• TABLE OF CONTENTS
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 Copyright
 Introduction
 Heat pumps for heating and cooling...
 A typical heat pump system for...
 Performance and energy efficie...
 Heating water
 Cooling water
 Summary






Group Title: Florida Cooperative Extension Service circular 1096
Title: Heat pump for heating and cooling water for aquacultural production
CITATION PAGE IMAGE ZOOMABLE PAGE TEXT
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00049208/00001
 Material Information
Title: Heat pump for heating and cooling water for aquacultural production
Series Title: Circular
Physical Description: 4 p. : ill. ; 28 cm.
Language: English
Creator: Baird, C. Direlle ( Carl Direlle )
Florida Cooperative Extension Service
Publisher: Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville
Publication Date: 1993
 Subjects
Subject: Heat pumps -- Florida   ( lcsh )
Aquaculture industry -- Equipment and supplies -- Florida   ( lcsh )
Aquaculture -- Water-supply -- Recycling -- Florida   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: C.D. Baird ... et al..
General Note: Title from caption.
General Note: "May 1993."
Funding: Florida Historical Agriculture and Rural Life
 Record Information
Bibliographic ID: UF00049208
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 28536198

Table of Contents
    Copyright
        Copyright
    Introduction
        Page 1
    Heat pumps for heating and cooling water
        Page 1
    A typical heat pump system for heating and cooling
        Page 1
    Performance and energy efficiency
        Page 2
    Heating water
        Page 2
    Cooling water
        Page 3
    Summary
        Page 4
Full Text





HISTORIC NOTE


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source
(EDIS)

site maintained by the Florida
Cooperative Extension Service.






Copyright 2005, Board of Trustees, University
of Florida







UNIVERSITY OF

FLORIDA


Circular 1096
May 1993

/1mn


Florida Cooperative Extension Service


Heat Pump for Heating and Cooling Water
for Aquacultural Production'
C. D. Baird, R. A. Bucklin, C. A. Watson and F. A. Chapman2


INTRODUCTION

Aquaculture, a significant industry in Florida,
includes the production of ornamental fish, catfish,
alligators, oysters, and other aquatic species. The larg-
est portion of aquaculture sales comes from ornamen-
tal fish produced primarily in open ponds. Fish are
also held and produced in buildings and greenhouses,
which often employ flow-through water systems.
These systems require large quantities of water and do
not provide optimum growing conditions; the energy
required to heat these buildings during the winter
represents a major production cost.

Some producers are considering indoor recirculat-
ing systems, where the only water pumped from the
well after the initial filling is makeup water to replace
water lost during evaporation and water used to
backflush filters. Even these systems require substan-
tial heating during the winter and heating of the make-
up well water at other times, since optimum growth
temperatures exceed the normal temperature of well
water. Cooling is also required during the summer
due to heat buildup inside the structure.

HEAT PUMPS FOR HEATING
AND COOLING WATER

A heat pump is ideal for this application, since the
same mechanical refrigeration system provides both
heating and cooling. The heat pump system described


here is similar to those used for residential air condi-
tioning systems, except that it is used to heat and cool
water instead of air.

A heat pump is a mechanical refrigeration system
that pumps heat from the outside to the inside during
the winter and from the inside to the outside in the
summer. A heat pump operates like an air
conditioner working in reverse. An air conditioner
removes heat from the air inside a house through an
evaporator (cold coil) and discharges it outside
through a condenser (hot coil) during warm weather.
During cold weather, the heat pump utilizes reversible
valves to interchange the evaporator and the
condenser. Thus, the hot coil inside and the cold coil
outside allow the system to remove heat from the
outside and discharge it inside.

A TYPICAL HEAT PUMP SYSTEM
FOR HEATING AND COOLING

The system described here uses a typical 2-ton
(24,000 Btuh) residential heat pump modified to heat
and cool water in the temperature range needed for
aquacultural production (Figure 1). Instead of cooling
air with an evaporator coil, which is usually located
inside the duct system in a residential application, this
system uses a copper coil made from copper tubing
and located in the water tank. Since copper is toxic
to fish, the copper tubing is painted with black epoxy
enamel. This coil utilizes two 50-foot circuits of 3/8-


1. This document was published May 1993 as Circular 1096, a series of the Florida Energy Extension Service, Florida Cooperative Extension Service,
Institute of Food and Agricultural Sciences, University of Florida.
2. C.D. Baird, Professor, and RA. Bucklin, Associate Professor, Agricultural Engineering; CA. Watson, Aquaculture Extension Agent II,
Hillsborough County, Seffner, and FA. Chapman, Assistant Professor of Fisheries and Aquaculture, Cooperative Extension Service, Institute
of Food and Agricultural Sciences, University of Florida, Gainesville FL 32611.
The Institute of Food and Agricultural Sciences is an equal opportunity/affirmative action employer authorized to provide research, educational
information and other services only to individuals and Institutions that function without regard to race, color, sex, age, handicap, or national
origin. For information on obtaining other extension publications, contact your county Cooperative Extension Service office.
Florida Cooperative Extension Service / Institute of Food and Agricultural Sciences / University of Florida / John T. Woeste, Dean


UNIVERSITY OF FLORFinA HAARIES







UNIVERSITY OF

FLORIDA


Circular 1096
May 1993

/1mn


Florida Cooperative Extension Service


Heat Pump for Heating and Cooling Water
for Aquacultural Production'
C. D. Baird, R. A. Bucklin, C. A. Watson and F. A. Chapman2


INTRODUCTION

Aquaculture, a significant industry in Florida,
includes the production of ornamental fish, catfish,
alligators, oysters, and other aquatic species. The larg-
est portion of aquaculture sales comes from ornamen-
tal fish produced primarily in open ponds. Fish are
also held and produced in buildings and greenhouses,
which often employ flow-through water systems.
These systems require large quantities of water and do
not provide optimum growing conditions; the energy
required to heat these buildings during the winter
represents a major production cost.

Some producers are considering indoor recirculat-
ing systems, where the only water pumped from the
well after the initial filling is makeup water to replace
water lost during evaporation and water used to
backflush filters. Even these systems require substan-
tial heating during the winter and heating of the make-
up well water at other times, since optimum growth
temperatures exceed the normal temperature of well
water. Cooling is also required during the summer
due to heat buildup inside the structure.

HEAT PUMPS FOR HEATING
AND COOLING WATER

A heat pump is ideal for this application, since the
same mechanical refrigeration system provides both
heating and cooling. The heat pump system described


here is similar to those used for residential air condi-
tioning systems, except that it is used to heat and cool
water instead of air.

A heat pump is a mechanical refrigeration system
that pumps heat from the outside to the inside during
the winter and from the inside to the outside in the
summer. A heat pump operates like an air
conditioner working in reverse. An air conditioner
removes heat from the air inside a house through an
evaporator (cold coil) and discharges it outside
through a condenser (hot coil) during warm weather.
During cold weather, the heat pump utilizes reversible
valves to interchange the evaporator and the
condenser. Thus, the hot coil inside and the cold coil
outside allow the system to remove heat from the
outside and discharge it inside.

A TYPICAL HEAT PUMP SYSTEM
FOR HEATING AND COOLING

The system described here uses a typical 2-ton
(24,000 Btuh) residential heat pump modified to heat
and cool water in the temperature range needed for
aquacultural production (Figure 1). Instead of cooling
air with an evaporator coil, which is usually located
inside the duct system in a residential application, this
system uses a copper coil made from copper tubing
and located in the water tank. Since copper is toxic
to fish, the copper tubing is painted with black epoxy
enamel. This coil utilizes two 50-foot circuits of 3/8-


1. This document was published May 1993 as Circular 1096, a series of the Florida Energy Extension Service, Florida Cooperative Extension Service,
Institute of Food and Agricultural Sciences, University of Florida.
2. C.D. Baird, Professor, and RA. Bucklin, Associate Professor, Agricultural Engineering; CA. Watson, Aquaculture Extension Agent II,
Hillsborough County, Seffner, and FA. Chapman, Assistant Professor of Fisheries and Aquaculture, Cooperative Extension Service, Institute
of Food and Agricultural Sciences, University of Florida, Gainesville FL 32611.
The Institute of Food and Agricultural Sciences is an equal opportunity/affirmative action employer authorized to provide research, educational
information and other services only to individuals and Institutions that function without regard to race, color, sex, age, handicap, or national
origin. For information on obtaining other extension publications, contact your county Cooperative Extension Service office.
Florida Cooperative Extension Service / Institute of Food and Agricultural Sciences / University of Florida / John T. Woeste, Dean


UNIVERSITY OF FLORFinA HAARIES







UNIVERSITY OF

FLORIDA


Circular 1096
May 1993

/1mn


Florida Cooperative Extension Service


Heat Pump for Heating and Cooling Water
for Aquacultural Production'
C. D. Baird, R. A. Bucklin, C. A. Watson and F. A. Chapman2


INTRODUCTION

Aquaculture, a significant industry in Florida,
includes the production of ornamental fish, catfish,
alligators, oysters, and other aquatic species. The larg-
est portion of aquaculture sales comes from ornamen-
tal fish produced primarily in open ponds. Fish are
also held and produced in buildings and greenhouses,
which often employ flow-through water systems.
These systems require large quantities of water and do
not provide optimum growing conditions; the energy
required to heat these buildings during the winter
represents a major production cost.

Some producers are considering indoor recirculat-
ing systems, where the only water pumped from the
well after the initial filling is makeup water to replace
water lost during evaporation and water used to
backflush filters. Even these systems require substan-
tial heating during the winter and heating of the make-
up well water at other times, since optimum growth
temperatures exceed the normal temperature of well
water. Cooling is also required during the summer
due to heat buildup inside the structure.

HEAT PUMPS FOR HEATING
AND COOLING WATER

A heat pump is ideal for this application, since the
same mechanical refrigeration system provides both
heating and cooling. The heat pump system described


here is similar to those used for residential air condi-
tioning systems, except that it is used to heat and cool
water instead of air.

A heat pump is a mechanical refrigeration system
that pumps heat from the outside to the inside during
the winter and from the inside to the outside in the
summer. A heat pump operates like an air
conditioner working in reverse. An air conditioner
removes heat from the air inside a house through an
evaporator (cold coil) and discharges it outside
through a condenser (hot coil) during warm weather.
During cold weather, the heat pump utilizes reversible
valves to interchange the evaporator and the
condenser. Thus, the hot coil inside and the cold coil
outside allow the system to remove heat from the
outside and discharge it inside.

A TYPICAL HEAT PUMP SYSTEM
FOR HEATING AND COOLING

The system described here uses a typical 2-ton
(24,000 Btuh) residential heat pump modified to heat
and cool water in the temperature range needed for
aquacultural production (Figure 1). Instead of cooling
air with an evaporator coil, which is usually located
inside the duct system in a residential application, this
system uses a copper coil made from copper tubing
and located in the water tank. Since copper is toxic
to fish, the copper tubing is painted with black epoxy
enamel. This coil utilizes two 50-foot circuits of 3/8-


1. This document was published May 1993 as Circular 1096, a series of the Florida Energy Extension Service, Florida Cooperative Extension Service,
Institute of Food and Agricultural Sciences, University of Florida.
2. C.D. Baird, Professor, and RA. Bucklin, Associate Professor, Agricultural Engineering; CA. Watson, Aquaculture Extension Agent II,
Hillsborough County, Seffner, and FA. Chapman, Assistant Professor of Fisheries and Aquaculture, Cooperative Extension Service, Institute
of Food and Agricultural Sciences, University of Florida, Gainesville FL 32611.
The Institute of Food and Agricultural Sciences is an equal opportunity/affirmative action employer authorized to provide research, educational
information and other services only to individuals and Institutions that function without regard to race, color, sex, age, handicap, or national
origin. For information on obtaining other extension publications, contact your county Cooperative Extension Service office.
Florida Cooperative Extension Service / Institute of Food and Agricultural Sciences / University of Florida / John T. Woeste, Dean


UNIVERSITY OF FLORFinA HAARIES





/01
S Heat Pump for Aquacultural Production

SCIENCE inch copper tubing, which cools the water in warm
LIBRARY weather and heats it in cool weather. Since the
temperature range required for aquaculture
production is different from that required for
residential air conditioning, the 2-ton compressor in
the heat pump must be replaced with a 1-ton compres-
sor. This allows the capacity of the compressor to
match that of the outside coil, a condition necessary
to create the operating temperatures used in aqua-
cultural production. Temperatures are most critical
in the cooling mode. If the size of the compressor
were not reduced, the outside coil (condenser) would
overheat in the cooling mode. Reducing the size of
the compressor is easier than increasing the size of the
condenser and has the additional advantage of
enhancing system efficiency. The system also must be
equipped with an automatic switch-over thermostat
with separate temperature settings for heating and
cooling. The difference between the high- and low-
temperature settings, which constitutes the neutral
zone, must be determined by the production
requirements of each fish species.

The heat pump system in this example is installed
in a 20 x 30-foot inflated double-poly greenhouse that
has been sprayed on the outside with a heavy coat of
white paint. Black polyethylene film has been placed
on the inside roof of the greenhouse to further reduce
the solar load. Another option would be to use white-
painted black polyethylene on the outside; however,
the white paint has a tendency to peel unless the black
polyethylene is treated prior to painting. An exhaust
fan, set to operate when the inside temperature ex-
ceeds 80 F, provides ventilation for the structure.

PERFORMANCE AND ENERGY EFFICIENCY

In the heating mode, the system produces approxi-
mately 18,000 Btuh when the water temperature is
80*F and the outside temperature is 50 F. The power
required to operate the system under these conditions
is 1.1 kW. This corresponds to an energy efficiency
ratio (EER) of 16 Btuh/kW, which represents nearly
five times the efficiency of electrical resistance heating.
Since it is more difficult to extract heat from air as the
temperature is lowered, however, the output of the air
source heat pump varies considerably with ambient
temperature. Figure 2 shows the performance of this
system as a function of ambient temperature; it also
demonstrates how the performance of the same unit
would change if the air source outdoor coil were
replaced with a water source coil using well water (or
water from another source) at 720F. These data are
based on a fish tank temperature of 80*F. The advan-


Page 2


tages of the water source heat pump can be seen
clearly in Figure 2. Not only does the pump's capacity
remain almost constant for varying ambient conditions,
it results in a significant increase in unit efficiency. In
the air source heat pump, reduced capacity for lower
ambient temperatures is compounded by the need for
more heat in cold weather. For most air source heat
pump applications, additional heat needed in cold
weather is supplied by electric resistance heaters,
which are very inefficient. Although it is difficult to
obtain water source heat pumps with very small capac-
ities and often impossible or impractical to obtain
water for this use, water source heat pumps should
always be considered.

HEATING WATER

As indicated earlier in this document, a heat
pump's low temperatures (in the 80*F range) make
it a very good choice for aquacultural production. The
higher the required temperature, the less efficient a
heat pump becomes. This is not true for other types
of heating systems, such as those that use electric
resistance, gas, or oil.

Gas and oil are usually considered to be the least
expensive methods of heating water. For low tem-
perature applications, however, a heat pump,
particularly a water source heat pump, is less
expensive. In Table 1, the costs of raising the
temperature of 10,000 gallons of water 10*F are
compared for several water-heating methods.

In the demonstration unit described here, the fish
tanks contain 500 gallons of water, as do the sump and
other components. The estimated annual heating
requirement for such a system in Gainesville, FL is
approximately 22 million Btu, using 1,300 kWh of
electrical energy. At 8 cents per kWh, the annual
heating cost would be approximately $100. This
represents a savings of approximately 5,000 kWh over
the use of electrical resistance heating, or
approximately $400 in operating costs.

This air source heat pump system maintains water
in the fish tank at temperatures ranging from 80 F to
an ambient temperature of approximately 400F.
Therefore, some supplemental heat, such as that
provided by electrical resistance heaters, is also
necessary. If a water source heat pump were used,
supplemental heat would not be needed.
Nevertheless, electrical resistance heaters or other
sources of emergency heat should be available for use
during periods of extremely cold weather or





/01
S Heat Pump for Aquacultural Production

SCIENCE inch copper tubing, which cools the water in warm
LIBRARY weather and heats it in cool weather. Since the
temperature range required for aquaculture
production is different from that required for
residential air conditioning, the 2-ton compressor in
the heat pump must be replaced with a 1-ton compres-
sor. This allows the capacity of the compressor to
match that of the outside coil, a condition necessary
to create the operating temperatures used in aqua-
cultural production. Temperatures are most critical
in the cooling mode. If the size of the compressor
were not reduced, the outside coil (condenser) would
overheat in the cooling mode. Reducing the size of
the compressor is easier than increasing the size of the
condenser and has the additional advantage of
enhancing system efficiency. The system also must be
equipped with an automatic switch-over thermostat
with separate temperature settings for heating and
cooling. The difference between the high- and low-
temperature settings, which constitutes the neutral
zone, must be determined by the production
requirements of each fish species.

The heat pump system in this example is installed
in a 20 x 30-foot inflated double-poly greenhouse that
has been sprayed on the outside with a heavy coat of
white paint. Black polyethylene film has been placed
on the inside roof of the greenhouse to further reduce
the solar load. Another option would be to use white-
painted black polyethylene on the outside; however,
the white paint has a tendency to peel unless the black
polyethylene is treated prior to painting. An exhaust
fan, set to operate when the inside temperature ex-
ceeds 80 F, provides ventilation for the structure.

PERFORMANCE AND ENERGY EFFICIENCY

In the heating mode, the system produces approxi-
mately 18,000 Btuh when the water temperature is
80*F and the outside temperature is 50 F. The power
required to operate the system under these conditions
is 1.1 kW. This corresponds to an energy efficiency
ratio (EER) of 16 Btuh/kW, which represents nearly
five times the efficiency of electrical resistance heating.
Since it is more difficult to extract heat from air as the
temperature is lowered, however, the output of the air
source heat pump varies considerably with ambient
temperature. Figure 2 shows the performance of this
system as a function of ambient temperature; it also
demonstrates how the performance of the same unit
would change if the air source outdoor coil were
replaced with a water source coil using well water (or
water from another source) at 720F. These data are
based on a fish tank temperature of 80*F. The advan-


Page 2


tages of the water source heat pump can be seen
clearly in Figure 2. Not only does the pump's capacity
remain almost constant for varying ambient conditions,
it results in a significant increase in unit efficiency. In
the air source heat pump, reduced capacity for lower
ambient temperatures is compounded by the need for
more heat in cold weather. For most air source heat
pump applications, additional heat needed in cold
weather is supplied by electric resistance heaters,
which are very inefficient. Although it is difficult to
obtain water source heat pumps with very small capac-
ities and often impossible or impractical to obtain
water for this use, water source heat pumps should
always be considered.

HEATING WATER

As indicated earlier in this document, a heat
pump's low temperatures (in the 80*F range) make
it a very good choice for aquacultural production. The
higher the required temperature, the less efficient a
heat pump becomes. This is not true for other types
of heating systems, such as those that use electric
resistance, gas, or oil.

Gas and oil are usually considered to be the least
expensive methods of heating water. For low tem-
perature applications, however, a heat pump,
particularly a water source heat pump, is less
expensive. In Table 1, the costs of raising the
temperature of 10,000 gallons of water 10*F are
compared for several water-heating methods.

In the demonstration unit described here, the fish
tanks contain 500 gallons of water, as do the sump and
other components. The estimated annual heating
requirement for such a system in Gainesville, FL is
approximately 22 million Btu, using 1,300 kWh of
electrical energy. At 8 cents per kWh, the annual
heating cost would be approximately $100. This
represents a savings of approximately 5,000 kWh over
the use of electrical resistance heating, or
approximately $400 in operating costs.

This air source heat pump system maintains water
in the fish tank at temperatures ranging from 80 F to
an ambient temperature of approximately 400F.
Therefore, some supplemental heat, such as that
provided by electrical resistance heaters, is also
necessary. If a water source heat pump were used,
supplemental heat would not be needed.
Nevertheless, electrical resistance heaters or other
sources of emergency heat should be available for use
during periods of extremely cold weather or








Heat Pump for Aquacultural Production Page 3


Figure 1. Heat pump system used for water heating and cooling n aquaculture.
Figure 1. Heat pump system used for water heating and cooling in aquaculture.


mechanical failure. Lowering the water temperature
to a level below 80*F is an option some producers
may wish to consider. Insulating the greenhouse
structure or using a well-insulated conventional struc-
ture would also significantly reduce the heating re-
quirement for such a heat pump system.

COOLING WATER

As previously stated, a heat pump can also be used
to cool water. To enable it to perform this function,
the system is automatically switched from heating to
cooling by the thermostat and reversible valves, as
shown in Figure 1. In some applications, both heating
and cooling are needed on the same day. How
frequently this occurs will depend on the temperature
range represented by the distance between the high
and low settings on the thermostat. Obviously, the
difference between these settings (i.e., the neutral
zone) should be as large as the fish can tolerate
without undesirable temperature stress. If the
thermostat has a very small neutral zone, some means
of storing heat should be considered for the system,
such as increasing the water capacity, incorporating
more mass in the structure, etc.


In the cooling mode, a heat pump operates more
efficiently for aquacultural production than for
conventional air conditioning because tank water is
normally maintained at a higher temperature than air
in air conditioned buildings. The cooling capacity of
the system is approximately 18,000 Btuh with a fish
tank temperature of 82*F, which requires
approximately 1.4 kW at an ambient temperature of
90*F. The heat pump's capacity is less variable with
ambient temperature than in the heating mode, since
the evaporator coil (cold coil) in the fish tank sump
is maintained at a relatively constant temperature. A
change in evaporator temperature causes a change in
the density of refrigerant vapor which, in turn,
produces a change in the flow rate of refrigerant
through the system. Lower temperatures in the
evaporator result in a lower cooling capacity, and the
effect of ambient temperature is a significant change
in the power requirements for compressor operation.
Thus, a water source heat pump is also much more
efficient than an air source heat pump for cooling,
since well water at 72 F is much cooler than the
average ambient temperature during cooling. A water
source heat pump is usually about 20% more efficient
than an air source heat pump in the cooling mode.


Modified Greenhouse




Outdoor Reversing To fish tank
Coil valve
II


|I I spray enamel
SAccumulatortue ith


Check Check
valve valve


Page 3


Heat Pump for Aquacultural Production







Heat Pump for Aquacultural Production


Figure 2. Performance of air source and water source heat pumps.


SUMMARY

If the systems used in ornamental fish production
are converted from flow-through to recirculating
systems, some type of heating and cooling will be
necessary. A heat pump system can provide both
heating and cooling and, for temperatures required in
aquacultural production systems, represents the least
expensive method of heating. It is also the most
energy efficient, with approximately six times the
efficiency of electrical resistance heating when a water
source heat pump is used. While the initial cost of the
system is significantly higher than that of other heating


options, this cost can be justified on the basis that
mechanical refrigeration is also needed for cooling.

When selecting a heat pump for aquacultural
applications, producers should carefully match the
capacities of the compressor, condenser, and evapora-
tor to ensure that the compressor is not overloaded
and that high efficiencies (EER) can be obtained.
Providing an adequately insulated production structure
and increasing thermal mass by incorporating
additional water storage capacity or structural mass
will also increase the overall efficiency of heat pump
systems.


Table 1. Compared costs for heating 10,000 gallons of water 10"F. Electricity $.08 per kWh; natural gas $.60 per therm; #2 fuel
oil $1.10 per gallon; propane $1.25 per gallon.

Water Source Air Source Natural Gas #2 Fuel Oil Propane Gas Electric
Heat Pump Heat Pump Resistance

$3.18 $4.06 $6.10 $9.20 $15.06 $19.42


24


22
Water Source Heat Pump

S20
o
0
x 18
I
I-

M 16

U
14

0 OtAir Source Heat Pump
c 12


10


8
10 20 30 40 50 60 70
Outdoor Air Tempemrature. F


Page 4




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