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Couture, Philip
Thermal-Hydraulic Design of Replacement Cooling Towers for
Vermont Yankee Nuclear Power Station
by
Philip L Couture
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF ENGINEERING IN MECHANICAL ENGINEERING
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
May 2010
CONTENTS
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
LIST OF SYMBOLS ......................................................................................................... v
ACKNOWLEDGMENT .................................................................................................. vii
ABSTRACT .................................................................................................................... viii
1. Introduction .................................................................................................................. 1
1.1
Cooling Tower Operating Principles .................................................................. 2
1.2
Types of Cooling Towers ................................................................................... 4
1.3
Vermont Yankee Cooling Towers ...................................................................... 5
2. Methodology ................................................................................................................ 9
2.1
Review of Cooling Tower Theory...................................................................... 9
2.2
Design Parameter Selection.............................................................................. 15
2.3
Methodology for Replacement Counterflow Cooling Tower Design .............. 17
2.3.1
Tower Sizing ........................................................................................ 17
2.3.2
Makeup Water Requirements ............................................................... 19
2.3.3
Tower Demand Curves and Determination of Characteristic Curve ... 20
3. Results ........................................................................................................................ 22
3.1
Counterflow Tower Size .................................................................................. 22
3.2
Tower Demand Curves ..................................................................................... 23
4. Conclusion ................................................................................................................. 25
5. References .................................................................................................................. 26
Appendix A - Mass-Energy Balances .............................................................................. 27
Appendix B - Design Parameter Calculations ................................................................. 31
Appendix C - Tower Demand Curve Excel Spreadsheets – Design A ............................ 34
Appendix D - Tower Demand Curve Excel Spreadsheets – Design B ............................ 40
ii
LIST OF TABLES
Table 1 - NPDES Permit Limits (May 16 - June 15)
15
Table 2 - Cooling Tower Design Parameters
17
Table 3 - Tower Height Sizing
18
Table 4 - Counterflow Tower Size
22
Table 5 - Makeup Water Requirements
22
iii
LIST OF FIGURES
Figure 1 - Aerial view of Vermont Yankee
1
Figure 2 - Counterflow Cooling Tower [6]
2
Figure 3 - Cross-flow Cooling Tower [6]
2
Figure 4 - Fill Material
3
Figure 5 - Water droplet interaction with air [6]
4
Figure 6 - Vermont Yankee Circulating Water Flow Diagram
8
Figure 7 - Cooling Tower Heat Balance [6]
12
Figure 8 - Example Tower Characteristic Curves [6]
13
Figure 9 - Nomograph of cooling tower characteristics [4]
14
Figure 10 - Counterflow Induced Draft Tower Sizing Chart [4]
18
Figure 11 - Fan Horsepower Sizing Chart [4]
19
Figure 12 - Tower Demand Curves: Design A
23
Figure 13 - Tower Demand Curves: Design B
24
iv
LIST OF SYMBOLS
K = tower characteristic or enthalpy transfer coefficient (lbm/hr-ft2)
a = contact area/tower volume (ft2/ft3)
V = active cooling volume/plan area (ft3/ft2)
L = water flow rate (lbm/hr-ft2)
T1, Tthw = Cooling tower hot water (inlet) temperature (°F)
T2, Ttcw = Cooling tower cold water (discharge) temperature (°F)
hw, h2 = enthalpy of air-water vapor mixture at bulk water temperature (Btu/lbm dry air)
ha, h1 = enthalpy of air-water vapor mixture at wet bulb temperature (Btu/lbm dry air)
G= air flow rate, (lbm dry air/hr-ft2)
Cp = specific heat capacity of water (Btu/lbm-°F)
x1, x2 = absolute humidity of the inlet and outlet air
b = blowdown rate (gal/min)
e = evaporation loss (gal/min)
r = ratio of solids in blowdown to solids in makeup, cycles of concentration
d = drift loss (gal/min)
M = makeup rate (gal/min)
∆Tcond = Condenser temperature rise (°F)
∆Tcwp = Circulating water pump temperature rise due to pump work (°F)
∆Tcwbp = Circulating water booster pump temperature rise due to pump work (°F)
∆Tt = Cooling tower range (°F)
& c = Condenser mass flow rate (lbm/hr)
m
& csw = Combined condenser and service water exit mass flow rate (lbm/hr)
m
& evapdrift = Cooling tower evaporation and drift losses (lbm/hr)
m
& fe = Circulating water mass flow rate exiting facility (lbm/hr)
m
& fi = Circulating water mass flow rate entering facility (lbm/hr)
m
& re = Downstream river mass flow rate (lbm/hr)
m
& ri = Upstream river mass flow rate (lbm/hr)
m
& recirc = Recirculation mass flow rate = R/100* m
& c (lbm/hr)
m
v
& sw = Service water mass flow rate (lbm/hr)
m
& ti , L1= Cooling tower inlet mass flow rate (lbm/hr)
m
& te , L2= Cooling tower outlet mass flow rate (lbm/hr)
m
& = Service water heat load (Btu/hr)
Q
sw
Tce = Condenser exit temperature (°F)
Tci = Condenser inlet temperature (°F)
Tcsw = Service water and condenser discharge mixed temperature (°F)
Tfe = Circulating water temperature exiting facility (°F)
Tri = Upstream river temperature (°F)
Tre = Downstream stream river temperature (°F)
& = River volumetric flow rate (ft3/s)
V
ri
vi
ACKNOWLEDGMENT
I would like to thank my family, friends, employers and professors for their support
while I worked on my Masters program.
vii
ABSTRACT
The purpose of this Engineering Project is to complete the thermal-hydraulic design of
replacement cooling towers for the Vermont Yankee Nuclear Power Station, located in
Vernon, VT. The need for new cooling towers is driven by State of Vermont
environmental discharge permit limitations and operation of the station at a higher power
rating. The cooling towers reduce the heat input to the river but are not always capable
of handling the increased heat load generated by the plant due to the power uprate
combined with the river temperature increase restrictions imposed by the discharge
permit.
The design parameters for the new towers were based on current design and operating
restrictions and developed using mass-energy balances over different portions of the
plant cooling water system, including the river. The sizing and makeup water
requirements were developed using available literature. The tower demand curves were
developed using a solution of the Merkel equation using the Chebyshev method.
The outcome of this project is that a thermal-hydraulic design was developed leading to
a new sizing requirements and demand curves of replacement counterflow cooling
towers that have sufficient heat removal capacity to operate in a closed cycle mode of
operation and therefore offset any need for permit-driven plant power reductions.
viii
1. Introduction
In 2006, Vermont Yankee Nuclear Power Station (VY) received approval from the US
Nuclear Regulatory Commission for an Extended Power Uprate (EPU) to operate at
120% of its originally designed core power output (1,912 MWth vs. 1,593 MWth) [1].
One of the limitations brought on by operating at this higher power output is that the
cooling towers at VY cannot adequately handle the entire heat load now generated when
operating at 100% power. As a result, a portion of the heated water from the plant
bypasses the cooling towers and is discharged to the Connecticut River. Limitations
imposed by the State of Vermont National Pollutant Discharge Elimination System
(NPDES) permit restrict the temperature rise of the river due to the VY thermal
discharge, as measured at various monitoring stations along the river in the vicinity of
the plant. The most restrictive temperature limitations occur during the period of May 16
through June 15 [2, 3]. During this time, operational restrictions imposed by the permit
can require VY to reduce power output in order to not exceed the thermal discharge
limitations. Figure 1 shows an aerial view of Vermont Yankee. The cooling towers are in
the lower left portion of the photograph.
Figure 1 - Aerial view of Vermont Yankee
1.1 Cooling Tower Operating Principles
Cooling towers are used in industrial applications to remove heat from cooling water. A
cooling tower system consists of a network of heat exchangers and pumps in open or
closed circuits. Additional water is introduced into the system to make up for inherent
losses in the process. The thermal performance of cooling towers plays an important role
in the operation of the system(s) being cooled.
There are two main types of cooling towers, natural draft and mechanical draft. Natural
(or atmospheric) draft cooling towers use large chimney-like structures to draw air
through the cooling water whereas mechanical draft cooling towers rely on fans to force
air through the water, allowing for close control of cold water temperature. There are
two types of mechanical draft cooling towers, counterflow and cross-flow, depending on
the relative flow direction between the air and water, as shown in Figures 2 and 3,
respectively. The analytical portion of this project will focus on counterflow towers.
Figure 3 - Cross-flow Cooling Tower [6]
Figure 2 - Counterflow Cooling Tower [6]
2
Mechanical draft cooling towers consist of large chambers filled with plastic slats called
fill material. The water to be cooled is pumped up to a distribution header at the top of
the tower and is distributed down evenly across the length of the tower. As the water
drops down and hits the fill material, it disperses into droplets in order to maximize the
heat transfer surface area and exchanges heat with the upward moving air. The cooled
water is then collected in a basin and pumped out to begin the heat exchange process
over again or simply discharged to a body of water. Figure 4 shows a picture of fill
material used in the Vermont Yankee cooling towers.
Figure 4 - Fill Material
Cooling towers operate on the principle of evaporative cooling in which the water that is
to be cooled is exposed to air. The heat transfer process consists of mass heat transfer, in
the form of evaporation, and sensible heat transfer due to the temperature difference
between the air and water. Approximately 80 percent of the heat transfer is due to
evaporation and 20 percent is due to sensible heat transfer [4]. This process is depicted
in Figure 5 [6].
3
Figure 5 - Water droplet interaction with air [6]
The theoretical possible heat removal per pound of air circulated in a cooling tower
depends on the temperature and moisture content of the air. An indication of the
moisture content of the air is the wet-bulb temperature. Ideally, the wet-bulb temperature
is the lowest temperature to which the water can be cooled. In practical applications, the
cold water temperature approaches but does not equal the air wet-bulb temperature
because it is impossible to contact all the water with fresh air as the water drops through
the fill to the basin. The magnitude of approach to the wet-bulb temperature is dependent
on tower design. Important factors are air-to-water contact time, amount of fill surface
and break up of water into drops [4]. The closer the approach, i.e. the smaller the
difference between wet-bulb temperature and cold water temperature, the more
expensive the cooling tower design will be.
1.2 Types of Cooling Towers
As mentioned in the previous section, there are three types of cooling towers:
counterflow, cross-flow and natural draft. Both the counterflow and cross-flow types fall
under the mechanical draft category.
The counterflow arrangement is the most thermodynamically efficient due to the coldest
water being in contact with the coldest air. This maximizes the enthalpy potential. The
4
advantages of the counterflow type are that greater cooling ranges and more difficult
approaches are able to be utilized.
Increasing the air flow to lower the L/G ratio and therefore reducing the tower
characteristic at very low approaches is the advantage of the cross-flow tower. The
increase in air flow is accomplished by lengthening the tower to increase the air flow
cross-sectional area. The disadvantage of doing this is an increase in fan power
requirements [4].
The natural draft tower relies on a difference density between cool inlet air and the hot
outlet air to drive air flow, rather than using fans. The advantages of this type are that no
electric power is necessary, except for pump head requirements, and no mechanical
equipment is necessary, which reduces maintenance costs. The disadvantages are that
they are dependent on atmospheric conditions, which can limit the cooling capacity; they
are inefficient at low wind velocities; they have relatively high water losses when wind
velocities are high and high pump head requirements to achieve maximum air-water
contact times [6].
1.3 Vermont Yankee Cooling Towers
The cooling tower system at Vermont Yankee (VY) currently consists of two cooling
towers, a deep water basin, three circulating water booster pumps and associated piping,
valves and instrumentation. Each tower consists of eleven partitioned cells containing an
individual fan unit. The fans are used to draw in air from outside of the towers [7].
A simplified schematic of the flow of circulating water through the intake structure,
circulating water pumps, main condenser, service water system, circulating water
booster pumps, cooling towers and discharge structure (forebay and afterbay) is depicted
in Figure 6. The service water system provides cooling to various pumps and auxiliary
heat exchangers throughout the plant. Water is drawn in from the Connecticut River into
the intake structure by the circulating water pumps. The discharge of the pumps is
5
directed to the main condenser where it removes heat from the reactor steam after it has
passed through the main turbine. The heated water leaving the condenser enters the
forebay in the intake structure where flow can then be directed to the cooling towers via
the circulating water booster pumps, depending on the mode of operation of the cooling
tower system. There are three circulating water booster pumps, each with a capacity of
122,000 gpm [7]. Water enters the cooling towers through two parallel discharge headers
at the top of the towers and flows down through the fill, exchanging heat with the air that
is drawn in by a 200-hp fan located at the top of each cell. The cooled water collects in
the deep basin and is gravity discharged to the afterbay in the discharge structure for
return to the river or recirculation back to the intake structure.
There are three modes of operation for the cooling towers. In the closed cycle mode
circulating water is supplied to the discharge structure where the bypass line is closed.
All flow is then directed to the cooling towers via the circulating water booster pumps to
the cooling towers. Return water from the cooling towers is directed from the afterbay to
through the recirculation line back into the intake structure and circulating water pumps.
This is the mode in which the heat transfer cycle is considered self-contained as no water
is discharged to the river. The increase in design heat load from the main condenser from
3.605 x 109 Btu/hr to 4.4 x 109 Btu/hr, due to the power uprate to 1912 MWth, has
resulted in the inability of the power plant to operate at 100% power in the closed cycle
mode during periods of high wet bulb temperature that occur primarily during the
summer months [7]. In the Recirculation or Hybrid mode of operation, circulating water
from the condenser is pumped from the discharge structure by the circulating water
booster pumps and through the cooling towers. Part of the flow is then directed back to
the river and the rest is diverted through the recirculation line back to the intake
structure. The closed cycle mode is actually a special case of the Hybrid mode. The third
operating mode is the Helper, or discharge mode, which is the same as the recirculation
mode except that all of the cooled water leaving the cooling towers is discharged straight
to the river. An additional mode, open cycle, occurs when all of the circulating water
discharged from the condenser bypasses the cooling towers altogether and is discharged
6
straight to the river. The four mass-energy balances (MEB 1-4) depicted in Figure 6 are
detailed in Appendix A.
The cooling towers have a 366,000 gpm and 2.6 x 109 Btu/hr design capacity. The
discharge from the towers was originally designed to be 87°F with a 101.2°F inlet and
75°F ambient wet-bulb temperature [7]. The design heat removal capacity is now
insufficient to meet the operational needs of VY since EPU was approved. A new set of
towers would allow closed cycle operation during the summer months when thermal
discharges to the Connecticut River are permit restricted and thus eliminate the need for
unnecessary power reductions due to these restrictions.
Construction of new cooling towers is an expensive proposition. Recently, the Oyster
Creek nuclear power plant in New Jersey has been threatening to close down if the NJ
Department of Environmental Protection requires it to build cooling towers at that site.
The new towers are estimated to cost between $700 million and $800 million [8].
7
Evaporative
Losses
mevapdrift
Cooling Tower
∆Tt
Ttcw, mte
Basin
Qsw
Tri, msw
Tthw, m ti
Service
Water
∆Tcond
Tce, mc
MEB-2
Tci, mc
Condenser
Tcsw, mcsw
MEB-3
Circulating
Water Pumps
Tri, mfi
Circulating
Water
Booster
Pumps
∆Tcwbp
∆Tcwp
Intake
Forebay
Afterbay
bypass
Trecirc, mrecirc
Tfe, mfe
recirculation
Tri, mre, Vri
Blowdown (not modeled)
River
MEB-1
Figure 6 - Vermont Yankee Circulating Water Flow Diagram
8
Tre, m re
2. Methodology
2.1 Review of Cooling Tower Theory
Cooling tower heat transfer analysis combines the sensible and mass heat transfer
mechanisms into an overall process that uses enthalpy potential as the driving force for
heat transfer. The combined sensible and mass heat transfer processes that are depicted
in Figure 6 are represented by the tower characteristic equation [6]
T
1
KaV
dT
= Cp ∫
L
h − ha
T2 w
where
K = tower characteristic or enthalpy transfer coefficient (lbm/hr-ft2)
a = contact area/tower volume (ft2/ft3)
V = active cooling volume/plan area (ft3/ft2)
L = water flow rate (lbm/hr-ft2)
Cp = specific heat capacity of water (Btu/lbm-°F)
T1 and T2 = entering and leaving water temperatures (°F)
hw = enthalpy of air-water vapor mixture at bulk water temperature
(Btu/lbm dry air)
ha = enthalpy of air-water vapor mixture at wet bulb temperature
(Btu/lbm dry air)
The heat balance across the cooling tower itself, where the laws of thermodynamics
require that the heat discharged by the water falling through the cooling tower equal the
heat absorbed by the air rising up through the tower, is governed by
h 2 − h1
L
=
G C p (T1 − T2 )
Where
L = water flow rate (lbm/hr-ft2)
T1=hot-water temperature (°F)
T2=cold-water temperature (°F)
G= air flow rate, (lbm dry air/hr-ft2)
Cp = specific heat capacity of water (Btu/lbm-°F)
9
h2=enthalpy of air-water vapor mixture at exhaust wet-bulb temperature
(Btu/lbm)
h1=enthalpy of air-water vapor mixture at inlet wet-bulb temperature,
(Btu/lbm)
The term L/G is the liquid to gas ratio. The tower characteristic, KaV/L, can be solved
numerically using the Chebyshev method [5].
T
1
T − T2
KaV
dT
= Cp ∫
= Cp 1
L
h − ha
4
T2 w
Where
 1
1
1
1 


+
+
+
 ∆h 1 ∆h 2 ∆h 3 ∆h 4 
∆h1=value of hw-ha at T2+0.1(T1-T2)
∆h2=value of hw-ha at T2+0.4(T1-T2)
∆h3=value of hw-ha at T1-0.4(T1-T2)
∆h4=value of hw-ha at T1-0.1(T1-T2)
These can also be written as
∆h1=value of hw-ha at T2+0.1Range
∆h2=value of hw-ha at T2+0.4Range
∆h3=value of hw-ha at T2+0.6Range
∆h4=value of hw-ha at T2+0.9Range
The enthalpy of the air exiting the cooling tower is determined by heat balance
Water HeatIn +Air HeatIn = Water HeatOut + Air HeatOut
This is equivalent to
CpL1T1 + Gh1 = CpL2T2 + Gh2
Where
Cp = specific heat capacity of water
L1 = flow rate of inlet water
L2 = flow rate of outlet water
The difference between the flow rates of the inlet and outlet water is due to evaporation
losses. Evaporation loss is expressed by
G(x2-x1) = L2-L1 => L2=L1-G(x2-x1)
where
x1, x2 = absolute humidity of the inlet and outlet air
From this we have
CpL1T1 + Gh1 = Cp[L1-G(x2-x1)]T2+Gh2
this can be written as
10
CpL1(T1-T2)=G(h2-h1)- CpT2G(x2-x1)
The evaporation rate is small compared to the water flow rates and can be considered to
be equal to zero [5]. Therefore G(x2-x1) ≈ 0 and
CpL1(T1-T2)=G(h2-h1)
The value of Cp=1 is valid for temperature ranges between 70°F-140°F. Solving for the
enthalpy of the exit air
h2=h1+L/G(T2-T1)
(T2-T1) is equal to the range
h2=h1+L/G x Range
Individual values of KaV/L are calculated using the method in Reference 5 as outlined
below:
1. The value of 1/( hw-ha) is determined at four points
1/( hw-ha) @ T2 + 0.1Range
1/( hw-ha) @ T2 + 0.4Range
1/( hw-ha) @ T2 + 0.6Range
1/( hw-ha) @ T2 + 0.9Range
2. The tower characteristic, KaV/L is then found by
KaV
R
1
= Cp ∑
(h w − h a )
L
4
Plotting several values of KaV/L as a function of L/G produces the tower demand
curves. The tower characteristic curve is then found for the design L/G by field testing
under variable flow and atmospheric conditions.
Figure 7 shows the water and air relationships and driving potential which exist in a
counterflow tower [6]. Line AB is the water operating line and is determined by the inlet
and outlet cooling water temperatures. The air operating line CD begins at C at appoint
with an enthalpy corresponding to the entering wet-bulb temperature. The line BC is the
initial enthalpy driving force. The liquid to gas ratio, L/G, is the slope of the air
operating line. The air exiting the tower is at point D and the cooling range is the
11
projected length of CD on the temperature scale or simply the difference between the hot
water temperature entering the tower and the cold water temperature leaving the tower.
The cooling tower approach is the difference between the cold water temperature leaving
the tower and the ambient wet-bulb. The tower characteristic, KaV/L, is the value of the
integral represented by the area ABCD and varies with the L/G ratio [4]. This value
varies with the rates of water and air flow. An increase in the entering air wet-bulb
temperature moves the origin C up and line CD shifts to the right to establish
equilibrium.
Figure 7 - Cooling Tower Heat Balance [6]
Once the wet-bulb temperature, the range, the approach and the L/G ratio are known, the
tower characteristic, KaV/L is found by referring to charts found in the Cooling Tower
12
Institute Blue Book (Figure 8) or the nomograph in Figure 9 rather than by direct
calculation [4,6]. To summarize, the three important points in cooling tower design to
consider regarding KaV/L are:
1. A change in wet-bulb temperature (due to atmospheric conditions) will not
change the tower characteristic.
2. A change in the cooling range will not change the tower characteristic.
3. Only a change in the L/G ratio will change KaV/L.
These numbers represent the approach (cold
water temperature – wet bulb temperature)
Figure 8 - Example Tower Characteristic Curves [6]
Cooling towers are designed according to the highest geographic wet bulb temperatures
for the region of operation. This temperature dictates the minimum performance
13
available by the tower. As the wet bulb temperature decreases, so will the available
cooling water temperature. For example, in the cooling tower represented by Figure 8, if
the wet bulb temperature dropped to 75°F, the cooling water would still be exiting 10°F
above this temperature (85°F) due to the tower design.
Figure 9 - Nomograph of cooling tower characteristics [4]
Mechanical draft cooling towers are normally designed for L/G ratios ranging from 0.75
to 1.50 and values of KaV/L vary from 0.50 to 2.50 [4].
Cooling towers are designed to meet a heat load specification as defined by plant
engineers. Once the cooling water flow rate is selected, the heat load specification can be
14
set. The cooling tower is specified to cool a quantity of water [gal/min] through a
definite temperature gradient (range) to a final temperature which is a certain number of
degrees above the design wet-bulb temperature (approach) [6].
2.2 Design Parameter Selection
Two different cooling tower designs are considered for this project. The first design
(Design A) utilizes the same wet-bulb temperature (75°F) and condenser inlet
temperature (75°) as the current design. Whereas the current towers are designed for a
12°F approach, Design A has a 5°F approach, which is the lowest practical value when
taking economic considerations into view as a design approach less than 5°F
significantly increases the required size, and therefore cost of the towers. The heat load
removed by Design A is equal to the increased heat load from the condenser due to
power uprate and the heat load due to the service water system (Qsw in Figure 6). The
purpose of Design A is to produce cooling towers that are capable of removing the
required heat loads from the plant while operating in the Helper or Recirculation Modes
(all or a portion of the cooled water is discharged back to the river) without exceeding
the NPDES permit limitations for a river temperature increase during periods of
operation that could require the plant to reduce power under the current design.
Operating experience at the plant has shown that periods of high wet-bulb temperature
(80°F) and low river flow (1200ft3/s) can cause the plant to reduce power to avoid
exceeding the NPDES permit limitations [9]. The NPDES permit river temperature
limitations for the most restrictive period of May 16 – June 15 are shown in Table 1.
Table 1 - NPDES Permit Limits (May 16 - June 15)
Upstream River
Temperature
Above 63°F
>59°F, ≤63°F
≥55°F, ≤59°F
Below 55°F
Increase in Temperature
Above Upstream
2°F
3°F
4°F
5°F
To summarize, the inputs for Design A are the wet-bulb temperature, approach, tower
outlet temperature, water flow rate and heat removal capability. The calculated values
for Design A are the tower inlet temperature and cooling range.
15
The second design (Design B) to be considered is one in which the cooling towers are
capable of removing the entire heat load produced by the plant (condenser and service
water) while operating in the closed cycle mode. Operating experience has shown that
this is not achievable with the current design while operating at full power during
periods of high wet-bulb temperature (80°F). Therefore, this high wet-bulb temperature
is one of the design parameters. The other design parameter based on operating
experience is that if the condenser inlet temperature exceeds approximately 90°F,
condenser backpressure cannot be maintained at levels high enough to support high
power operation. Therefore, as Figure 6 shows, a maximum condenser inlet temperature
of 90°F is achieved by setting the tower outlet temperature to the same value, with an
accounting for the heat added by the circulating water pump. Operating in the closed
cycle mode at 100% power eliminates concerns related to meeting the NPDES permit
limitations. The heat load for Design B is the same as that for Design A.
To summarize, the inputs for Design B are the wet-bulb temperature, tower outlet
temperature, water flow rate and heat removal capability. The calculated values for
Design B are the tower inlet temperature, approach and cooling range.
For both designs, the cooling water flow rate through the towers remains unchanged
from the current design. Table 2 summarizes the parameters for the current design,
Design A and Design B. The mass-energy balances depicted in Figure 6 are solved in
Appendix A. The calculations using these mass-energy balances to determine the
unspecified parameters are in Appendix B. Appendix B also contains the calculations
used to determine if the NPDES permit limitations are exceeded with Design A in the
Helper mode and, if so, what amount of recirculation is required with this design to meet
the permit limitations.
16
Table 2 - Cooling Tower Design Parameters
Parameter
Current Design
Design A
Design B
Ambient Wet-bulb temp
75°F
75°F
80°F
Tower water flow rate
366,000 gpm
366,000 gpm
366,000 gpm
Cooling range
14.2°F
18.7°F
23.6°F
Tower inlet temp
101.2°F
98.7°F
113.6°F
Tower outlet temp
87°F
80°F
90°F
Approach
12°F
5°F
10°F
Heat removal capacity
2.6 x 109 Btu/hr 4.4 x 109 Btu/hr 4.4 x 109 Btu/hr
2.3 Methodology for Replacement Counterflow Cooling Tower Design
There are three fundamental components to the design of cooling towers:
1. Tower sizing
2. Makeup water requirements
3. Tower demand curves and determination of characteristic curve
2.3.1
Tower Sizing
For counterflow cooling towers, required size is determined using the following criteria:
1. Cooling range (hot water temperature minus cold water temperature)
2. Approach to wet-bulb temperature (cold water temperature minus wet-bulb
temperature)
3. Quantity of water to be cooled
4. Wet-bulb temperature
5. Tower height
6. Fan horsepower
Items 1-4 were determined in the previous section and are used to find the active tower
area. The nomograph shown in Figure 10 utilizes the cold water temperature, wet bulb
temperature, and hot water temperature to find the required water concentration in
gal/min-ft2. The tower area is then calculated by dividing the water circulated (tower
17
flow rate) by the water concentration. Reference 4 specifies the rules usually used to
determine tower height and are summarized in Table 3:
Table 3 - Tower Height Sizing
Approach to Wet-bulb (°F)
Cooling Range (°F)
Tower Height (ft)
15-20
25-35
15-20
10-15
25-35
25-30
5-10
25-35
35-40
Figure 10 - Counterflow Induced Draft Tower Sizing Chart [4]
Once the required tower area is found, the necessary fan horsepower for the tower is
found using the nomograph in Figure 11.
18
Figure 11 - Fan Horsepower Sizing Chart [4]
2.3.2
Makeup Water Requirements
To find the makeup water requirements due to operational losses (evaporation, drift and
blowdown) the following criteria are used [6]:
•
The evaporation loss is estimated as 0.1% of the circulating water flow rate for
each °F of cooling range.
•
Drift loss is due to entrained liquid water droplets discharged in the exiting air
and is estimated as 0.008% of the water circulation rate.
•
Cooling tower blowdown is a portion of the circulating water that is discharged
from the system to prevent excessive buildup of solids. The maximum
concentration of solids that can be tolerated is determined by the effects on the
various components of the cooling system and is a plant specific determination.
The required blowdown rate is calculated by
b=
Where
e
−d
r −1
b = blowdown rate (gal/min)
e = evaporation loss (gal/min)
r = ratio of solids in blowdown to solids in makeup, cycles of
concentration
19
d = drift loss (gal/min)
The ratio of solids in blowdown to solids in makeup is assumed to have a value of 25.
The makeup water rate is then determined as
M = b+e+d
Where
M = makeup rate (gal/min)
b = blowdown rate (gal/min)
e = evaporation loss (gal/min)
d = drift loss (gal/min)
2.3.3 Tower Demand Curves and Determination of Characteristic Curve
The tower demand curves are developed using the method described in Section 2.1. For
each design, A and B, the design approach, wet-bulb temperature (WBT), cold water
temperature (CWT) and range (R) are used as the starting point. The enthalpy of water
(hw) is obtained using Reference 10 at each of the four following temperatures:
hw0.1= CWT+0.1R
hw0.4= CWT+0.4R
hw0.6= CWT+0.6R
hw0.9= CWT+0.9R
The enthalpy of air (ha) at the wet bulb temperature (hwb) is obtained using Reference 4
and the following
ha0.1=hwb+0.1*L/G*R
ha0.4=hwb+0.4*L/G*R
ha0.6=hwb+0.6*L/G*R
ha0.9=hwb+0.9*L/G*R
At each increment (0.1, 0.4, 0.6, 0.9) the quantity 1/(hw-ha) is found. These four values
of 1/(hw-ha) are then used to find KaV/L at a discrete value of L/G by
KaV
R
1
= Cp ∑
(h w − h a )
L
4
Results are then plotted for KaV/L as a function of L/G.
20
With Design B, for approaches less than the design 10°F, the cooling range and cold
water temperature are kept constant while the wet-bulb temperature is increased. For
both designs, for approaches greater than design values, the cold water temperature and
range are held constant while the wet-bulb temperature is reduced.
The tower characteristic curve (the straight line in Figure 8) can be determined by field
testing after construction of the towers which results in two characteristic points at
different L/G ratios. Each characteristic point is determined experimentally by
measuring the wet-bulb temperature, air discharge temperature and cooling water inlet
and outlet temperatures. The line through the two characteristic points is the
characteristic curve and defines the design KaV/L and L/G ratio for the tower at a
specified approach. Alternatively, the tower characteristic curve is provided by the
vendor who performs the tower construction [5].
21
3. Results
As shown in Appendix B, Design A was found to exceed the NPDES permit
requirements if operated in the Helper mode. A recirculation rate of 45% is required to
meet the permit limitations for the design wet-bulb temperature of 75°F. If this
temperature is increased to 80°F, then the required recirculation rate is 74%.
3.1 Counterflow Tower Size
Table 4 shows the counterflow tower size requirements, developed using the methods
described in Section 2.3, based on the new design criteria selected in Section 2.2.
Table 4 - Counterflow Tower Size
Hot
Cold WetWater
Water
Tower Tower
water water bulb
Flow
Fan
Concentration
Area
Design
Height
Temp Temp Temp
Rate
Horsepower
2
2
(gal/min-ft )
(ft )
(ft)1
(°F)
(°F)
(°F) (gal/min)
A
98.7
80
75
366,000
2.0
7503
183,000 35-40
B
113.6
90
80
366,000
2.8
5359
130,714
25-30
Note 1 – Tower height approximated from Table 2
Table 5 shows the makeup water requirements, developed from Section 2.3, for the new
tower designs. The flow rate of river water (10,000gal/min) through the service water
system heat exchangers is sufficient to meet the makeup water requirements for either
design as they are both less than the service water flow rate. The evaporation loss as a
percentage of total circulating water flow was found to be 1.8% for Design A and 2.4%
for Design B and supports the approximation G(x2-x1) ≈ 0 used in Section 2.1.
Table 5 - Makeup Water Requirements
Design
Cooling
Range (°F)
Evaporation
Loss (gal/min)
Drift Loss
(gal/min)
Blowdown
Rate (gal/min)
A
18.7
6844.2
29
256.2
Makeup
Water Rate
(gal/min)
7129.4
B
23.6
8637.6
29
330.9
8997.5
22
3.2 Tower Demand Curves
The tower demand curves were developed using the methodology described in Section
2.3. Figure 12 shows the demand curves for Design A and Figure 13 shows the demand
curves for Design B. Appendix C contains a sample spreadsheet used in the
determination of the curves for Design A and Appendix D contains a sample spreadsheet
used to generate the Design B curves. As discussed in section 2.3.3, the tower
characteristic curve would be created based on test data obtained after the new towers
are constructed.
Approach
Range = 18.7°F
gpm = 366,000
WBT = 75°F
CWT = 80°F
HWT = 98.7°F
Fan hp = 7503
Figure 12 - Tower Demand Curves: Design A
23
Approach
Range = 23.6°F
gpm = 366,000
WBT = 80°F
CWT = 90°F
HWT = 113.6°F
Fan hp = 5359
Figure 13 - Tower Demand Curves: Design B
24
4. Conclusion
Two new proposed designs for replacement cooling towers at VYNPS were investigated.
They consisted of Design A, which utilizes the current design wet-bulb temperature and
lowest practical approach value to reduce the tower outlet temperature to minimize the
increase in river water temperature due to the return of plant cooling water to the river
and Design B, which utilizes the maximum observed wet-bulb temperature and closedcycle operation to eliminate the need to return cooling water to the river.
Design B is the choice for the new cooling towers based on the following:
•
Smaller tower footprint (29% less area than Design A)
•
Lower tower height
•
Lower fan horsepower requirements (29% less than Design A)
•
Unrestricted plant operations. The thermal discharge permit does not apply
to the use of closed cycle operations.
All of these bases result in lower construction and/or operating costs. The option for
unrestricted plant operations is especially valuable given that the thermal discharge
permit could be challenged in court by opposition groups, revised to strengthen
discharge restrictions or completely revoked.
25
5. References
1. Letter, USNRC to Entergy “Vermont Yankee Nuclear Power Station – Issuance
of Amendment RE: Extended Power Uprate (TAC No. MC0761),” NVY 06028, dated March 2, 2006
2. Letter, State of Vermont Agency of Natural Resources to Entergy Nuclear
Vermont Yankee, LLC “Final Amended Discharge Permit #3-1199,” dated
March 30, 2006
3. Letter, State of Vermont Agency of Natural Resources to Entergy Nuclear
Vermont Yankee, LLC “Renewal of Permit 3-1199,” dated September 20, 2005
4. Perry, Robert H., Perry’s Chemical Engineering Handbook, McGraw-Hill, 1994
5. Cooling Tower Thermal Design Manual, Daiel Aqua Co., Ltd.
6. Rosaler, Robert A., Standard Handbook of Plant Engineering, McGraw-Hill,
1995
7. Vermont Yankee Updated Final Safety Analysis Report, Revision 23
8. http://www.nj.com/news/index.ssf/2010/02/oyster_creek_plant_hearings_fo.html
9. Vermont Yankee Calculation, Cooling Water Plant Settings for OP-2180, VYC2403, Rev 0.
10. Cengel, Yunus A. and Turner, Robert F., Fundamentals of Thermal-Fluid
Sciences, McGraw-Hill, 2001
26
Appendix A - Mass-Energy Balances
River MEB-1
Tri,msw
Tri,mfi
Tre,mre
Tri,mri
Tfe,mfe
∑ m&
o
& ihi +
ho − ∑ m
dE & &
=Q−W
dt
dE &
& =0⇒
=Q=W
dt
& sw h ri + m
& fi h ri + m
& ri h ri − m
& fe h fe = 0
m
Open cycle
& fe = m
& fi + m
& sw
m
& re = m
& ri = m
&r
m
Tfe = Tcsw
& fi = m
&c
m
& fe = m
& c +m
& sw
m
so
& sw h ri + m
& c h ri + m
& r h re − m
& r h ri − (m
& c +m
& sw )h fe = 0
m
& r (h re − h ri ) + m
& c (h fi − h fe ) + m
& sw (h swi − h fe ) = 0
m
substitute ∆h=Cp∆T, Cp=1 Btu/lb-°F
& r (Tre − Tri ) + m
& c (Tri − Tcsw ) + m
& sw (Tri − Tcsw ) = 0
m
⇒
Tre =
& c (Tcsw − TTri ) + m
& sw (Tcsw − Tri )
m
+ Tri
&r
m
27
(1)
Helper mode
& fi = m
&c
m
& fe = m
& te = m
& fi + m
& sw − m
& evapdrift
m
& re = m
& ri − m
& evapdrift
m
Tfe = Ttcw
from Eq 1
& sw h ri + m
& c h ri + (m
& ri − m
& evapdrift )h re − m
& ri h ri − (m
& c +m
& sw − m
& evapdrift )h fe = 0
m
collect terms and substitute ∆h=Cp∆T, Cp=1 Btu/lb-°F
(m&
Tre =
c
& sw − m
& evapdrift )Ttcw + (m
& ri − m
& c −m
& sw )Tri
+m
& ri − m
& evapdrift
m
Hybrid cycle
& fe = m
& fi + m
& sw − m
& evapdrift
m
& re = m
& ri − m
& evapdrift
m
Tfe = Ttcw
from Eq 1
& sw h ri + m
& fi h ri + (m
& ri − m
& evapdrift )h re − m
& ri h ri − (m
& fi + m
& sw − m
& evapdrift )h fe = 0
m
collect terms and substitute ∆h=Cp∆T, Cp=1 Btu/lb-°F
(m&
Tre =
fi
& sw − m
& evapdrift )Ttcw + (m
& ri − m
& fi − m
& sw )Tri
+m
& ri − m
& evapdrift
m
Condenser/Service Water MEB-2
Tswe,msw
Tce,mc
∑ m&
Tcsw,mcsw
o
& ihi +
ho − ∑ m
dE & &
=Q−W
dt
dE &
& =0⇒
=Q=W
dt
& csw h csw − m
& c h ce − m
& sw h swe = 0
m
28
& csw = m
& sw + m
&c
m
& =m
& sw C p (Tswe − Tri )
Q
sw
Tswe =
&
Q
sw
+ Tri
& sw C p
m
& csw h csw − m
& c h ce − m
& sw h swe = 0
m
(m& sw + m& c )h csw − m& c h ce − m& sw h swe = 0
& c (h csw − h ce ) + m
& sw (h csw − h swe ) = 0
m
substitute ∆h=Cp∆T, Cp=1 Btu/lb-°F
&


Q
& c (Tcsw − Tce ) + m
& sw  Tcsw −  sw + Tri   = 0 ⇒
m

m


 & sw

&
& T +m
& c Tce + Q
m
sw
Tcsw = sw ri
+ ∆TCWP
& sw + m
&c
m
where ∆TCWP is the temperature rise due to the work of the circulating water pumps
Tthw = Tcsw + ∆TCWBP
where ∆TCWBP is the temperature rise due to the work of the circulating water booster
pumps
Recirculation MEB-3
Tci,mc
Tri, mfi
∑ m&
o
& ihi +
ho − ∑ m
Trecirc,mrecirc
dE & &
=Q−W
dt
dE &
& =0⇒
=Q=W
dt
& c h ci − m
& fi h ri − m
& recirc h recirc = 0
m
29
R = %Recirc
& fi = (1 − R )m
&c
m
& recirc = Rm
&c
m
Trecirc = Ttcw
& c h ci − m
& fi h ri − m
& recirc h recirc = 0
m
& c h ci − (1 − R )m
& c h ri − Rm
& c h recirc = 0
m
& c h ci − m
& c h ri + Rm
& c h ri − Rm
& c h recirc = 0
m
substitute ∆h=Cp∆T, Cp=1 Btu/lb-°F
& c (Tci − Tri ) + Rm
& c (Tri − Ttcw ) = 0
⇒m
⇒ Tci = Tri + R (Ttcw − Tri )
Closed Cycle
The closed cycle mode is a special case of Hybrid operation in which the circulating
water system is operating at 100% recirculation flow. The full cooling tower discharge
flow is directed back to the circulating water intake structure (R=1).
30
Appendix B - Design Parameter Calculations
Constants and Conversion Factors
1 gallon = 0.13368 ft3
CWBPhead = 73 ft
1 Btu = 778.171 lbf-ft
Cp=1.0 Btu/lbm-°F
1 lbf= 1 lbm
∆Tsw= 10°F
ν75 = 0.016062 ft3/lbm
& = 10,000 gal/min
V
sw
ν90 = 0.016099 ft3/lbm
& = 366,000 gal/min
V
c
ηCWP = 0.86
9
&
Q
cond = 4.4x10 Btu/hr
CWPhead = 86 ft
ηCWBP = 0.89
∆TCWP =
CWPhead
86ft lbm − °F
Btu
=
= 0.1285°F
C p ηCWP 0.86 1Btu 778.171lbf − ft
∆TCWBP =
CWBPhead
73ft lbm − °F
Btu
=
= 0.1054°F
C p ηCWBP 0.89 1Btu 778.171lbf − ft
Design A
Tci = 75°F
Twb = 75°F
Tri = Tci - ∆TCWP = 74.8715°F
& sw
m
10000gal 60min 0.13366ft 3
lbm
&
= Vsw ν75 =
= 4.993x10 6 lbm/hr
3
min
hr
gal
0.016062ft
4.993x10 6 lbm 1Btu 10°F
& =m
&
Q
C
∆T
= 4.994x10 7 Btu/hr
=
sw
sw p
sw
hr
lbm − °F
3
lbm
& ν75 = 366000gal 60min 0.13366ft
& cw = V
= 1.828x108 lbm/hr
m
c
min
hr
gal
0.016062ft 3
∆Tcond =
&
Q
4.4x10 9 Btu
hr
lbm − °F
cond
=
= 24.07°F
8
& cw C p
m
hr
1.828x10 lbm 1Btu
⇒ Tce = Tci + ∆Tcond = 75°F + 24.07°F = 99.07°F
31
Tcsw =
&
& sw Tri + m
& cw Tce + Q
m
sw
+ ∆TCWP = 98.58°F [MEB - 2]
& sw + m
& cw
m
Tthw = Tcsw + ∆TCWBP = 98.69°F
Ttcw = 80°F ⇒ Range = Tthw - Ttcw = 18.7°F, Approach = Ttcw - Twb = 5°F
Check to see if NPDES limit from Table 3 is exceeded in Helper Mode (no recirculation)
with minimum river flow:
3
lbm
3600s
& = 1200ft 3 /s ⇒ m
& ν75 = 1200ft
&
=
= 2.69x10 8 lbm/hr
V
V
ri
ri
ri
3
s
hr
0.016062ft
& evapdrift = 6844gal/min + 29gal/min = 6871gal/min [Table 4]
m
& evapdrift =
m
Tre =
(m&
6871gal
lbm
60min 0.13368ft 3
= 57054lbm/hr
min 0.016099ft 3 hr
gal
c
& sw − m
& evapdrift )Ttcw − (m
& ri − m
& c −m
& sw )Tri
+m
= 78.45°F [MEB - 1]
& ri − m
& evapdrift
m
∆Trmax= 2°F => Tre – Tri = 3.58°F > ∆Trmax => No Helper Mode allowed
where ∆Trmax is the maximum allowed river temperature increase as specified by the
NPDES permit
What % Recirculation is required to get ∆Trmax = 2°F?
Need Tre = 76.87°F to get ∆Trmax = 2°F
& fi = (1 − R )m
&c⇒
m
Tre =
(m&
fi
& fi
&
m
m
= 1 − R ⇒ R = 1 − fi [MEB-3]
&c
&c
m
m
& sw − m
& evapdrift )Ttcw − (m
& ri − m
& fi − m
& sw )Tri
+m
= 76.87°F [MEB - 1,3]
& ri − m
& evapdrift
m
& fi , m
& fi = 9.9915x107 lbm/hr
Solve for m
9.9915x10 7 lbm
hr
⇒ R = 1−
= 0.45 = 45%
hr
1.828x10 8 lbm
What if Twb = 80°F?
& fi = 4.816x10 7 lbm/hr ⇒ R = 1 −
⇒ Ttcw = 85°F ⇒ m
32
4.816x10 7
= 0.74 = 74%
1.828x10 8
Design B
This design utilizes closed cycle operation of the circulating water system with all of the
plant heat rejected by the cooling towers. This is equivalent to operating with 100%
recirculation.
Input assumptions:
•
Tci max = 90°F Loss of condenser backpressure above this temperature leads to a
required reduction in reactor power
•
Twb = 80°F Maximum observed by operating experience at VY
•
Tri = 75°F Consistency with Design A
3
lbm
60min
& ν90 = 366000gal 0.13368ft
&c =V
m
= 1.82348x108 lbm/hr
c
3
min
gal
hr
0.016099ft
∆Tcond =
&
Q
4.4x10 9 Btu
hr
lbm - °F
cond
=
= 24.13°F
8
& cCp
m
hr
1.82348x10 lbm Btu
Tce = Tci max + ∆Tcond = 114.13°F
Tcsw =
&
& sw Tri + m
& c Tce + Q
m
sw
+ ∆TCWP = 113.48°F [MEB-2]
& sw + m
&c
m
Tthw = Tcsw + ∆TCWBP = 113.6°F
For 100% recirculation, the tower exit temperature needs to be equal to the condenser
inlet temperature
Ttcw = Tci max = 90°F => Range = Tthw - Ttcw = 23.6°F
Approach = Ttcw – Twb = 10°F
33
80
Cold Water Temperature (CWT) (°F) =
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
0.11
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
CWT +
0.1R
0.1
L/G
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
CWT +
0.4R
98.7
Hot Water Temperature (HWT) (°F) =
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
Water Side
CWT
+
hCWT +
CWT +
0.9R 0.1R
0.6R
5
18.7
Cooling Range (R) (°F) =
Approach (°F) =
75
38.6
Enthalpy of sat. air at WBT (Btu/lbm) =
29.9
Wet-bulb Temperature (°F)@ inlet =
Barometric Pressure (in. Hg) =
hCWT +
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
0.4R
hCWT
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
+ 0.6R
hCWT
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
+ 0.9R
39.049
39.03
39.011
38.993
38.974
38.955
38.937
38.918
38.899
38.881
38.862
38.843
38.824
38.806
38.787
hWB+0.1*L/G*R
34
40.395
40.32
40.246
40.171
40.096
40.021
39.946
39.872
39.797
39.722
39.647
39.572
39.498
39.423
39.348
hWB+0.4*L/G*R
41.293
41.181
41.068
40.956
40.844
40.732
40.62
40.507
40.395
40.283
40.171
40.059
39.946
39.834
39.722
hWB+0.6*L/G*R
Air Side
42.639
42.471
42.303
42.134
41.966
41.798
41.629
41.461
41.293
41.125
40.956
40.788
40.62
40.451
40.283
hWB+0.9*L/G*R
0.092
0.091
0.091
0.091
0.091
0.091
0.091
0.091
0.09
0.09
0.09
0.09
0.09
0.09
0.09
1/(hw0.1ha0.1)
0.0659
0.0656
0.0653
0.0649
0.0646
0.0643
0.064
0.0637
0.0634
0.0631
0.0628
0.0625
0.0622
0.0619
0.0616
1/(hw0.4ha0.4)
0.0556
0.0552
0.0549
0.0545
0.0542
0.0539
0.0536
0.0532
0.0529
0.0526
0.0523
0.052
0.0517
0.0514
0.0511
1/(hw0.6ha0.6)
Enthaply Difference
Appendix C - Tower Demand Curve Excel Spreadsheets – Design A
0.0449
0.0446
0.0443
0.0439
0.0436
0.0433
0.043
0.0427
0.0424
0.0421
0.0418
0.0415
0.0412
0.0409
0.0406
1/(hw0.9ha0.9)
1.2063
1.2009
1.1955
1.1902
1.1849
1.1798
1.1746
1.1695
1.1645
1.1595
1.1546
1.1497
1.1449
1.1401
1.1354
KaV/L
81.9
81.9
81.9
0.51
0.52
81.9
0.48
81.9
81.9
0.47
0.5
81.9
0.49
81.9
81.9
0.4
0.46
81.9
0.39
0.45
81.9
0.38
81.9
81.9
0.37
0.44
81.9
0.36
81.9
81.9
0.35
0.43
81.9
0.34
81.9
81.9
0.33
81.9
81.9
0.32
0.41
81.9
0.31
0.42
81.9
81.9
0.28
81.9
81.9
0.27
0.3
81.9
0.26
0.29
81.9
0.25
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
39.572
39.554
39.535
39.516
39.498
39.479
39.46
39.442
39.423
39.404
39.385
39.367
39.348
39.329
39.311
39.292
39.273
39.255
39.236
39.217
39.198
39.18
39.161
39.142
39.124
39.105
39.086
39.068
35
40.47
42.49
42.415
42.34
42.265
42.19
42.116
42.041
41.966
41.891
41.816
41.742
41.667
41.592
41.517
41.442
41.368
41.293
41.218
41.143
41.068
40.994
40.919
40.844
40.769
40.694
40.62
40.545
44.434
44.322
44.21
44.098
43.986
43.873
43.761
43.649
43.537
43.425
43.312
43.2
43.088
42.976
42.864
42.751
42.639
42.527
42.415
42.303
42.19
42.078
41.966
41.854
41.742
41.629
41.517
41.405
47.352
47.183
47.015
46.847
46.678
46.51
46.342
46.174
46.005
45.837
45.669
45.5
45.332
45.164
44.995
44.827
44.659
44.491
44.322
44.154
43.986
43.817
43.649
43.481
43.312
43.144
42.976
42.808
0.096
0.096
0.096
0.096
0.096
0.095
0.095
0.095
0.095
0.095
0.095
0.094
0.094
0.094
0.094
0.094
0.094
0.093
0.093
0.093
0.093
0.093
0.093
0.092
0.092
0.092
0.092
0.092
0.0765
0.076
0.0756
0.0752
0.0747
0.0743
0.0739
0.0735
0.0731
0.0727
0.0723
0.0719
0.0715
0.0712
0.0708
0.0704
0.07
0.0697
0.0693
0.069
0.0686
0.0683
0.0679
0.0676
0.0672
0.0669
0.0666
0.0662
0.0673
0.0668
0.0663
0.0658
0.0653
0.0649
0.0644
0.0639
0.0635
0.063
0.0626
0.0622
0.0617
0.0613
0.0609
0.0605
0.0601
0.0597
0.0593
0.0589
0.0585
0.0581
0.0577
0.0574
0.057
0.0566
0.0563
0.0559
0.057
0.0564
0.0559
0.0554
0.0549
0.0544
0.0539
0.0534
0.0529
0.0525
0.052
0.0515
0.0511
0.0507
0.0502
0.0498
0.0494
0.049
0.0486
0.0482
0.0478
0.0474
0.0471
0.0467
0.0463
0.046
0.0456
0.0453
1.3886
1.3808
1.3732
1.3657
1.3583
1.351
1.3438
1.3366
1.3296
1.3227
1.3159
1.3091
1.3024
1.2959
1.2894
1.283
1.2766
1.2704
1.2642
1.2581
1.2521
1.2461
1.2402
1.2344
1.2287
1.223
1.2174
1.2118
81.9
81.9
81.9
0.79
0.8
81.9
0.76
81.9
81.9
0.75
0.77
81.9
0.78
81.9
81.9
0.68
0.74
81.9
0.67
0.73
81.9
0.66
81.9
81.9
0.65
0.72
81.9
0.64
81.9
81.9
0.63
0.71
81.9
0.62
81.9
81.9
0.61
81.9
81.9
0.6
0.7
81.9
0.59
0.69
81.9
81.9
0.56
81.9
81.9
0.55
0.57
81.9
0.54
0.58
81.9
0.53
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
40.096
40.077
40.059
40.04
40.021
40.003
39.984
39.965
39.946
39.928
39.909
39.89
39.872
39.853
39.834
39.816
39.797
39.778
39.759
39.741
39.722
39.703
39.685
39.666
39.647
39.629
39.61
39.591
36
42.564
44.584
44.509
44.434
44.36
44.285
44.21
44.135
44.06
43.986
43.911
43.836
43.761
43.686
43.612
43.537
43.462
43.387
43.312
43.238
43.163
43.088
43.013
42.938
42.864
42.789
42.714
42.639
44.547
47.576
47.464
47.352
47.239
47.127
47.015
46.903
46.791
46.678
46.566
46.454
46.342
46.23
46.117
46.005
45.893
45.781
45.669
45.556
45.444
45.332
45.22
45.108
44.995
44.883
44.771
44.659
47.52
52.064
51.896
51.727
51.559
51.391
51.223
51.054
50.886
50.718
50.549
50.381
50.213
50.044
49.876
49.708
49.54
49.371
49.203
49.035
48.866
48.698
48.53
48.361
48.193
48.025
47.857
47.688
0.096
0.101
0.101
0.101
0.101
0.101
0.1
0.1
0.1
0.1
0.1
0.099
0.099
0.099
0.099
0.099
0.099
0.098
0.098
0.098
0.098
0.098
0.097
0.097
0.097
0.097
0.097
0.097
0.0769
0.091
0.0904
0.0898
0.0892
0.0886
0.088
0.0875
0.0869
0.0863
0.0858
0.0852
0.0847
0.0841
0.0836
0.0831
0.0826
0.0821
0.0816
0.0811
0.0806
0.0801
0.0796
0.0792
0.0787
0.0782
0.0778
0.0773
0.0678
0.0854
0.0846
0.0838
0.083
0.0822
0.0815
0.0807
0.08
0.0793
0.0786
0.0779
0.0772
0.0766
0.0759
0.0753
0.0746
0.074
0.0734
0.0728
0.0722
0.0716
0.0711
0.0705
0.07
0.0694
0.0689
0.0683
0.0575
0.0779
0.0769
0.0759
0.075
0.074
0.0731
0.0722
0.0714
0.0705
0.0697
0.0689
0.0681
0.0673
0.0666
0.0658
0.0651
0.0644
0.0637
0.063
0.0624
0.0617
0.0611
0.0605
0.0599
0.0593
0.0587
0.0581
1.6628
1.6505
1.6385
1.6267
1.6151
1.6037
1.5925
1.5815
1.5707
1.5602
1.5497
1.5395
1.5295
1.5196
1.5098
1.5003
1.4908
1.4816
1.4725
1.4635
1.4546
1.4459
1.4374
1.4289
1.4206
1.4124
1.4044
1.3964
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
81.9
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
81.9
0.88
0.92
81.9
0.87
81.9
81.9
0.86
0.91
81.9
0.85
81.9
81.9
0.84
81.9
81.9
0.83
0.9
81.9
0.82
0.89
81.9
0.81
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
40.62
40.601
40.582
40.564
40.545
40.526
40.507
40.489
40.47
40.451
40.433
40.414
40.395
40.377
40.358
40.339
40.32
40.302
40.283
40.264
40.246
40.227
40.208
40.19
40.171
40.152
40.133
40.115
37
46.678
46.604
46.529
46.454
46.379
46.304
46.23
46.155
46.08
46.005
45.93
45.856
45.781
45.706
45.631
45.556
45.482
45.407
45.332
45.257
45.182
45.108
45.033
44.958
44.883
44.808
44.734
44.659
50.718
50.605
50.493
50.381
50.269
50.157
50.044
49.932
49.82
49.708
49.596
49.483
49.371
49.259
49.147
49.035
48.922
48.81
48.698
48.586
48.474
48.361
48.249
48.137
48.025
47.913
47.8
47.688
52.232
56.776
56.608
56.44
56.272
56.103
55.935
55.767
55.598
55.43
55.262
55.093
54.925
54.757
54.589
54.42
54.252
54.084
53.915
53.747
53.579
53.41
53.242
53.074
52.906
52.737
52.569
52.401
0.102
0.107
0.107
0.107
0.106
0.106
0.106
0.106
0.106
0.105
0.105
0.105
0.105
0.105
0.104
0.104
0.104
0.104
0.104
0.103
0.103
0.103
0.103
0.103
0.102
0.102
0.102
0.102
0.0916
0.1125
0.1115
0.1106
0.1097
0.1088
0.1079
0.1071
0.1062
0.1054
0.1046
0.1037
0.1029
0.1022
0.1014
0.1006
0.0999
0.0991
0.0984
0.0977
0.097
0.0963
0.0956
0.0949
0.0942
0.0936
0.0929
0.0923
0.1167
0.1151
0.1137
0.1122
0.1108
0.1095
0.1082
0.1069
0.1056
0.1044
0.1032
0.102
0.1008
0.0997
0.0986
0.0975
0.0965
0.0954
0.0944
0.0934
0.0925
0.0915
0.0906
0.0897
0.0888
0.0879
0.087
0.0862
0.1231
0.1206
0.1182
0.1159
0.1137
0.1115
0.1095
0.1075
0.1056
0.1038
0.102
0.1003
0.0986
0.097
0.0954
0.0939
0.0925
0.091
0.0897
0.0883
0.087
0.0858
0.0846
0.0834
0.0822
0.0811
0.08
0.0789
2.1471
2.123
2.0996
2.0769
2.0549
2.0334
2.0126
1.9923
1.9726
1.9534
1.9346
1.9164
1.8986
1.8812
1.8642
1.8477
1.8315
1.8157
1.8003
1.7852
1.7704
1.756
1.7418
1.728
1.7144
1.7011
1.6881
1.6753
81.9
81.9
81.9
1.25
1.26
1.27
1.28
81.9
81.9
1.24
1.36
81.9
1.23
81.9
81.9
1.22
1.35
81.9
1.21
81.9
81.9
1.2
81.9
81.9
1.19
1.34
81.9
1.18
1.33
81.9
1.17
81.9
81.9
1.16
1.32
81.9
1.15
81.9
81.9
1.14
1.31
81.9
1.13
81.9
81.9
1.12
81.9
81.9
1.11
1.3
81.9
1.1
1.29
81.9
81.9
1.09
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
40.638
41.143
41.125
41.106
41.087
41.068
41.05
41.031
41.012
40.994
40.975
40.956
40.938
40.919
40.9
40.881
40.863
40.844
40.825
40.807
40.788
40.769
40.751
40.732
40.713
40.694
40.676
40.657
38
48.773
48.698
48.623
48.548
48.474
48.399
48.324
48.249
48.174
48.1
48.025
47.95
47.875
47.8
47.726
47.651
47.576
47.501
47.426
47.352
47.277
47.202
47.127
47.052
46.978
46.903
46.828
46.753
50.83
53.859
53.747
53.635
53.523
53.41
53.298
53.186
53.074
52.962
52.849
52.737
52.625
52.513
52.401
52.288
52.176
52.064
51.952
51.84
51.727
51.615
51.503
51.391
51.279
51.166
51.054
50.942
61.489
61.321
61.152
60.984
60.816
60.647
60.479
60.311
60.142
59.974
59.806
59.638
59.469
59.301
59.133
58.964
58.796
58.628
58.459
58.291
58.123
57.955
57.786
57.618
57.45
57.281
57.113
56.945
0.113
0.113
0.113
0.113
0.112
0.112
0.112
0.112
0.112
0.111
0.111
0.111
0.111
0.11
0.11
0.11
0.11
0.109
0.109
0.109
0.109
0.109
0.108
0.108
0.108
0.108
0.107
0.107
0.1471
0.1455
0.144
0.1424
0.1409
0.1394
0.138
0.1366
0.1352
0.1339
0.1325
0.1312
0.13
0.1287
0.1275
0.1263
0.1251
0.1239
0.1228
0.1217
0.1206
0.1195
0.1184
0.1174
0.1164
0.1154
0.1144
0.1134
0.1841
0.1804
0.1768
0.1734
0.1701
0.1669
0.1638
0.1609
0.158
0.1553
0.1526
0.15
0.1476
0.1452
0.1428
0.1406
0.1384
0.1363
0.1342
0.1322
0.1303
0.1284
0.1266
0.1248
0.1231
0.1214
0.1198
0.1182
0.2932
0.2794
0.2668
0.2554
0.2448
0.2351
0.2262
0.2179
0.2102
0.203
0.1963
0.19
0.1841
0.1786
0.1734
0.1685
0.1638
0.1594
0.1553
0.1513
0.1476
0.144
0.1406
0.1373
0.1342
0.1313
0.1284
0.1257
2.172
3.4493
3.3589
3.275
3.1971
3.1243
3.0561
2.9921
2.9318
2.8749
2.821
2.77
2.7215
2.6753
2.6312
2.5892
2.549
2.5105
2.4736
2.4382
2.4041
2.3713
2.3398
2.3093
2.28
2.2516
2.2242
2.1977
81.9
81.9
1.47
1.48
81.9
81.9
1.46
1.53
81.9
1.45
81.9
81.9
1.44
1.52
81.9
1.43
81.9
81.9
1.42
1.51
81.9
1.41
81.9
81.9
1.4
81.9
81.9
1.39
1.5
81.9
1.38
1.49
81.9
1.37
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
87.48
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
91.22
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
96.8
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
49.96
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
55.57
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
59.3
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
64.9
41.461
41.442
41.424
41.405
41.386
41.368
41.349
41.33
41.312
41.293
41.274
41.255
41.237
41.218
41.199
41.181
41.162
39
50.044
49.97
49.895
49.82
49.745
49.67
49.596
49.521
49.446
49.371
49.296
49.222
49.147
49.072
48.997
48.922
48.848
55.767
55.654
55.542
55.43
55.318
55.206
55.093
54.981
54.869
54.757
54.645
54.532
54.42
54.308
54.196
54.084
53.971
64.35
64.182
64.013
63.845
63.677
63.508
63.34
63.172
63.004
62.835
62.667
62.499
62.33
62.162
61.994
61.825
61.657
0.118
0.117
0.117
0.117
0.117
0.116
0.116
0.116
0.116
0.115
0.115
0.115
0.115
0.114
0.114
0.114
0.114
0.181
0.1786
0.1762
0.1739
0.1717
0.1695
0.1674
0.1653
0.1633
0.1613
0.1594
0.1575
0.1557
0.1539
0.1521
0.1504
0.1488
0.188
0.2838
0.2751
0.2668
0.2591
0.2517
0.2448
0.2383
0.2321
0.2262
0.2206
0.2153
0.2102
0.2053
0.2007
0.1963
0.1921
1.8179
1.392
1.1278
0.9479
0.8175
0.7186
0.6411
0.5786
0.5273
0.4843
0.4478
0.4164
0.3892
0.3652
0.3441
0.3252
0.3084
11.221
9.177
7.8912
7.0019
6.3464
5.8406
5.4364
5.1047
4.8265
4.589
4.3833
4.2029
4.043
3.9001
3.7712
3.6542
3.5474
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
0.16
0.17
0.18
0.19
0.2
0.21
0.22
0.23
0.24
0.25
92.4
0.13
92.4
92.4
0.12
0.14
92.4
0.15
92.4
0.1
0.11
L/G
Approach (°F) =
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
CWT +
0.6R
90
10
Cold Water Temperature (CWT) (°F) =
CWT +
0.4R
114
Hot Water Temperature (HWT) (°F) =
CWT +
0.1R
23.6
Cooling Range (R) (°F) =
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
CWT
+
0.9R
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
hCWT
+
0.1R
Water Side
43.7
80
29.9
Wet-bulb Temperature (°F)@ inlet =
Enthalpy of sat. air at WBT (Btu/lbm)
=
Barometric Pressure (in. Hg) =
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
hCWT
+
0.4R
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
hCWT
+
0.6R
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
hCWT
+ 0.9R
44.29
44.266
44.243
44.219
44.196
44.172
44.148
44.125
44.101
44.078
44.054
44.03
44.007
43.983
43.96
43.936
hWB+0.1*
L/G*R
40
46.06
45.966
45.871
45.777
45.682
45.588
45.494
45.399
45.305
45.21
45.116
45.022
44.927
44.833
44.738
44.644
hWB+0.4*
L/G*R
47.24
47.098
46.957
46.815
46.674
46.532
46.39
46.249
46.107
45.966
45.824
45.682
45.541
45.399
45.258
45.116
hWB+0.6*
L/G*R
Air Side
49.01
48.798
48.585
48.373
48.16
47.948
47.736
47.523
47.311
47.098
46.886
46.674
46.461
46.249
46.036
45.824
hWB+0.9*
L/G*R
0.062
0.062
0.062
0.062
0.062
0.062
0.061
0.061
0.061
0.061
0.061
0.061
0.061
0.061
0.061
0.061
1/(hw0.1ha0.1)
0.0466
0.0464
0.0462
0.046
0.0458
0.0456
0.0454
0.0452
0.045
0.0448
0.0447
0.0445
0.0443
0.0441
0.0439
0.0437
1/(hw0.4ha0.4)
0.04
0.0398
0.0396
0.0394
0.0392
0.0389
0.0387
0.0385
0.0383
0.0381
0.0379
0.0377
0.0375
0.0373
0.0371
0.0369
1/(hw0.6ha0.6)
Enthaply Difference
Appendix D - Tower Demand Curve Excel Spreadsheets – Design B
0.0331
0.0328
0.0326
0.0324
0.0322
0.0319
0.0317
0.0315
0.0313
0.0311
0.0309
0.0307
0.0305
0.0303
0.0301
0.0299
1/(hw0.9
-ha0.9)
1.0719
1.0675
1.0631
1.0588
1.0545
1.0502
1.046
1.0419
1.0377
1.0336
1.0296
1.0256
1.0216
1.0177
1.0138
1.0099
KaV/L
99.44
99.44
99.44
99.44
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
0.28
0.29
0.3
0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0.39
0.4
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
0.5
0.51
0.52
0.53
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
92.4
0.27
99.44
92.4
0.26
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
44.314
44.951
44.927
44.904
44.88
44.856
44.833
44.809
44.786
44.762
44.738
44.715
44.691
44.668
44.644
44.62
44.597
44.573
44.55
44.526
44.502
44.479
44.455
44.432
44.408
44.384
44.361
44.337
41
48.703
48.609
48.514
48.42
48.326
48.231
48.137
48.042
47.948
47.854
47.759
47.665
47.57
47.476
47.382
47.287
47.193
47.098
47.004
46.91
46.815
46.721
46.626
46.532
46.438
46.343
46.249
46.154
51.205
51.063
50.922
50.78
50.638
50.497
50.355
50.214
50.072
49.93
49.789
49.647
49.506
49.364
49.222
49.081
48.939
48.798
48.656
48.514
48.373
48.231
48.09
47.948
47.806
47.665
47.523
47.382
54.957
54.745
54.532
54.32
54.108
53.895
53.683
53.47
53.258
53.046
52.833
52.621
52.408
52.196
51.984
51.771
51.559
51.346
51.134
50.922
50.709
50.497
50.284
50.072
49.86
49.647
49.435
49.222
0.065
0.065
0.064
0.064
0.064
0.064
0.064
0.064
0.064
0.064
0.064
0.064
0.063
0.063
0.063
0.063
0.063
0.063
0.063
0.063
0.063
0.063
0.063
0.062
0.062
0.062
0.062
0.062
0.0532
0.0529
0.0526
0.0524
0.0521
0.0519
0.0516
0.0514
0.0511
0.0509
0.0506
0.0504
0.0502
0.0499
0.0497
0.0494
0.0492
0.049
0.0488
0.0485
0.0483
0.0481
0.0479
0.0477
0.0475
0.0472
0.047
0.0468
0.0403
0.0476
0.0473
0.047
0.0467
0.0464
0.0461
0.0458
0.0455
0.0452
0.0449
0.0446
0.0443
0.044
0.0438
0.0435
0.0432
0.043
0.0427
0.0425
0.0422
0.042
0.0417
0.0415
0.0412
0.041
0.0407
0.0405
0.0333
0.0411
0.0408
0.0404
0.0401
0.0398
0.0394
0.0391
0.0388
0.0385
0.0381
0.0378
0.0375
0.0372
0.0369
0.0367
0.0364
0.0361
0.0358
0.0356
0.0353
0.035
0.0348
0.0345
0.0343
0.034
0.0338
0.0335
1.0764
1.2185
1.2124
1.2063
1.2004
1.1945
1.1886
1.1829
1.1772
1.1716
1.166
1.1606
1.1551
1.1498
1.1445
1.1393
1.1341
1.129
1.1239
1.119
1.114
1.1091
1.1043
1.0995
1.0948
1.0901
1.0855
1.0809
99.44
99.44
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
0.56
0.57
0.58
0.59
0.6
0.61
0.62
0.63
0.64
0.65
0.66
0.67
0.68
0.69
0.7
0.71
0.72
0.73
0.74
0.75
0.76
0.77
0.78
0.79
0.8
0.81
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
92.4
0.55
99.44
92.4
0.54
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
45.612
45.588
45.564
45.541
45.517
45.494
45.47
45.446
45.423
45.399
45.376
45.352
45.328
45.305
45.281
45.258
45.234
45.21
45.187
45.163
45.14
45.116
45.092
45.069
45.045
45.022
44.998
44.974
42
51.346
51.252
51.158
51.063
50.969
50.874
50.78
50.686
50.591
50.497
50.402
50.308
50.214
50.119
50.025
49.93
49.836
49.742
49.647
49.553
49.458
49.364
49.27
49.175
49.081
48.986
48.892
48.798
55.17
55.028
54.886
54.745
54.603
54.462
54.32
54.178
54.037
53.895
53.754
53.612
53.47
53.329
53.187
53.046
52.904
52.762
52.621
52.479
52.338
52.196
52.054
51.913
51.771
51.63
51.488
51.346
55.17
60.904
60.692
60.48
60.267
60.055
59.842
59.63
59.418
59.205
58.993
58.78
58.568
58.356
58.143
57.931
57.718
57.506
57.294
57.081
56.869
56.656
56.444
56.232
56.019
55.807
55.594
55.382
0.067
0.067
0.067
0.067
0.067
0.067
0.067
0.067
0.067
0.067
0.066
0.066
0.066
0.066
0.066
0.066
0.066
0.066
0.066
0.066
0.065
0.065
0.065
0.065
0.065
0.065
0.065
0.065
0.0619
0.0615
0.0612
0.0608
0.0605
0.0601
0.0598
0.0594
0.0591
0.0588
0.0585
0.0581
0.0578
0.0575
0.0572
0.0569
0.0566
0.0563
0.056
0.0557
0.0554
0.0551
0.0548
0.0545
0.0543
0.054
0.0537
0.0534
0.0587
0.0582
0.0577
0.0573
0.0568
0.0563
0.0559
0.0555
0.055
0.0546
0.0542
0.0538
0.0534
0.053
0.0526
0.0522
0.0518
0.0514
0.051
0.0507
0.0503
0.05
0.0496
0.0493
0.0489
0.0486
0.0483
0.0479
0.0545
0.0539
0.0532
0.0527
0.0521
0.0515
0.0509
0.0504
0.0499
0.0493
0.0488
0.0483
0.0478
0.0474
0.0469
0.0464
0.046
0.0455
0.0451
0.0447
0.0442
0.0438
0.0434
0.043
0.0426
0.0423
0.0419
0.0415
1.4308
1.4216
1.4124
1.4035
1.3946
1.3859
1.3774
1.369
1.3607
1.3526
1.3446
1.3367
1.3289
1.3212
1.3137
1.3062
1.2989
1.2917
1.2846
1.2775
1.2706
1.2638
1.2571
1.2504
1.2439
1.2374
1.231
1.2247
99.44
99.44
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
0.88
0.89
0.9
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1
1.01
1.02
1.03
1.04
1.05
1.06
1.07
1.08
1.09
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
92.4
92.4
0.85
99.44
92.4
92.4
0.84
99.44
99.44
0.86
92.4
0.83
0.87
92.4
0.82
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
46.272
46.249
46.225
46.202
46.178
46.154
46.131
46.107
46.084
46.06
46.036
46.013
45.989
45.966
45.942
45.918
45.895
45.871
45.848
45.824
45.8
45.777
45.753
45.73
45.706
45.682
45.659
45.635
43
53.99
53.895
53.801
53.706
53.612
53.518
53.423
53.329
53.234
53.14
53.046
52.951
52.857
52.762
52.668
52.574
52.479
52.385
52.29
52.196
52.102
52.007
51.913
51.818
51.724
51.63
51.535
51.441
59.134
58.993
58.851
58.71
58.568
58.426
58.285
58.143
58.002
57.86
57.718
57.577
57.435
57.294
57.152
57.01
56.869
56.727
56.586
56.444
56.302
56.161
56.019
55.878
55.736
55.594
55.453
55.311
66.852
66.639
66.427
66.214
66.002
65.79
65.577
65.365
65.152
64.94
64.728
64.515
64.303
64.09
63.878
63.666
63.453
63.241
63.028
62.816
62.604
62.391
62.179
61.966
61.754
61.542
61.329
61.117
0.071
0.071
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.07
0.069
0.069
0.069
0.069
0.069
0.069
0.069
0.069
0.069
0.068
0.068
0.068
0.068
0.068
0.068
0.068
0.068
0.068
0.074
0.0734
0.0729
0.0724
0.072
0.0715
0.071
0.0705
0.07
0.0696
0.0691
0.0687
0.0682
0.0678
0.0674
0.067
0.0665
0.0661
0.0657
0.0653
0.0649
0.0645
0.0641
0.0637
0.0633
0.063
0.0626
0.0622
0.0592
0.0765
0.0757
0.0749
0.0741
0.0733
0.0725
0.0718
0.0711
0.0704
0.0697
0.069
0.0683
0.0677
0.067
0.0664
0.0658
0.0652
0.0646
0.064
0.0634
0.0629
0.0623
0.0618
0.0612
0.0607
0.0602
0.0597
0.0551
0.0806
0.0792
0.0779
0.0767
0.0754
0.0742
0.0731
0.072
0.0709
0.0698
0.0688
0.0678
0.0669
0.0659
0.065
0.0641
0.0633
0.0624
0.0616
0.0608
0.06
0.0593
0.0585
0.0578
0.0571
0.0564
0.0558
1.7798
1.7633
1.7471
1.7314
1.716
1.701
1.6863
1.672
1.658
1.6443
1.6309
1.6178
1.605
1.5924
1.5801
1.5681
1.5563
1.5447
1.5334
1.5222
1.5113
1.5006
1.4901
1.4798
1.4696
1.4597
1.4499
1.4403
99.44
99.44
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
1.12
1.13
1.14
1.15
1.16
1.17
1.18
1.19
1.2
1.21
1.22
1.23
1.24
1.25
1.26
1.27
1.28
1.29
1.3
1.31
1.32
1.33
1.34
1.35
1.36
1.37
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
92.4
99.44
92.4
1.1
1.11
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
46.933
46.91
46.886
46.862
46.839
46.815
46.792
46.768
46.744
46.721
46.697
46.674
46.65
46.626
46.603
46.579
46.556
46.532
46.508
46.485
46.461
46.438
46.414
46.39
46.367
46.343
46.32
46.296
54.084
44
56.633
56.538
56.444
56.35
56.255
56.161
56.066
55.972
55.878
55.783
55.689
55.594
55.5
55.406
55.311
55.217
55.122
55.028
54.934
54.839
54.745
54.65
54.556
54.462
54.367
54.273
54.178
59.276
63.099
62.958
62.816
62.674
62.533
62.391
62.25
62.108
61.966
61.825
61.683
61.542
61.4
61.258
61.117
60.975
60.834
60.692
60.55
60.409
60.267
60.126
59.984
59.842
59.701
59.559
59.418
67.064
72.799
72.586
72.374
72.162
71.949
71.737
71.524
71.312
71.1
70.887
70.675
70.462
70.25
70.038
69.825
69.613
69.4
69.188
68.976
68.763
68.551
68.338
68.126
67.914
67.701
67.489
67.276
0.071
0.074
0.074
0.074
0.074
0.074
0.073
0.073
0.073
0.073
0.073
0.073
0.073
0.073
0.072
0.072
0.072
0.072
0.072
0.072
0.072
0.072
0.071
0.071
0.071
0.071
0.071
0.071
0.0919
0.0911
0.0904
0.0896
0.0889
0.0881
0.0874
0.0867
0.086
0.0853
0.0846
0.0839
0.0833
0.0826
0.082
0.0813
0.0807
0.0801
0.0795
0.0789
0.0783
0.0778
0.0772
0.0766
0.0761
0.0755
0.075
0.0745
0.0773
0.1098
0.1081
0.1065
0.1049
0.1033
0.1018
0.1004
0.099
0.0976
0.0963
0.095
0.0937
0.0925
0.0913
0.0901
0.089
0.0879
0.0868
0.0858
0.0847
0.0837
0.0828
0.0818
0.0809
0.0799
0.079
0.0782
0.082
0.1548
0.1498
0.1452
0.1409
0.1368
0.1329
0.1293
0.1258
0.1225
0.1194
0.1165
0.1137
0.111
0.1084
0.106
0.1037
0.1014
0.0993
0.0972
0.0953
0.0934
0.0916
0.0898
0.0881
0.0865
0.085
0.0834
2.5403
2.4959
2.4537
2.4134
2.375
2.3383
2.3032
2.2696
2.2373
2.2063
2.1764
2.1477
2.12
2.0933
2.0676
2.0426
2.0185
1.9952
1.9726
1.9507
1.9295
1.9089
1.8889
1.8694
1.8505
1.8321
1.8142
1.7968
99.44
99.44
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
92.4
1.4
1.41
1.42
1.43
1.44
1.45
1.46
1.47
1.48
1.49
1.5
1.51
1.52
1.53
1.54
1.55
1.56
1.57
1.58
1.59
1.6
1.61
1.62
1.63
1.64
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
99.44
92.4
1.39
99.44
92.4
1.38
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
104.16
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
111
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
60.43
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
67.51
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
72.2
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
79.3
47.57
47.547
47.523
47.5
47.476
47.452
47.429
47.405
47.382
47.358
47.334
47.311
47.287
47.264
47.24
47.216
47.193
47.169
47.146
47.122
47.098
47.075
47.051
47.028
47.004
46.98
46.957
56.727
45
59.182
59.087
58.993
58.898
58.804
58.71
58.615
58.521
58.426
58.332
58.238
58.143
58.049
57.954
57.86
57.766
57.671
57.577
57.482
57.388
57.294
57.199
57.105
57.01
56.916
56.822
63.241
66.922
66.781
66.639
66.498
66.356
66.214
66.073
65.931
65.79
65.648
65.506
65.365
65.223
65.082
64.94
64.798
64.657
64.515
64.374
64.232
64.09
63.949
63.807
63.666
63.524
63.382
73.011
78.534
78.321
78.109
77.896
77.684
77.472
77.259
77.047
76.834
76.622
76.41
76.197
75.985
75.772
75.56
75.348
75.135
74.923
74.71
74.498
74.286
74.073
73.861
73.648
73.436
73.224
0.074
0.078
0.078
0.077
0.077
0.077
0.077
0.077
0.077
0.077
0.076
0.076
0.076
0.076
0.076
0.076
0.076
0.076
0.075
0.075
0.075
0.075
0.075
0.075
0.075
0.074
0.074
0.0927
0.1201
0.1187
0.1174
0.1161
0.1149
0.1136
0.1124
0.1112
0.1101
0.109
0.1078
0.1068
0.1057
0.1047
0.1036
0.1026
0.1016
0.1007
0.0997
0.0988
0.0979
0.097
0.0961
0.0952
0.0944
0.0936
0.1115
0.1891
0.1842
0.1795
0.1751
0.1708
0.1668
0.1629
0.1593
0.1558
0.1524
0.1492
0.1461
0.1431
0.1403
0.1376
0.1349
0.1324
0.13
0.1276
0.1253
0.1232
0.121
0.119
0.117
0.1151
0.1133
0.16
1.3767
1.0652
0.8687
0.7334
0.6345
0.5592
0.4998
0.4518
0.4123
0.3791
0.3508
0.3265
0.3053
0.2867
0.2703
0.2556
0.2424
0.2306
0.2198
0.21
0.201
0.1928
0.1852
0.1782
0.1717
0.1657
2.5871
10.405
8.5298
7.334
6.501
5.8847
5.4081
5.0273
4.7148
4.453
4.2298
4.0368
3.8679
3.7184
3.5849
3.4649
3.3561
3.2569
3.166
3.0822
3.0047
2.9328
2.8657
2.8029
2.7441
2.6887
2.6364
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