CHAPTER 12 DESIGN OF COOLING TOWER
Design Condition:
Temperature of entering Water
Temperature of leaving Water…………………...... Condition of Entering Air
……………………………...
Condition of Leaving Air
……………………………...
Temperature o make-up water
30C
……………………..
25C
………………………
26C , 60% RH 32C , 90% RH
240C
Atmospheric Pressure, Patm ……………………………….
101.325 kPa
Air gas constant, Ra ……………………………………….
0.287 kJ/ kg K
Mass of Condenser cooling water, mcw
……………….
0.869 kg/sec
Mass of Compressor jacket water, mjw
……………….
0.0235kg/sec
Water velocity, Vwater
……………………………….
80
1.68 m/sec
Amount of water to be handled by the cooling tower, mwt m wt m w CONDENSER m w COMPRESSOR
(0.869 0.0235) mwt
kg kg 0.8925 sec sec
Air Properties Using Psychometrics Chart At
26C and 60% RH
h1 59 KJ
kg da
HR1 0.01275kg of moisture
m3 V1 = 0.865 At
kg of dry air
kg of dry air
32C and 90% RH
h5 103KJ
kg da HR5 0.0295kg of moisture
V2
0.9025 m
kg of dry air
3
kg da
For water:
81
AT 30 0C , h3 h f 125.79 kJ
kg da
AT 25 0C , h4 h f 104.89 kJ
kg da AT 24 0C , h5 h f 100.74 kJ kg da
Cooling tower analysis:
Energy balance: m1 (h1) + m3 (h3) + m5 (h5) = m2 (h2) +m4 (h4)
Where: m1= m2 = ma m3 = m4 = mwct
mwct (h3 - h4) + m5 (h5) = ma (h2 - h1) But:
m5 = ma (HR2 - HR1)
29.5 1275 1000 m5 0.01675 ma 1 m5 ma
Therefore: 0.8925 (125.79 – 104.89) + 0.01675(ma)(100.74) = ma (103- 59) 82
ma
18.65 44 1.687395
ma 0.44 kg air
Mass of Make-up water,
sec
mw5
From Equation 1
mw5 0.01675ma kg mw5 0.01675 0.44 sec kg mw5 0.0074 of water sec
Va Volume flow rate of air,
At 26C and 60% RH , Psat 3.3844 KPa Pv RH Psat 0.60 3.3844 KPa 2.03064 KPa
PV MRT 0 0.2871KJ 24 273 K 0 sec kg K 101.325 2.030064 KPa or KN m3
0.44 kg
Va
ma RaTa PB PS
Va= 0.378 m3/sec. Where: R.H= relative humidity PS a t saturation pressure at 24C PV partial pressure of water vapor 83
Cooling Tower Area, C.T.A
From Figure 6, Mechanical Draft Cooling Tower Sizing Chart,Kent’s Mechanical Engineer’s Handbook, page 9 – 25.
At 30 0C (86 0F) hot water temperature, 25 0C (77 0F) cold water temperature and 21.9 0C (71.42 0F) wet bulb temperature of air and for Induced Draft Tower with effective filling depth of 22 ft, the water concentration is 2.8 gpm / ft2.
Therefore,
Volume of water, VW
0.8925 kg 1000 kg
0.0008925 = = 14.15 gpm
Cooling Tower Area, C.T.A =
14.15 gpm 2.8 gpm / ft 2
5.05 ft 2 x
1 m2 (3.28) 2 ft 2
= 84
sec
m3
m3 1gal 60 sec x x 3 sec 0.003785m 1 min
= 0.47
m2
Using square cross-sectional area, L = W C..T . A
C.T.A. = L2 ; L = L =
√ 0.47
L = 0.69 m Cooling tower range, C.T.R. C.T.R. =
t1 t 2 5 o C
Cooling tower approach, C.T.A. o
At 26
C
and 60% RH ;
C.T.A. =
t wb 20.5 o C
t1 t wb 25 20.5 4.5 o C
Cooling tower efficiency, C.T.E.
C.T.R. =
t1 t 2 30 25 x 100 % x 100 % t1 t wb 30 20.5
= 52.63 %
Number of nozzles required From Principles of Refrigeration, by R. J. Dossat P 270, nozzles are spaced to deliver 0.10 to 0.40
gpm / ft 2
of pool surface and about 7 to 10 gpm capacity per nozzle.
Using 8 gpm capacity per nozzle
Vw 14.15 gpm capacity / nozzle 8 No. of nozzle = = 1.77 or 2 nozzles 85
Nozzle arrangement No. of rows = 1 rows No. of nozzle/row = 2 nozzle/row
Dimensions of headers For headers, use economic water velocity of 1.52 m/sec
Primary header,Hp
Qcw A w
( D ) 2 w 4
;D
4 Qcw w
Where:
Qcw = Volume flow rate of cooling water, 0.0008925 m3/sec
B
= Water velocity, 1.68 m/sec
Therefore,
86
D
4 0.0008925 m3 / sec 0.0260 m or 26 mm 1.68 m / sec
Use 40 mm NPS, schedule 40, Di= 40.9 mm, Do = 48.26 mm.
Secondary header, Hs QN N nozzles A w
( Di ) 2 w ; Di 4
4 QN N nozzles w
Where:
QN = Capacity per nozzle, 0.00054 m3/sec
Nnozzles = Number of nozzles per header , 3 nozzles
B
= Water velocity, 1.68 m/sec
Therefore,
Di
4 0.00054 m 3 / sec nozzle 3 nozzles 0.035 m or 35 mm 1.68 m / sec
Use 40 mm NPS, schedule 40, Di= 40.9 mm, Do = 48.26 mm.
DESIGN OF INDUCE DRAFT FAN
87
“All cooling tower fans are of the axial - flow type. The number of blades varies from two to six. Most cooling – tower fans are 30 to 55 % efficient.”
- Kent’s Mechanical Engineer’s Handbook, page 9 – 27.
From Table 3, Outlet Areas for Wheel Diameters 12 in to 132 in, Kent’s Mechanical Engineer’s Handbook, page 1 – 60.
Using Fan index (M), the following data were obtained.
Index Number for Fans M
Maximum Outlet Area, ft2
Maximum Wheel Diameter Theoretical
Practical
Single Width
Double Width
Diameter
Diameter
Single Inlet
Double Inlet
40.17
40 ¼
9.35
16.830
Total Head,hT
hT hS hV
hw w V 2 air 2g
Velocity head, hv
Q hV air ; air air 2g Af 2
88
Where:
air
= Velocity of air, m/sec
Qair = Volume flow rate of air, 0.495 m3/sec
Af = Area of the fan outlet 0.87 m2
g = Acceleration due to gravity, 9.81 m/sec2
Therefore,
air
0.495 m3 / sec m 0.569 2 0.87 m sec
Also,
hV
0.569 m / sec 2
2 9.81 m / sec 2
89
0.029 m of air
Static head,hs
From Operating Limits for Classes I,II,II, & IV Fans, Kent’s Mechanical Engineer’s Handbook, page 1 – 59.
For tube axial fan (class II) with maximum total pressure of 6 ¾ in. (0.1714 m of H2O) with outlet velocity of 7.63 m / sec (1501.58 ft / min) the static pressure (hS) is equal to 6.6 in (0.1676 m of H2O).
Converting m of H2O to m of air,
air
P 101.325 kPa kg 1.17 3 Ra Ta 0.287 kJ kg K 302 K m
Therefore,
hS
0.1676 m of
H 2 O 1000 kg / m 3 143.25 m of air 1.17 kg m 3
Also,
hT 143.25 m of air 0.029 m of air 143.27 m of air Fan or Air Power, Pair
90
Pair Vair Velocity of air hT
0.495 m sec 1.17 kg m 143.27 m 3
3
kg m J KJ 814.03 0.814 or KW sec sec sec 1 hp Pair 0.814 KW 0.746 KW Pair 82.98
Pair
1 hp
Motor or Fan Power, Pm
Using fan efficiency of 85 %
Pm
Pair 1 hp 1.18 hp 0.85 0.85
From METC, using standard sizes motor use 1.5 hp for fan motor
Motor Kw
1.1
Efficiency
(RPM)
%
1750
77
Motor type
(Rated Hp) 1.5
Nominal
3-phase
SPECIFICATIONS
Cooling Tower
91
No. of units to install ……………………………………
1 units
Type
Induced draft
……………………………………………
Cooling tower area, ACT
……………………………
0.613 m2
Length, L
……………………………………
0.78 m
Width, W
……………………………………
0.78 m
Cooling tower range, C.T.R. ……………………………
5 0C
Cooling tower approach, C.T.A.
……………………
4.50C
Cooling tower efficiency, C.T.E.
……………………
52.63 %
No. of nozzles, Nnozzles
………………………………3
No. of rows
……………………………………………
Primary header, HP
…………………………………… 92
1
40 mm NPS
Inside diameter, Di
……………………………
40.9 mm
Outside diameter, Do ……………………………
48.3 mm
Schedule
40
……………………………………
Secondary header, HS ……………………………………
Inside diameter, Di
40 mm NPS
……………………………
40.90 mm
Outside diameter, Do ……………………………
48.26 mm
Schedule
……………………………………
40
Air Power, Pair
……………………………………
1 hp
Motor Power, Pm
……………………………………
1.5 hp
Temperature of water in, twi ……………………………
30 0C
93
Temperature of water out, two
……………………………
25 0C
Mass of cooling water, MCW ……………………………
1.1635 kg / sec
Mass of air, ma
0.575 / sec
……………………………………
Make – up water, mmw
……………………………
0.0097 kg /
sec
Volume flow rate of air, Qair ……………………………
94
0.495 m3 / sec
