Football Field Project

8/3/2019 Football Field Project

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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



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


Type Slab Mount Soil Sensor

Model 983046HW

Price $1729.95Quantity 8

Total Cost $13,839.6




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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


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.



APPENDIX



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,



∆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



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



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.

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9. Pump Systems, LLC

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11. http://inditherm.com/default.asp?ContentID=40

12. http://www.suntouch.com/promelt/mats/

13. http://www.wattsradiant.com/products/promelt/www.e-comfortusa.com

14. www.360flooring.com

15. www.grainger.com

16. www.dynamiccontrolsystems.com

http://www.univfoam.com/pricing


http://www.usplastic.com/


http://www.hukseflux.com/thermalscience/thermalconductivity.html


http://www.reimersinc.com/


http://www.aurorapump.com/



http://inditherm.com/default.asp?ContentID=40



http://www.suntouch.com/promelt/mats/



http://www.wattsradiant.com/products/promelt/



http://www.360flooring.com/



http://www.grainger.com/



http://www.dynamiccontrolsystems.com/















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Football Field Project