
Locating this point of H = 0.0225 and t = 60C on the chart, the percentage humidity
HPis found to be 14%, by linear interpolation vertically between the 10 and 20% lines.The humidity heat of H = 0.0225 is, from eq.(6).
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The humidity volume at 60C (140F), from eq. 7 is
)0225.0(88.1005.1 sc
KkgJorKairdrykgkJ ./10047.1/047.1 3
)0225.0(45.024.0 sc
Fairdrylbbtuc ms ./250.0
)27360)(0225.01056.41083.2( 33 Hv
airdrykgm /977.0 3
In English units,
airdrylbftv mH /67.15)140460)(0225.00405.00252.0( 3
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5.2 Vapor Pressure of Water and Humidity
Adiabatic Saturation Temperature
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5.2 Vapor Pressure of Water and Humidity
Adiabatic Saturation Temperature
Total enthalpy of the entering gas mixture = enthalpy of the leaving gas mixture
(SI)
(English)
(6.12
)
(6.13
)
(6.11)
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Ex 6.3An air stream at 87.8C having a humidity H = 0.030 kg H2O/kgdry air is contacted in an adiabatic saturator with water. It is cooled and
humidified to 90% saturation.
(a) What are the final values of H and T?(b) For 100% saturation, what would be the values of H and T?
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Solution:For part (a), the point H = 0.030 and T = 87.8C is located on the humidity chart.
The adibatic saturation curve through this point is followed upward to the left
until it interests the 90% line at 42.5C and followed upward to the left until it
intersects the 90% line at 42.5C and H = 0.0500 kg H2O/kg dry air.
For part (b), the same line is followed to 100% saturation, where T = 40.5C andH = 0.0505 kg H2O/kg dry air.
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5.2 Vapor Pressure of Water and Humidity
Wet Bulb Temperature
For air-water vapor mixture, the adiabatic saturation lines can also be used for wet bulb lines with
reasonable accuracy.
Hence, the wet bulb temperature determination is often used to determine the humidity of an air-water vapor mixture.
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Ex 6.4A water vapor-air mixture having a dry bulb temperature of T =60C is passed over a wet bulb as shown in slide 17, and the wet bulb
temperature obtained is TW= 29.5C. What is the humidity of the
mixture?
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Solution:The wet bulb temperature of 29.5C can be assumed to be the same as the
adiabatic saturation temperature TS, as discussed. Following the adiabaticsaturation curve of 29.5C until it reaches the dry bulb temperature of 60C, the
humidity is H = 0.0135 kg H2O/kg dry air.
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Theory and Calculation of Water-CoolingTowers
Pressure gradient
Water vapor diffuses from the
interface to the bulk gas phase with a
driving force in the gas phase:
HiHGkg H2O/kg dry air
No driving force in liquid phase, sincewater is pure liquid
Temperature gradient
The temperature driving force is TLTiin the liquid phase and TiTGK or C in gas
phase.
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Theory and Calculation of Water-CoolingTowers
L = water flow , kg water/s.m2(lbm/h.ft2)TL= temperature of water, C or K (F)
G = dry air flow, kg/s.m2(lbm/h.ft2)TG = temperature of air, C or K (F)
H = humidity of air, kg water/ kg dry air (lb water/ lb dry air)
Hy= enthalpy of air-water vapor mixture, J/kg dry air (btu/lbmdry air)
(English)
(SI)
(6.15
)
(6.14
)
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Theory and Calculation of Water-CoolingTowers
Total heat balance for the dash line box
(6.17
)
(6.16
)
(6.18
)
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Design of water-cooling tower UsingFilm Mass transfer Coefficients
The tower design is done using the following steps.
1. The enthalpy of saturated air Hy1is plotted versus Tion an H versus T plot as shown in Fig. in
slide 24 This enthalpy is calculated with eq. using the saturation humidity from the humidity chartfor a given temperature, with 0C (273K) as a base temperature. Calculated values are tabulated
in Table in slide 27
2. Knowing the entering air conditions TG1
and H1, the enthalpy of this air H
y1is calculated from eq.
6.8. The point Hy1and TL1(desired leaving water temperature) is plotted in Fig. in slide 24 as one
point on the operating line. The operating line is plotted with a slope Lc L/G and ends at point TL2,
which is the entering water temperature. This gives Hy2 . Alternatively, Hy2can be calculated from
eq. 6.16.
3. Knowing hLa and kGa, lines with a slope of hLa/kGaMBP are plotted as shown in Fig. in slide 24.
From eq. 6.18 point P represents Hyand TL on the operating line, and point M represents Hyi and
Ti, the interface conditions. Hence, line MS or Hyi -Hyrepresents the driving force in eq. 6.17.
4. The driving force Hyi - Hy is computed for various values of TL between TL1 and TL2. Then by
plotting 1/(Hyi -Hy) versus Hy from Hy1 to Hy2, a graphical integration is performed to obtain thevalue of the integral in eq. 6.17. Finally, the height z is calculated from eq. 6.17.
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Ex 6.5 A packed countercurrent water-cooling tower using a gasflow rate of G = 1.356 kg dry air/s.m2 and a water flow rate ofL=1.356 kg water/s.m2is to cool the water from TL2= 43.3 C (110
F) to TL1=29.4 C (85 F). The entering air at 29.4 C has a wet
bulb temperature of 23.9 C. The mass-transfer coefficient kGa is
estimated as 1.207x10-7 kgmol/s.m3.Pa and hLa/kGaMBP as4.187x104J/kg/K (10.0 btu/lbm. F). Calculate the height of packed
tower z. The tower operates at a pressure of 1.013x105Pa.
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