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ENME 3773: Design of Fluid Thermal Systems
Design Project 2
FIELD HEATING SYSTEM FOR GREENBAY, WI
FOOTBAL FIELD
SPRING 2011
Group 2
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TABLE OF CONTENTS:
Problem Statement---------------------------------------------------------------------------------1
Executive Summary--------------------------------------------------------------------------------2
Design Approach-----------------------------------------------------------------------------------4
Design Approach 1: Hydronic System-------------------------------------------------6
Design Approach 2: Electrical Heating System--------------------------------------11
Economic Analysis--------------------------------------------------------------------------------14
Operability, Health and Safety and Manufacturability---------------------------------------19
Conclusions-------------------------------------------------------------------------XXXXXXXXX
APPENDIX
APPENDIX A: CalculationsAPPENDIX B: References
APPENDIX C: Manuals and Brochures
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PROBLEM STATEMENT
NFL football stadiums operating in northern climates have problems with the field
surface freezing in the winter, when conditions of extended freezing can occur. In addition to
making the surface difficult to play on, extended periods of freezing can kill the grass, making
the playing surface even worse. In order to prevent this, several NFL stadiums have installed
subterranean heating systems to keep the surface temperature above freezing during the winter
months and extend the grass growing season. The systems can also alleviate snow build up (but
not totally prevent it) on the field during games if snow occurs during a game.
The objective of this project is to design two different kinds of field heating systems that
will be able to prevent ground freezing during the winter months and will be able to help
alleviate snow build up during games. The system will operate in Green Bay, WI. Weather data
from Green Bay should be used in the design of the system.
Design Data
Location: Green Bay, WI
Surface: Grass
Desired surface temperature: 40-45 degrees
Desired “root zone” temperature: 75 -80 degrees
Operating Life: 20 years
Figure 1: Football field dimensions
Important considerations:
Root zone is the lower half of the sand layer which, in this case, has been considered to be 6-10
inches below the surface. The system has to be designed for the most extreme conditions.
However, much of the time, the conditions will be less severe, and the system will not be
operating at full capacity. This is the purpose of the temperature sensor/feedback control system.
It will adjust the system to the given conditions.
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EXECUTIVE SUMMARY:
The two propositions for keeping the football surface in playing conditions during
severely cold and snowy conditions are underground hydronic heating system and electrical
heating system. These systems can prevent the grass from dying from cold as well as provide
enough heat at the root zone of the grass to allow it to grow well.
Hydronic system uses four pumps and four boilers to heat the working fluid (water) and
recirculate it through the piping. A piping system has been laid out under the root zone in order
to provide the required heat to keep the root zone temperature at 75 F and surface temperature at
40 F. Each piping system has a header that distributes hot water into the field in small diameter
pipes. These pipes lose heat energy to the field and the cold water is collected by another large
pipe which carries it to the pump and eventually to the boiler. The function of the pump is to
make up for the pressure drop in the pipes and recirculate the fluid. A brief summary of hydronic
system is given below:
TABLE 1: Summary for the Hydronic system design
Number of Zones 4
Size of Zones 13,500 ft 2
Heat Provided by Boiler 992,000 Btu/hr
Number of Boilers 4
Number of Pumps 4Mass Flow Rate of Water 107 gpm
Temperature of Water 200 °F
Pipe Sizes 1/2” Sch 40 and 4” Sch 40
Pipe Material PVC
Depth of Pipes 30.54 inches
Loop Length 150 ft
Number of Loops 120Material Cost $159,751.4
Operation Cost (5 Months) $436,838.06
Operation Cost (12 Months) $1,050,811.54
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The electrical heating system uses Sun-touch Promelt heatig mats in order to provide the
heat energy required to maintain the desired root zone and the surface temperature. The design
has been based on extreme weather conditions and therefore, a feedback control system has been
installed in order to control the heat supplied at times when the conditions are not as severe.
There are eight zones which can be individually controlled. Each zone uses 66 2ft x 30 ft Promelt
heating mats resulting in a total of 528 mats. The mats are placed with a spacing of 17.7 inches.
The wiring is done in parallel so that malfunction to one network does not hinder the
performance of another. Mats installed at a depth of 7.14 inches below the root zone provide the
desired temperatures in extreme weather conditions. A brief summary of hydronic system is
given below:
TABLE 2: Summary for the Electric heating system design
Number of Zones 8Size of Zones 6750 ft 2
Number of Mats 528
Size of Mats 2 x 30 ft
Power of Mats 38 W
Temperature of Mats 100 °F
Depth of Mats 17.14 inches
Material Cost $375,821.2Operation Cost (5 Months) $438149
Operation Cost (12 Months) $1051559
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DESIGN APPROACH:
The project required every group to come up with two design approaches. The two means
of heating the field our group came up with were electrical heating system using electrical mats
and a hydronic system using pumps and boilers. Both the design approaches have been aimed at
worst possible weather scenario based on the weather data obtained for the Green Bay, WI area.
Most of the parameters that are vital to the calculation of required heating loads are common to
both the designs. However, the concepts regarding how the heat is actually supplied to the
surface in the desired manner (evenly throughout the field, and in appropriate quantity) is
different for the two cases.
Our priority is to keep the grass alive in inclement weather conditions and therefore, we
focus first and foremost on the root zone temperature and base our design on that. The design
root zone depth is 10 in to allow more space for the grass roots. Also, the given requirements of
temperature are met only if the soil with correct thermal properties is used. Therefore, saturated
sand should be used in the field because it has a thermal conductivity in the range of 1.16 to 2.31
Btu/hrft.
The first step is to determine the heat load. Heat load is basically the amount of heat lost
from the field surface. Under no losses (that every pipe has been perfectly insulated and there is
no loss of heat and all the heat input is being used to heat the root zone soil), and operating under
steady state, the system would have to provide this amount of heat to the surface in order tomaintain the temperature of the surface. Neglecting radiation, the major source of heat loss from
the surface in the extreme case is by forced convection from the cold wind blowing across the
field. It is acceptable to neglect the heat loss due to radiation because it does not result in
substantial amount of heat loss at such low temperatures and freezing conditions. The convection
co-efficient as well as the heat load was calculated using the tabulated values of the wind speeds
for Green bay climate and the air properties at the air temperature provided in the weather tables.
The value of heat load per square feet was calculated to be 73.45 Btu/hr. These quantities are
applicable to both the designs.
Antifreezes (chemical compounds) have been added to water to reduce the freezing point
of the mixture below the lowest temperature that the system is likely to encounter. Disadvantages
to using antifreeze are that it causes breakdown of the system over time, accelerated corrosion of
boilers and other system components and reduces efficiency of the system.
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In areas with cold winters, Expanded Polystyrene panels are used to insulate under slabs
and the perimeter of foundations. Because EPS is available in a variety of different densities with
different compression strengths, the material can accommodate any design load requirements
from a residential basement to an industrial warehouse floor with concentrated loads. A typical
application would be a floor with hydronic heating where insulating below the heat system is
critical to its economical operation.
An insulation of Styrofoam 2 inch thick is used 2 inches below the piping and the electric
pads, as well as on the sides to force the heat lost from the pipes to flow in upward direction and
insure no heat losses.
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Design Approach 1: Hydronic SystemThe major components of this hydronic system are a boiler, pump and a piping system.
Basically, this design requires piping under the field surface (preferably right below the root
zone) through which runs warm water resulting in heat transfer from the warm fluid to pipematerial and eventually to the soil. The fluid is heated using boilers, and a feed pump is used to
recirculate the fluid throughout the system. The theory used for the calculations is very similar to
a heat exchanger. Water has been used as the working fluid because it is readily available, cheap
and dealing with water is easier than any other fluids because we are well familiar with its
properties. The overall system flow diagram is provided below in figure 2.
Figure 2: Hydronic system heat flow and layout
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The team decided to divide the field into four zones so that heat input into each of four
zones could be controlled individually. Each zone has a boiler to heat the cold water coming out
of the piping network after losing heat to the field. A pump has been installed in order to
recirculate the same fluid. Given below is a figure of piping network for one zone.
Figure 3: Hydronic system piping layout for one out of four zones
FIGURE 4 given below shows a 3D orientation of hot water pipe, cold water pipe and
approximate boiler and pump location.
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Figure 4a and 4b: Different views of the hydronic system (a pump, a boiler and one piping loop)
The piping layout is basically a group of loops placed next to each other in parallel. There
is one 4” diameter hot water pipe (header), running through the length of one zone (parallel to
length of the field), out of which 30 different smaller ½” diameter pipes branch out at every 6
feet distance. Carrying hot water from the boiler , this 4” pipe releases hot water into thirty 1/2”
diameter pipes which run into the center of the field and make a U-turn back to the sides of the
field (one out of those 30 loops has been shown in the figure above). When these 30 pipes return
back on the side of the field, cold water in them is recollected into a 4” diameter cold water pipe.
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This cold water pipe, just like the hot wat er 4” diameter pipe, runs parallel to the length of the
field for every zone. Another 4” diameter pipes starts at the boiler and carries hot water to hot
water pipe. This pipe is insulated with Styrofoam wrapped around it to minimize the heat loss.
Another 4” pipe connects to the cold water pipe and circulates that water back to the pump. The
pump and the boiler can be installed in a mechanical room under the stands, about 75 ft away
from the actual playing surface. Also, the piping has been laid out about 20 inches below the root
zone temperature in order to make sure that the heat lost from the pipes distributes evenly in all
directions and by the time it reaches the root zone area, it has distributed throughout in all
directions, although in reality, it is not possible. The temperature distribution in real life situation
will fluctuate with highest temperature right above the pipe and lowest at the point between the
two pipes.
Since the temperature of the surrounding is very low, freezing of water is a possibilitywhich we would like to avoid. Therefore, antifreeze chemicals have been added to water in order
to prevent freezing.
Formulae used for calculation:
A boiler was first chosen which could provide an acceptable temperature difference
between inlet and exit for a given volume flow rate for each zone. After that, the piping network
was designed using the software PIP-FLO software in order to calculate the head loss for the
whole system. Various 90 degree elbows, tank entrant, as well as branch through were also
incorporated while performing the calculations. It was realized that PIP-FLO uses Darcy-
weisbach equation to solve the piping networks.
The software provided us with a pressure drop as well as the required head across the
pump for a constant speed pump. The NPSHa was calculated in order to make sure that NPSHr
for the selected pump was less that NPSHa available.
The thermal properties of water were calculated at the average of the inlet and exit
temperature. Convection co-efficient for the hot water running through the pipes was calculated
using the following equation,
Rearranging, we get,
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Where, h is the convective heat transfer coefficient, Re is the Reynolds number, Pr is the Prandtl
number, K f is the thermal conductivity of water, and D is the inside diameter of the tube.
The temperature drop of the water between entrance of the piping layout and the exit was
calculated using the following equation,
Where, Q is the total heat transfer rate, which is the heat load, is the mass flow rate of water
and C P is the specific heat of the water.
Knowing heat load (Q), depth of root zone (L), surface area of the field (A), root zone
temperature and the field surface temperature, the equation given below is used in order to find
the appropriate thermal conductivity value of the soil.
( )
Surface temperature of the pipe is vital to determining how deep below the root zone the
piping must be laid out in order to achieve the desired root zone temperature. The surface
temperature of the pipe was calculated using the following equation,
[ ]
Where, ODp is the outer pipe diameter, IDp is the inner pipe diameter, Q is the heat load, h is the
convective heat transfer coefficient, and L is the length of the pipe. Once the temperature of the
outer pipe surface is calculated, the depth of the pipe below the root zone can also be calculated
using the following equation,
( )
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Design Approach 2: Electrical Heating SystemThis design approach of the field heating system uses electrically heated mats. The main
components of this system are electrical heating mats, terminal boards, transformers, a main
control box and wiring. There are various kinds of heating mats available in the market forhousehold use to commercial use. Electrical heating pads are used in various places to remove
ice from the surface in extreme weather conditions. It is a very simplistic design compared to a
hydronic system since problems related to fluid are not an issue anymore and the pads can be
bought as manufactured by different companies.
In this design, the whole field is divided into eight different zones as shown in figure 5
below.
Figure 5: Electrical heating: system division of field into eight zones
Unlike in hydronic system, the heat transfer here takes place only due to conduction (no
convection). Each zone has three rows of heating pads installed. Twenty two 2ft x 30 ft pads are
installed in every row at spacing of about 17.7 inches. There are 66 pads in one zone and 528
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pads in total. Running at full capacity, the 37 Watt heating pads can reach temperatures of 300 F.
However, for this case, the temperature feedback sensor control system has been installed in
order to maintain the surface temperature of the pads at 100 F.
Figure 6: Electrical heating system: layout of mats in one zone
The wiring will be done in parallel so that if one of the terminals malfunctions, or needs
to be repaired, the others will still run fine. Figure 6 provided above is a top view of one out of
eight zones. This outlines how the components and the wiring are divided into different parts.
The way the mats will be laid out, there is a terminal box for each of the couple of rows of mats
which are connected to a field side junction box. Each of four zones has one of these field side
junction boxes enabling one to control the temperature at each zone individually. The two
junction boxes are further connected to a main control panel. Figure below shows the side viewof the system which further explains the positioning of the components. There is insulation
(Styrofoam) inside the ground on top of which the pads have been placed. There is spacing of
7.14 inches between the root zone and the pads in order to provide the desired root zone
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temperature. Finally, the grass is on the top. The thickness of the insulation, which has been
placed under the field and on the sides to prevent heat loss, is 2 inches.
Figure 7: Side view of the electric heating system design
Formula used for calculation:
The appropriate pads were first chosen based on the heat load for the field and the heating
density provided by the pads. Then based on the temperature of the pads and the heat load for
steady state heat conduction, the depth of the placement of the heating pads were calculated
using the Fourier’s conduction law given below,
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ECONOMIC ANALYSIS :
Hydronic System:
Hydronic Design Material Costs
PumpsCompany Pump Systems, LLC
Type AURORA End Suction Centrifugal Pump
Model 344ABF 2x2.5x7A
Price $1,691
Quantity 4
Total Cost $6,764
Boilers
Company Reimers Electra Steam, Inc.
Model HLR-300
Price $21,000
Quantity 4
Total Cost $84,000
Pipes
Company U.S. Plastic Corp.
Material PVC
Type 1/2" Schedule 40
4” Schedule 40
Price $0.34 - 1/2" Schedule 40
$3.81 - 4 ” Schedule 40
Quantity 18,120 - 1/2" Schedule 40
2,040 - 4 ” Schedule 40
Total Cost $12,231.84Fittings
Company U.S. Plastic Corp.
Types 90° Elbows
Tee-branches
Price $0.19 - 90° Elbows
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$3.04 - Tee-branches
Quantity 240 - 90° Elbows
240 - Tee-branches
Total Cost $770.64
Insulation
Company Universal Foam Products
Material Foam sheets 75x45’
Price $3,499.03
Quantity 16
Total Cost $55,984.48
Grand Total $159,751.4
Hydronic Design Operation Costs
After the installation of the system has been completed the cost to operate and maintain
the boilers and pumps must still be taken into account.
Pumps
We are using 1 HP motors to run the pumps.
1 HP = 0.746 kW
With 4 pumps in the systemTotal Power of pumps = 2.984 kW
Boilers
The boilers in the system have a 300 kW rating
With 4 boilers in the system
Total Power of the boilers = 1200 kW
Cost
Using the electric rate, found from the US energy information administration, for commercial
operations:
10.11 cents/kWhr
Take operating time in hours multiplied by the total power of the pumps or boilers.
Time * Power = kWhr
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To get the cost, multiply the kWhr with the rate from the electric company
kWhr * cents/kWhr = cents
Dollars = cents/100
Operation Cost for Different Operating Periods
Operation Time Pump Cost Boiler Cost Total Cost
3 Months $651.634 $262,051.2 $262,702.8
5 Months $1086.06 $436,752 $436,838.06
8 Months $1737.69 $698,803.2 $700,540.82
12 Months $2606.54 $1,048,205 $1,050,811.54
Electrical Heating System:
Electric Design Material Costs
Pads
Company SunTouch Watts Radiant
Type Promelt Mats
Model SM3812003024HW
Price $679.95
Quantity 528
Total Cost $359013.6
Sensors
Company SunTouch Watts Radiant
Type Slab Mount Soil Sensor
Model 983046HW
Price $1729.95Quantity 8
Total Cost $13,839.6
Company SunTouch Watts Radiant
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Type Pole mount Ambient Air Sensor
Model PM-824
Price $480
Quantity 4
Total Cost $1,920
Wires
Company Grainger
Model 4WZH8
Price $978
Quantity 2
Total Cost $1,956
Main Power SupplyCompany Dynamic Control System
Price $
Quantity 1
Total Cost $
Contactor Panels
Company SunTouch Watts Radiant
Model CP-200EX
Price $390
Quantity 2
Total Cost $780
Grand Total $375,821.20
Electric Design Operation Costs
After the installation of the system has been completed the cost to operate and maintain the
heating mats must still be taken into account.
Mats
We are using 38W mats, with a total of 528 mats in the system.
Total Power of mats = 20,064 W = 20.064 kW
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Cost
Using the electric rate, found from the US energy information administration, for commercial
operations: 10.11 cents/kWhr
Take operating time in hours multiplied by the total power of the mats.
Time * Power = kWhr
To get the cost, multiply the kWhr with the rate from the electric company
kWhr * cents/kWhr = cents
Dollars = cents/100
Operation Cost for Different Operating Periods
Operation Time Mats Cost
3 Months $262,889
5 Months $438,149
8 Months $701,039
12 Months $1,051,559
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Operability:
Both the hydronic system and electric heating system are widely used methods of heating
houses, buildings as well as fields and playing surfaces. Both these designs work just like any
other thermal system where there is a main control room and the feedback from the sensors is
used to increase or decrease the power supply based on the desired conditions.
The hydronic system requires lowering or increasing of mass flow rate through the boiler
in order to increase or decrease the heat supply. This can be easily done from the control room
using control valves. Also, the boiler used in this case has a feature where the temperature of the
heated water can be controlled. For the electrical heating system, thermostats are used to restrain
the soil temperatures at the operation zones so that the desired temperature is maintained. A
control room with electric switches is best for this purpose and can be operated by moderately
skilled individual.
Health and safety:
The boilers and pumps installed in the hydronic system have been manufactured from
licensed companies and therefore they are safe for the given operation conditions. Pressure relief
valves are installed at various locations in order to prevent explosion hazards and in case of
emergency. The wiring used in electrical heating system has been insulated so that there is no
issue of short circuit of someone being affected by electric charge. Since, both these systemsoperate on electricity, there is no health hazard resulting from burning any gases or emissions.
Manufacturability:
As mentioned earlier, all the parts used in this design project are standard and hence,
there is no need for custom manufacturing any parts. Different components only need to be
installed as designed to achieve the operating conditions.
Listed below are some key maintenance checks:
Hydronic System
1. Ensure proper operating pressure
2. System should not be flushed unless pressure is too low. Adding new water to the system
will contribute to corrosion by introducing oxygen to the fluid.
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3. Pressure test the system to check for leaks (Not all leaks will be visible)
4. Listen to pump for excessive noise. Pump is water lubricated and should be maintenance
free. Ensure pump is not leaking, flow capacity, gaskets and seals, check impeller wear,
heat coming off of pump, speed of operation, and power consumption.
5. Check boiler for leaks, excessive banging, water level, test low water cutoff switch,
visually check combustion chamber, ensure flame stays in fire box, check pressure and
temperature of boiler, check pressure and temperature of feed water, open chamber and
inspect for scaling.
6. Clean filters
Electric System
1. Check power to control panel.2. Check power to transformer.
3. Monitor voltage drop across each pad from terminal boxes. (Check for shorts)
4. Ensure control box and transformers stay moisture free.
5. Place ice on snow sensors to ensure thermostat operability.
6. Monitor power consumption of each zone.
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APPENDIX
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Calculations:
Hydronic System:
Total Heat Load:
Total area of the field (A): 360ft x 150ft = 54000ft2
Ambient wind temperature (T ∞) = -13F
Field surface temperature (T s) = 40F
Film temperature (T film): [40 + (-13)] / 2 = 13.5 F
Wind speed (extreme condition) (v): 8 Knots= 48609ft/hr
Properties of air @ film temperature:
Prandtl Number (Pr) = .72219
Kinematic Viscosity (ν) = .48197 ft 2 /hr
Thermal Conductivity (K f ) = .013457 Btu/hr ft F
Reynolds Number, Re = vL/ ν = [(48609)*(360)] / 0.48197 = 36307737 (turbulent)
Nusselt Number, Nu L = hL/K f = 0.037 Re .8Pr1/3 = 37075.32
Therefore, h = Nu LKf / L= [37075.32 x 0.013457] / 360 = 1.3858 Btu/ hr ft 2F
Then, the total heat load, Q, for the field =∆T/R th =[40 – (-13)]/[1/hA] = 3966434 Btu/hr
The total heat head load per ft 2 = 3966434/54000 = 73.452Btu/hr
Soil thermal conductivity selection:Root zone temperature (T R) = 75F
Field surface temperature, (T s) = 40F
Root zone depth (L) = 10 in = 0.833ft
Thermal Conductivity (K) = QL/A x (T R – Ts ) = [3966434 x 0.833]/54000*(75-40)
= 1.7488 Btu/ hr ft FPiping Layout
Number of zones = 4
Number of piping loops in one zone = 30
Heat load for one loop zone = 33053.62 Btu/hr
Available mass flow rate for the boiler @ 200F for one zone = 106.6 GPM = 53014.97 lbm/hr
So, for one loop zone, average available mass flow rate = 1767.166 lbm/hr = 28.502 ft 3 /hr
Temperature drop based on the heat load for one loop,
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∆T = Q/mC p = 33053.62/(1767.166 x 0.971) = 19.26F
Pipe selection:
½ in nominal diameter sch 40 PVC
Thermal Conductivity of pipe = 0.2025Btu/hr ft F
ID = .05183ft OD = .07ft
Flow area = 0.00211 ft 2
Surface Area = πDL = π (.05183) (150) = 24.4243ft 2
Velocity, V = Q/A = 28.502/.00211 = 13509.31 ft/hr = 3.75ft/sec
Inlet temperature, T i = 200F
Exit temperature, T e = 200 - ∆T = 200 - 19.26 = 180.73F
Average temperature of water= [200 + 180.73]/2 = 190.36F
Properties of water at average temperature, 190.36 F
Density, (ρ) = 60.299 lbm/ft 3
Kinematic Viscosity, ( ν) = .01261 ft 2 /hr
Prandtl Number (Pr) = 1.8971
Specific heat (C p) = .97274 Btu/hr ft F
Thermal Conductivity (K f ) = .39025 Btu/hr ft F
Reynolds Number (Re D) = VD/ = [13509 x 0.05183] / 0.01261 = 55526.39
Nusselt Number, Nu D = hD/K f = 0.023Re 4/5Pr0.3 = 174.0822
So, convection heat transfer coefficient, h = Nu D x K f / D= 1310.739 Btu/hr ft 2 F
Outside surface temperature of the pipe using thermal circuit
Ts = 200 – 33053(1/1310.73 x 24.42 + Ln (.07/.05183)/ 2π x 0.2025 x 150)
Placement of pipes under root zone:
L = (T pipe – TR) x K soil / Q = (147- 75) x 1.7488/73.45 = 1.712ft = 20.54in
Pipes must be laid out 20.54 inches below the root zone.
Pump selection using PIP-FLO
Total pressure drop = 100-93= 7psi
Head across the pump = ∆P/ γ = 7 x 144/62 = 16.25ft
NPSH r = P tank / γ + ∆Z – hL – Pv / γ = 100 x 144/62 + 0 – 16.25 – 9.33 x 144/62 = 194ft
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Since NPSH a > NPSHr, the selection is valid.
Electrical Heating Syetm:
Number of Zones = 8 Area of one zone= 90ft x 75 ft = 6750 ft2
Heating load per square foot = 73.45 BTU/hr
Heating load per one zone = 495787.5 BTU/hr
Heating density provided by the pad = 130 BTU/hr/ft 2
So, the area of the pad required for heating= (495787.5BTU/HR)/ (130 BTU/hr/ft 2) = 3813.75ft 2
Now,
Length of one pad = 30 ft Width of one pad = 2 ft
Area of one pad = 30ft x 2ft= 60 ft 2
Number of pads required for one zone= 3813.75ft 2 /60 ft 2=63.5735 pads
Number of columns of pads in one zone= 3
Therefore, number of pads required in one column,
63.5735 pads/3 columns= 21.18 ≈ 22 pads/column
Total width of pads being used in one column of one zone = 44ft
Remaining width for 21 spacing = 75ft- 44ft = 31ft
So, width of each spacing = 1.476 ft = 17.7in
Total number of pads in one zone = 22 pads x 3 columns = 66pads
Total number of pads for the whole field = 66 pads x 8 zones = 528 pads
Surface temperature of pads is maintained to a temperature of 100 F, Therefore, the required
depth of installation of pads below root zone is,L = (T pad – TRoot zone ) x K soil / Q = (100- 75) x 1.7488/73.45 = 0.5952 ft = 7.14 in
8/3/2019 Football Field Project
http://slidepdf.com/reader/full/football-field-project 27/27
References
1. Cengel, Yunus A. Heat transfer – An Engineering Approach 2 nd edition. New York:
McGraw-Hill. 2002.
2. Sonntag, R.E. Borgnakke C. and Van Wylen, Fundamentals of Engineering Thermodynamics
3. Janna, William S. Design of Fluid Thermal Systems. “Appendix Tables” Ed. 3. pp 601 -615.
4. Lecture Notes.
5. www.univfoam.com/pricing
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7. www.hukseflux.com/thermalscience/thermalconductivity.html
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