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CHAPTER 1Formulas and Design Data
1-1
HEAT TRANSFER
This equation is used to determine the amount of
heat required to heat or cool a given amount of any
specific substance.
BTU Specific heat lbs. T
BTU British Thermal Unit
T Temperature Difference (F)
The specific heat of a substance is the amount of
heat in BTU that it takes to change the temperature
of one pound of that substance by one degree
Fahrenheit.
For example, the specific heat of water is 1.0 BTU/
lb.F. Therefore, to raise the temperature of 1 pound
of water by 1 degree F takes 1 BTU. Specific heats
of other materials vary.
BTU/h 1.08 CFM T
BTU/h
BTU per hour, a quantity of heatCFM Cubic feet per minute of air flow
(for sensible heat only)
HEATING AND COOLING CAPACITY
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BTU/h 4.5 CFM H
H Difference between return & supply air, in
BTU/lb.
(all systems, including both sensible & latent heats)
Sensible heat 1.08 CFM T
Sensible heat 1.1 CFM T
Latent heat 0.68 CFM WGR.Latent heat 4840 CFM WLB.
Total heat 4.5 CFM H
Total heat HS HL
Total heat UA T
HS Sensible heat (BTU/h)
HL Latent heat (BTU/h)
HT Total heat (BTU/h)
T Temperature difference (F)
WGR. Humidity ratio difference (Gr.H2O/Lb.DA)
WLB. Humidity ratio difference (Lb.H2O/Lb.DA)
H Enthalpy difference (BTU/Lb.DA)
CFM Air flow rate (cubic feet per minute)
U U-value (BTU/h/sq. ft./F)A Area (sq. ft.)
SHR Sensible heat ratio
HFG Latent heat of vaporization at design pressure
SHR HS
HT
HS
HS HL
COOLING AND HEATING
TOTAL HEAT CAPACITY
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1-3
R-VALUES/U-VALUES
R R-value (hr. sq. ft. F/BTU)
U U-value (BTU/h sq. ft. F)
C Conductance (BTU/h sq. ft.F)
K Conductivity (BTU in./hr. sq. ft. F)aR Sum of the individual R-values
Blower RPM Motor pulley diameter RPM of motor
Diameter of blower pulley
TBTU/h
1.08 CFM
CFM Watts 3.42 (BTU/Watt)
1.08 T
CFM
BTU/h
1.08 T
U1
gR
R 1
C
1
K Thickness
OBTAINING CFM FROM CAPACITY
CFM OF AN ELECTRIC FURNACE
CHANGE IN TEMPERATURE
OBTAINING RPM OF EXISTING BLOWER
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1-4
C Distance, center to center, between pulleys
D Larger pulley diameter
d Smaller pulley diameter
Compression ratio Absolute head pressure in psiaAbsolute suction pressure in psia
Diameter of the driver Diameter of driven RPM
RPM of driver
Diameter of driven Diameter of driver RPM
RPM of driven
RPM of driver Diameter of driven
RPMDiameter of driver
RPM of driven Diameter of driver RPM
Diameter of driven
Belt length 2 C 1.57 D d(D d)2
(4 C)
CHANGE IN PULLEY, NEW BELT LENGTH
PULLEY LAWS
COMPRESSION RATIO
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1-5
GPM Gallons per minute of flow
T Temperature Difference (F)
H 500 GPM T
H Total heat (BTU/h)
GPM Water flow rate (gallons per minute)
T Temperature difference (F)
Tons Air conditioning load (tons)
GPMEVAP. Evaporator water flow rate(gallons per minute)
GPMCOND. Condenser water flow rate
(gallons per minute)
GPMCOND. Tons 30
T
GPMEVAP. Tons 24
T
Chiller tons GPM Tchiller water
30
CONDENSER TONNAGE
CHILLER TONNAGE
WATER SYSTEM
GPM Gallons per minute of flow
T Temperature Difference (F)
Condenser tons GPM 1.25 Tconditioned water
24
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COOLING TOWERS AND HEAT EXCHANGERS
EWT Entering water temperature (F)
LWT Leaving water temperature (F)
AWBAmbient wet bulb temperature (design WB,F)
CT Cooling Tower
HE Heat Exchange
HS Hot side
CS Cold side
RANGE EWT LWT
APPROACHHE EWTHS LWTCS
APPROACHCT LWT AWB
NPSHAVAIL Net positive suction available at pump (ft.)NPSHREQD Net positive suction required at pump (ft.)
HA Pressure at liquid surface (ft.34 ft. for water
at atmospheric pressure)
HS Height of liquid surface above () or below
() pump (ft.)
HF Friction loss between pump and source (ft.)
HVP Absolute pressure of water vapor at liquid
temperature
NPSHAVAIL HA; HS HF HVP
NPSHAVAIL NPSHREQD
PUMP NET POSITIVE SUCTION HEAD (NPSH)
1-6
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GPM Gallons per minute
RPM Revolutions per minute
HD Feet of water
BHP Break horsepower
Pump size Constant
Water density Constant
BHP2
BHP1 a GPM2
GPM1b 3 a RPM2
RPM1b 3 a HD2
HD1b1.5
HD2
HD1 c GPM2
GPM1d 2 c RPM2
RPM1d 2
GPM2
GPM1
RPM2
RPM1
PUMP LAWS
1-7
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1-8
PUMP LAWS (cont.)
SP.GR. Specific gravity of liquid withrespect to water
SP.GR. (water) 1.0
PUMPEFF 6080%
M/DEFF 8595%
M/D Motor/drive
MHP Motor horsepower
P Pressure in psi
VH Velocity head in ft.
V Velocity in ft./sec.
g Acceleration due to gravity
(32.16 ft./sec.2)
HD P 2.31
SP.GR.
VH V2
2g
MHP BHP
M/DEFF
BHP GPM HD SP.GR.
3960 PUMPEFF
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1-9
REFRIGERATIO
NFORMULAS
Enthalpyof
Entha
lpyof
Netrefr
igerating
vaporleaving
liquid
entering
effect(B
TU/lb.)
evaporator(BTU/lb.)
evapo
rator(BTU/lb.)
Compre
ssionwork
Heatofcompre
ssion
Refrigerantcirculated
(BTUm
in.)
(BTU/lb.)
(lb./m
in.)
Compre
ssionHP
Compressionw
ork(BTU/min.)/42
.4
Compre
ssionHP
Capacity(BTU/m
in.)/42.4
COP
Compre
ssionHP
4.715/COP
(perton
)
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Power(Watts)
CompressionHPperton
745.7
COP
Netrefrigeratingeffect(BTU/
lb.)
Heatofco
mpression(BTU/lb.)
REFRIGERATIONF
ORMULAS(cont.)
C
apacity(BTU/min.)
Refrigerantcirculated
N
etrefrigerating
(lb./min.)
e
ffect(BTU/lb.)
Compre
ssordisplacemen
t
(ft.3/min
.)
Enthalpyo
f
E
nthalpyof
Heatofcompression
vaporleaving
v
aporentering
(B
TU/lb.)
compresso
r(BTU/lb.)
c
ompressor(BTU/lb.)
(BTU/min.)
Netrefrigeratingeffect(BTU/lb.)
V
olumeofgasente
ring
c
ompressor(ft.3/lb.)
Capacity
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1-11
Volumetricefficien
cy
100
Compressionratio
R
efrigerantcirculat
ed,
lb.(min.)(ton)
42.4
heatflow,BTU/(min.)(hp);200
BTU/(min
.)(ton);COP
coefficientofperformance
200
Refrigeratingeffect
Headpressure,psia(absolute)
Suctionpressure,psia(abso
lute)
b
Actualweightofre
frigerant
Theoreticalweightofrefrigerant
a
REFRIGERATIONF
ORMULAS(cont.)
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1-12
AIR FLOW
CFM FPM area (ft.2)
FPM CFM/area (ft.2)
Area CFM/FPM
Q
A V
CFM
ft.2 FPM
AIR CHANGE RATE
AC/HR Air change rate per hour
CFM Air flow rate (cubic feet per minute)VOLUME Space volume (cubic feet)
SA RA OA RA EA RFA
If minimum OA (ventilation air) is greater than EA,OA EA RFA
If EA is greater than minimum OA (ventilation air),
OA EA RFA 0
For economizer cycle: OASAEARFA RA0
SA Supply air
RA Return airOA Outside air
EA Exhaust air
RFA Relief air
CFM AC/HR VOLUME
60
AC/HR
CFM 60
VOLUME
AIR BALANCE EQUATIONS
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1-13
CFM Cubic feet per minute
RPM Revolutions per minute
SP In. W.G.
BHP Break horsepower
Fan size Constant
Air density Constant
SP2 SP1 a RPM2RPM1
b 2
SP2
SP1 a CFM2
CFM1b 2 a RPM2
RPM1b 2
RPM2 RPM1 CFM
2CFM1
CFM2 CFM1 RPM2
RPM1
CFM2
CFM1
RPM2
RPM1
FAN LAWS
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1-14
CFM Cubic feet per minute
RPM Revolutions per minute
SP In. W.G.
BHP Break horsepower
Fan size Constant
Air density Constant
SP.GR. (air) 1.0
FANEFF 6585%
M/DEFF 8095%
M/D Motor/drive
MHP Motor horsepower
MHP BHP
M/DEFF
BHP CFM SP SP.GR.
6356 FANEFF
BHP2 BHP1 a RPM2RPM1
b 3BHP2
BHP1
aCFM2
CFM1 b
3
aRPM2
RPM1 b
3
aSP2
SP1 b
1.5
FAN LAWS (cont.)
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1-15
MIXED AIR TEMPERATURE
CFMSA Supply air (CFM)
CFMRA Return air (CFM)
CFMOA Outside air (CFM)
TMA Mixed air temperature (F)
TROOM Room design temperature (F)
TRA Return air temperature (F)
TOA Outside air temperature (F)
GPMAC COND Air conditioning condensate flow
(gallons/min.)
CFM Air flow rate (cu. ft./min.)
SpV Specific volume of air (cu. ft./lb.DA)
WLB. Specific humidity (lb.H2O/lb.DA)
WGR. Specific humidity (gr.H2O/lb.DA)
GPMACCOND CFM WGR.
SpV 8.33 7000
GPMACCOND CFM WLB.
SpV 8.33
TMA aTRA CFMRACFMSA
b aTOA CFMOACFMSA
b
TMA aTROOM CFMRACFM
SA
b aTOA CFMOACFM
SA
b
AIR CONDITIONING CONDENSATE
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1-16
condensation occurs)
T Temperature (F)
R R-value (hr. sq. ft. F/BTU)
U
U-value (BTUH sq. ft.F)
IA Inside airfilm
OA Design outside air temperature
DP Dew point
HS (0.244 Q T) (L 380)
HS Sensible heat gain (BTUH)
Q Steam flow (lb. steam/hr.)
T Steam temperature supply air temperature (F)
L Length of humidifier manifold (ft.)
(if TGLASS DPROOM
TGLASS TROOM cUGLASSUIA
(TROOM TOA) d
TGLASS TROOM c RIAR
GLASS
(TROOM TOA) dMOISTURE CONDENSATION ON GLASS
HUMIDIFIER SENSIBLE HEAT GAIN
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1-17
GRAINSREQD Grains of moisture required (gr.H2O/cu. ft.)
POUNDSREQD Pounds of moisture required (lb.H2O/ cu. ft.)
CFM Air flow rate (cu. ft./min.)
SpV Specific volume of air (cu. ft./lb.DA)
WGR. Specific humidity (gr.H2O/lb.DA)
WLB. Specific humidity (lb.H2O/lb.DA)
CFM POUNDSREQD 60
Lb. STM/hr. CFM GRAINSREQD 60
7000
POUNDSREQD aWGR.SpV
bROOM AIR
aWGR.SpV
bSUPPLY AIR
GRAINSREQD aWGR.SpV
bROOM AIR
aWGR.SpV
bSUPPLY AIR
HUMIDIFICATION
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1-18
VT Volume of expansion tank (gal.)
VS Volume of water in piping system (gal.)
T T2 T1 (F)
T1 Lower system temperature (F)
Heating water T1 4550F tempera-ture at fill condition
Chilled water T1 Supply water
temperature
Dual temperature T1 Chilled water supply
temperature
T2 Higher system temperature (F)
Heating water T2 Supply water
temperature
Chilled water T2 95F ambient
temperature (designweather data)
Dual temperature T2 Heating water
supply temperature
Diaphragm VT VS [(v2>v1) 1] 3T
1 (P1
>P2)
Open VT 2 5(VS [(v2>v1) 1]) 3T6
Closed VT VS [(v2>v1) 1 ] 3T
[(PA
>P1) (PA
>P2)]
EXPANSION TANKS
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PA Atmospheric pressure (14.7 psia)
P1 System fill pressure/minimum system pressure
(psia)
P2 System operating pressure/maximum operating
pressure (psia)
V1 SpV of H2O at T1 (cu. ft./lb.H2O)V2 SpV of H2O at T2 (cu. ft./lb.H2O)
Linear coefficient of expansion
6.5 106
9.5 106
System volume estimate:
12 gal./ton
35 gal./BHP
System fill pressure/minimum system pressureestimate:
To height of system add 5 to 10 psi
System operating pressure/maximum operating
pressure estimate:
150-lb. systems 45125 psi250-lb. systems 125225 psi
COPPER
STEEL
EXPANSION TANKS (cont.)
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1-20
EFFICIENCIES
EER Energy efficiency ratio
COP = Coefficient of Performance
or
Turndown ratio Maximum firing rate: Minimum firing
rate (5:1, etc.)
Overall thermal efficiency range 75%90%
Combustion efficiency range 85%95%
Combustion eff. BTU input BTU stack loss
BTU input 100%
Overall thermal eff. Gross BTU output
Gross BTU input 100%
COP BTU output
Input watts 3.413 (BTU per watt)
COP BTU output
BTU input
EER
3.413
EER BTU output
Watts input
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1-21
Unitof
Measure
Multiply
By
ToObtain
Symbol
Ductwork
CFM
0.0004719
cubicmeters/sec.
m3/s
airflow
FPM
0.00508
meters/sec.
m/s
FPM
0.508
centimeters/sec.
cm/s
FPS
0.3048
meters/sec.
m/s
MPH
0.447
meters/sec.
m/s
Ductwork
In.H2O
0.25
kilopascals
kPa
pressure
In.H2O
249(use250)
pascals
Pa
In.H2O/100
8.176
pascals(N/m2)
Pa
In.Hg
3.386
kilopascals(kN/m
2)
kPa
Ductwork
In.
25.4
millimeters
mm
length&
In.
2.54
centimeters
cm
area
In.
0.0254
meters
m
D
UCTWORKHVAC
CONVERSIONS
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1-22
Unitof
Measure
Multiply
By
ToObtain
Symbol
Ductwork
In.2
6.452
centimeterssquared
cm2
length&
Ft.
0.3048
meters
m
area
Ft.2
0.0929
meterssquared
m2
Ft.3
0.02832
meterscubed
m3
Fan
CFM
0.4719
liters/sec.
l/s
duty
In.H2O
249(use250)
pascals
Pa
HP
0.7460
kilowatts
kW
RPM
0.10472
radians/sec.
rad/s
RPM
60
revolutions/sec.
rev/s
Pump
Psf
47.88(use50)
pascals(N/m2)
Pa
duty
Psi
6895(use7000)
pascals(N/m2)
Pa
Psi
6.895
kilopascals(kN/m
2)
kPa
FANANDPUMPDUTY
HVACCONVERS
IONS
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1-23
General
Total heat 300400 sq. ft./ton (range 230520)
Total heat 3040 BTU/h/sq. ft.(range 2352)
Room sens. heat 2528 BTU/h/sq. ft.(range 1937)
SHR 0.750.93
Perimeter spaces 1.03.0 CFM/sq. ft.
Interior spaces 0.51.5 CFM/sq. ft.
Building block CFM 1.01.5 CFM/sq. ft.
Air change rate 410 AC/hr.
Large, Perimeter
Total heat 225275 sq. ft./ton
Total heat 4353 BTU/h/sq. ft.
Large, Interior
Total heat 300350 sq. ft./ton
Total heat 3440 BTU/h/sq. ft.
Small
Total heat 325375 sq. ft./ton
Total heat 3237 BTU/h/sq. ft.
OFFICE DESIGN CRITERIA
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GENERALDES
IGNVALUES
Roo
m
Air
TotalHeat
TotalHeat
Sens.Heat
Change
(Ton)
BTUh/sq.ft.
BTUh/s
q.ft.
SHR
S
paces
AirFlow
Rate
Banks,Court
200250
4
860
2838
0.750.90
410AC/hr.
Houses,
sq.ft./ton
B
TUh/sq.ft.
BTUh/s
q.ft.
Municipal
(range160340)
(range3575)
(range2148)
Buildings
PoliceStations
,
250350
3
448
2535
0.750.90
410AC/hr.
FireStations,
sq.ft./ton
B
TUh/sq.ft.
BTUh/s
q.ft.
PostOffices
(range200400)
(range3060)
(range2040)
Precision
50300
4
0240
32228
0.800.95
1050AC/hr.
Manufacturing
sq.ft./ton
B
TUh/sq.ft.
BTUh/s
q.ft.
Computer
50150
8
0240
64228
0.800.95
2.04.0
1520AC/hr.
Rooms
sq.ft./ton
B
TUh/sq.ft.
BTUh/s
q.ft.
CFM/sq.ft.
Restaurants
100250
4
8120
2162
0.650.80
1.54.0
812AC/hr.
sq.ft./ton
B
TUh/sq.ft.
BTUh/s
q.ft.
CFM/sq.ft.
(range75300)
(range40155)
(range2080)
Kitchens
150350
3
480
2056
0.600.70
1.52.5
1215AC/hr.
sq.ft./ton
B
TUh/sq.ft.
BTUh/s
q.ft.
CFM/sq.ft.
(at85Fspace)
(at85Fspace)
(at85F
space)