Equations

3PA R T3

H VA C E Q U AT I O N S , D ATA , A N D R U L E S O F T H U M B

20 PART 3

3.01 Airside System Equations and Derivations

A. Equations

HS 1.08 rCFM r$THS 1.1 rCFM r$THL 0.68 rCFM r$WGR.HL 4840 rCFM r $WLB.HT 4.5 rCFM r $ hHT HS HL

SHRH

H

H

H HS

T

S

S L

HS Sensible Heat (Btu/hr.)HL Latent Heat (Btu/hr.)HT Total Heat (Btu/hr.)$T Temperature Difference (F)$WGR. Humidity Ratio Difference (Gr.H2O/lbs.DA)$WLB. Humidity Ratio Difference (lbs.H2O/lbs.DA)$h Enthalpy Difference (Btu/lbs.DA)CFM Air Flow Rate (Cubic Feet per Minute)SHR Sensible Heat Ratiom Mass flow (lbs.DA/hr.)ca Specific Heat of Air (0.24 Btu/lbs.DA F)DA Dry Air

B. Derivations

1. Standard air conditions:a. Temperature: 60Fb. Pressure: 14.7 psia (sea level)c. Specific volume: 13.33 ft.3/lbs.DAd. Density: 0.075 lbs./ft.3

e. LV Latent heat of water @60F: 1060 Btu/lbs.2. Sensible heat equation:

HS m rca r$TcP 0.24 (Btu/lbs.DA . F) r 0.075 lbs.DA/ft.3 r 60 min./hr.

1.08 Btu min./hr. ft.3 FHS 1.08 (Btu min./hr. ft.3 F) r CFM (ft.3/min.) r $T (F)HS 1.08 r CFM r $T

3. Latent heat equation:HL m r LV r $WGRLV 1060 Btu/lbs.H2O r 0.075 lbs.DA/ft.3 r 60 min./hr. r 1.0 lbs.H2O/7,000 Gr.H2O

0.68 Btu lbs.DA min./hr.ft.3 Gr.H2OHL 0.68 (Btu lbs.DA min./hr.ft.3 Gr.H2O) r CFM (ft.3/min.) r $WGR (Gr.H2O/lbs.DA)HL 0.68 r CFM r $WGR

4. Total heat equation:HT m r $hFactor 0.075 lbs.DA/ft.3 r 60 min./hr. 4.5 lbs.DA min./hr.ft.3HT 4.5 (lbs.DA min./hr.ft.3) r CFM (ft.3/min.) r $h (Btu/lbs.DA)HT 4.5 r CFM r $h

Equations 21

3.02 Waterside System Equations and Derivations

A. Equations

H 500 rGPM r$T

GPMTONS

TEVAP. r 24

$

GPMTONS

TCOND. r 30

$

H Total Heat (Btu/hr.)GPM Water Flow Rate (Gallons per Minute)$T Temperature Difference (F)TONS Air Conditioning Load (Tons)GPM EVAP. Evaporator Water Flow Rate (Gallons per Minute)GPM COND. Condenser Water Flow Rate (Gallons per Minute)cw Specific Heat of Water (1.0 Btu/lbs.H2O)

B. Derivations

1. Standard water conditions:a. Temperature: 60Fb. Pressure: 14.7 psia (sea level)c. Density: 62.4 lbs./ft.3

2. Water equationH m r cw r $Tcw 1.0 Btu/Lb H2O F r 62.4 lbs.H2O/ft3 r 1.0 ft3 / 7.48052 gal. r 60 min./hr.

500 Btu min./hr. F gal.H 500 Btu min./hr. F gal. r GPM (gal./min.) r $T (F)H 500 r GPM r $T

3. Evaporator equation:GPMEVAP H/(500 r $T)Factor 12,000 Btu/hr./1.0 tons 500 Btu min./hr. F gal.

24F gal./tons min.GPMEVAP tons (tons) r 24 (F gal./tons min.) / $T (F)GPMEVAP tons r 24 / $T

4. Condenser equation:GPMCOND 1.25 r GPMEVAP = 1.25 r tons r 24 / $TGPMCOND tons r 30 / $T

3.03 Air Change Rate Equations

AC

HR

CFM

VOLUME r60

CFM

AC

HRVOLUME

r

60

AC/HR. Air Change Rate per HourCFM Air Flow Rate (Cubic Feet per Minute)VOLUME Space Volume (Cubic Feet)

22 PART 3

3.04 English/Metric Airside System Equations Comparison

A. Sensible Heat Equations

H .Btu min

Hr ft FCFM TS r r1 08 3

.F $

H .kJ min

hr m CCMM TSM M r r72 42 3

.

. F$

B. Latent Heat Equations

H .Btu min Lb DA

hr ft Gr H OCFM WL r r0 68 3

2

.

.$

H , .kJ min kg DA

hr m kg H OCLM r177 734 8 3

2

.

.MMM WMr $

C. Total Heat Equations

H .lb min.

hr. ft.CFM hT r r4 5 3 $

H .kg min

hr. mCMM hTM M r r72 09 3

.$

HT HS HLHTM HSMHLM

HS Sensible Heat (Btu/hr.)HSM Sensible Heat (kJ/hr.)HL Latent Heat (Btu/hr.)HLM Latent Heat (kJ/hr.)HT Total Heat (Btu/hr.)HTM Total Heat (kJ/hr.)$T Temperature Difference (F)$TM Temperature Difference (C)$W Humidity Ratio Difference (Gr.H2O/lbs.DA)$WM Humidity Ratio Difference (kg.H2O/kg.DA)$h Enthalpy Difference (Btu/lbs.DA)$hM Enthalpy Difference (kJ/lbs.DA)CFM Air Flow Rate (Cubic Feet per Minute)CMM Air Flow Rate (Cubic Meters per Minute)

3.05 English/Metric Waterside System Equation Comparison

HBtu min.

hr. gal. FGPM T r r500

$

H .kJ min.

hr. Liters CLPM TM M r r250 8

$

Equations 23

H Total Heat (Btu/hr.)HM Total Heat (kJ/hr.)$T Temperature Difference (F)$TM Temperature Difference (C)GPM Water Flow Rate (Gallons per Minute)LPM Water Flow Rate (Liters per Minute)

3.06 English/Metric Air Change Rate Equation Comparison

AC

HR

CFMmin.

hr.VOLUME

r60

AC

HR

CMMmin.

hr.VOLUMEM M

r60

AC/HR. Air Change Rate per Hour EnglishAC/HR.M Air Change Rate per Hour MetricAC/HR. AC/HR.MVOLUME Space Volume (Cubic Feet)VOLUMEM Space Volume (Cubic Meters)CFM Air Flow Rate (Cubic Feet per Minute)CMM Air Flow Rate (Cubic Meters per Minute)

3.07 English/Metric Temperature and Other Conversions

F 1.8 C 32

C F.

321 8

F degrees FahrenheitC degrees CelsiuskJ/hr. Btu/hr. r 1.055CMM CFM r 0.02832LPM GPM r 3.785kJ/kg Btu/lbs. r 2.326meters ft. r 0.3048sq. meters sq. ft. r 0.0929cu. meters cu. ft. r 0.02832kg lbs. r 0.45361.0 GPM 500 lbs. steam/hr.1.0 lb. stm. / hr. 0.002 GPM1.0 lb. H2O / hr. 1.0 lbs. steam/hr.kg / cu. meter lbs. / cu. ft. r 16.017 (Density)cu. meters / kg cu. ft. / lbs. r 0.0624 (Specific Volume)kg H2O / kg DA Gr.H2O / lbs.DA / 7,000 lbs.H2O/lbs.DA

24 PART 3

3.08 Steam and Condensate Equations

A. General

LBS.STM. / HRBTU / HR

H

BTU / HR

FG

960

LBS.STM.COND. / HREDR

4

EDRBTU / HR

240

LBS.STM.COND. / HRGPM SP.GR. C T

Hw

FG

r r r r500 $

LBS.STM.COND. / HRCFM D C T

Ha

FG

r r r r60 $

B. Approximating Condensate Loads

LBS.STM.COND. / HRGPM WATER T

r$2

LBS.STM.COND. / HRGPM FUEL OIL T

r$4

LBS.STM.COND. / HRCFM AIR T

r$900

stm. SteamGPM Quantity of Liquid in Gallons per MinuteCFM Quantity of Gas or Air in Cubic Feet per MinuteSP.GR. Specific GravityD Density in lbs./cubic feetCa Specific Heat of Air (0.24 Btu/lb.)Cw Specific Heat of Water (1.00 Btu/lb.)HFG Latent Heat of Steam in Btu/lbs. at Steam Design Pressure (ASHRAE Fundamen-

tals or Part 45)$T Final Temperature minus Initial TemperatureEDR Equivalent Direct Radiation

3.09 Building Envelope Heating Equation and R-Values/U-Values

H U r A r $T

RC K

Thickness r1 1

UR

1

$T Temperature Difference (F)A Area (sq.ft.)U U-Value (Btu./hr. sq.ft. F): See Part 35 for Definitions.R R-Value (hr. sq.ft. F/Btu.): See Part 35 for Definitions.

Equations 25

C Conductance (Btu./hr. sq.ft. F): See Part 35 for Definitions.K Conductivity (Btu. in./hr. sq.ft. F): See Part 35 for Definitions.3R Sum of the Individual R-Values

3.10 Fan Laws

CFM

CFM

RPM

RPM2

1

2

1

SP

SP

CFM

CFM

RPM

RPM2

1

2

1

2

2

1

2

BHP

BHP

CFM

CFM

RPM

RPM

SP2

1

2

1

3

2

1

3

22

1

1 5

SP

.

BHPCFM SP SP.GR.

FANEFF. r r

r6356

MHPBHP

M / DEFF

.

CFM Cubic Feet/Minute Air Density ConstantRPM Revolutions/Minute SP.GR.(Air) 1.0SP in. W.G. FANEFF 6585%BHP Break Horsepower M/DEFF 8095%Fan Size Constant M/D Motor/Drive

3.11 Pump L.ws

GPM

GPM

RPM

RPM2

1

2

1

HD

HD

GPM

GPM

RPM

RPM2

1

2

1

2

2

1

2

BHP

BHP

GPM

GPM

RPM

RPM

HD2

1

2

1

3

2

1

3

22

1

1 5

HD

.

BHPGPM HD SP.GR.

PUMPEFF. r r

r3960

MHPBHP

M / DEFF.

VHV

g

2

2

HDP .

SP.GR. r 2 31

GPM Gallons/MinuteRPM Revolutions/MinuteHD ft. H2OBHP Break Horsepower

26 PART 3

Pump Size ConstantWater Density ConstantSP.GR. Specific Gravity of Liquid with respect to WaterSP.GR.(Water) 1.0PUMPEFF 6080%M/DEFF 8595%M/D Motor/DriveP Pressure in psiVH Velocity Head in ft.V Velocity in ft./sec.g Acceleration due to Gravity (32.16 ft./sec.2)

3.12 Pump Net Positive Suction Head (NPSH) Calculations

NPSHAVAIL NPSHREQDNPSHAVAIL HA HS HF HVP

NPSH AVAIL Net Positive Suction Available at Pump (feet)NPSH REQD Net Positive Suction Required at Pump (feet)HA Pressure at Liquid Surface (Feet 34 feet for Water at Atmospheric Pressure)HS Height of Liquid Surface Above () or Below () Pump (feet)HF Friction Loss between Pump and Source (feet)HVP Absolute Pressure of Water Vapor at Liquid Temperature (feet ASHRAE

Fundamentals or Part 45)

Note: Calculations may also be performed in psig, provided that all values are in psig.

3.13 Mixed Air Temperature

T TCFM

CFMT

CFM

CFMMA ROOMRA

SAOA

OA

SA

r

r

T TCFM

CFMT

CFM

CFMMA RARA

SAOA

OA

SA

r

r

CFMSA Supply Air CFMCFMRA Return Air CFMCFMOA Outside Air CFMTMA Mixed Air Temperature (F)TROOM Room Design Temperature (F)TRA Return Air Temperature (F)TOA Outside Air Temperature (F)

3.14 Psychrometric Equations

W 0 622.

P

P PW

W

r

RHW

WACTUAL

SAT

r100%

Equations 27

RHP

PW

SAT

r100%

HS m r cP r $T

HL Lv r m r $W

HT m r $h

W. T W T TWB SAT WB DB WB

2501 2 381

2501 1.. T . TDB WB805 4 186

W. T W . T TWB SAT WB DB WB

1093 0 556 0 2401093 0 444 . T TDB WB

W Specific Humidity, lbs.H2O/lbs.DA or Gr.H2O/lbs.DAWACTUAL Actual Specific Humidity, lbs.H2O/lbs.DA or Gr.H2O/lbs.DA WSAT Saturation Specific Humidity at the Dry Bulb TemperatureWSAT WB Saturation Specific Humidity at the Wet Bulb TemperaturePW Partial Pressure of Water Vapor, lb./sq.ft.P Total Absolute Pressure of Air/Water Vapor Mixture, lb./sq.ft.PSAT Saturation Partial Pressure of Water Vapor at the Dry Bulb Temperature,

lb./sq.ft.RH Relative Humidity, %HS Sensible Heat, Btu/hr.HL Latent Heat, Btu/hr.HT Total Heat, Btu/hr.m Mass Flow Rate, lbs.DA/hr. or lbs.H2O/hr.cP Specific Heat, Air0.24 Btu/lbs.DA, Water1.0 Btu/lbs.H2OTDB Dry Bulb Temperature, FTWB Wet Bulb Temperature, F$T Temperature Difference, F$W Specific Humidity Difference, lbs.H2O/lbs.DA or Gr.H2O/lbs.DA$h Enthalpy Difference, Btu/lbs.DALV Latent Heat of Vaporization, Btu/lbs.H2O

3.15 Ductwork Equations

TP SPVP

VPV V

4005 4005

2 2

2

VQ

A

Q

W H r

r144

D. A B

A BEQ

.

.

r r

1 30 625

0 25

28 PART 3

TP Total PressureSP Static Pressure, Friction LossesVP Velocity Pressure, Dynamic LossesV Velocity, ft./min.Q Flow through Duct, CFMA Area of Duct, sq.ft.W Width of Duct, in.H Height of Duct, in.DEQ Equivalent Round Duct Size for Rectangular Duct, in.A One Dimension of Rectangular Duct, in.B Adjacent Side of Rectangular Duct, in.

3.16 Equations for Flat Oval Ductwork

FS MAJORMINOR

AFS MINOR

MINOR

r r P

2

4144

PMINOR FS

r r P 2

12

D. A

PEQ

.

.

r

1 550 625

0 25

FS Flat Span Dimension in InchesMAJOR Major Axis Dimension in Inches (Larger Dimension)MINOR Minor Axis Dimension in Inches (Smaller Dimension)A Cross-sectional Area in Square FeetP Perimeter or Surface Area in Square Feet per Lineal FeetDEQ Equivalent Round Duct Diameter

3.17 Steel Pipe Equations

A 0.785 r ID2

WP 10.6802 r T r (OD T)

Equations 29

WW 0.3405 r ID 2

OSA 0.2618 r OD

ISA 0.2618 r ID

AM 0.785 r (OD2 ID2)

A Cross Sectional Area (sq.in.)WP Weight of Pipe per Foot (lbs.)WW Weight of Water per Foot (lbs.)T Pipe Wall Thickness (in.)ID Inside Diameter (in.)OD Outside Diameter (in.)OSA Outside Surface Area per Foot (sq.ft.)ISA Inside Surface Area per Foot (sq.ft.)AM Area of the Metal (sq.in.)

3.18 Steam and Steam Condensate Pipe Sizing Equations

A. Steam Pipe Sizing Equations

$P. W

.

ID

D ID r r

r r

0 01306 13 6

3600

2

5

WP D ID

..

ID

r r r

r

60

0 01306 13 6

5$

W 0.41667 r V r AINCHES r D 60 r V r AFEET r D

V. W

A D

W

A DINCHES FEET r

r

r r2 4

60

$P Pressure Drop per 100 ft. of Pipe, psig/100 ft.W Steam Flow Rate, lbs./hr.ID Actual Inside Diameter of Pipe, in.D Average Density of Steam at System Pressure, lbs./cu.ft.V Velocity of Steam in Pipe, ft./min.AINCHES Actual Cross Sectional Area of Pipe, sq.in.AFEET Actual Cross Sectional Area of Pipe, sq.ft.

B. Steam Condensate Pipe Sizing Equations

FSH H

H

S S

L

SS CR

CR

r100

WFS

WCR r100

FS Flash Steam, Percentage %HSSS Sensible Heat at Steam Supply Pressure, Btu/lbs.HSCR Sensible Heat at Condensate Return Pressure, Btu/lbs.HLCR Latent Heat at Condensate Return Pressure, Btu/lbs.

30 PART 3

W Steam Flow Rate, lbs./hr.WCR Condensate Flow based on percentage of Flash Steam created during condensing

process, lbs/hr. Use this flow rate in the preceding steam equations to determine the condensate return pipe size.

3.19 Air Conditioning Condensate

GPMCFM W

SpV .AC CONDLB.

rr$8 33

GPMCFM W

SpV .AC CONDGR.

rr r

$8 33 7000

GPMAC COND Air Conditioning Condensate Flow (gal./min.)CFM Air Flow Rate (cu.ft./min.)SpV Specific Volume of Air (cu.ft./lbs.DA)$WLB. Specific Humidity (lbs.H2O/lbs.DA)$WGR. Specific Humidity (Gr.H2O/lbs.DA)

3.20 Humidification

GRAINSW

SpV

W

SpVREQ'DGR.

ROOM AIR

GR.

SUPPLY AIR

POUNDSW

SpV

W

SpVREQ'DLB.

ROOM AIR

LB.

SUPPLY AIR

LBS STM HRCFM GRAINS

CFM POUNREQ D. . / 'r r

r60

7000DDSREQ D' r 60

GRAINSREQD Grains of Moisture Required (Gr.H2O/cu.ft.)POUNDSREQD Pounds of Moisture Required (lbs.H2O/cu.ft.)CFM Air Flow Rate (cu.ft./min.)SpV Specific Volume of Air (cu.ft./lbs.DA)WGR. Specific Humidity (Gr.H2O/lbs.DA)WLB. Specific Humidity (lbs.H2O/lbs.DA)

3.21 Humidifier Sensible Heat Gain

HS (0.244 r Q r $T) (L r380)

HS Sensible Heat Gain (Btu/hr.)Q Steam Flow (lbs. steam/hr.)$T Steam Temperature Supply Air Temperature (F)L Length of Humidifier Manifold (ft.)

Equations 31

3.22 Expansion Tanks

CLOSED V V

v

vT

P

P

T S

A

r

2

1

1

1 3A$

PP

PA

2

OPEN V Vv

vT S r r

2 1 32

1

A$TT

DIAPHRAGM V V

v

vT

T S r

2

1

1 3

1

A$

PP

P1

2

VT Volume of Expansion Tank (Gallons)VS Volume of Water in Piping System (Gallons)$T T2 T1 (F)T1 Lower System Temperature (F)

Heating Water T1 4550F Temperature 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 (Design Weather Data) Dual Temperature T2 Heating Water Supply Temperature

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./lbs.H2O) ASHRAE Fundamentals or Part 45v2 SpV of H2O at T2 (cu.ft./lbs.H2O) ASHRAE Fundamentals or Part 45A Linear Coefficient of Expansion ASTEEL 6.5 r 106 ACOPPER 9.5 r 106System Volume Estimate: 12 gal./ton 35 gal./BHPSystem Fill Pressure/Minimum System Pressure Estimate: Height of System 5 to 10 psi OR 510 psi, whichever is greater.System Operating Pressure/Maximum Operating Pressure Estimate: 150 lbs. Systems 45125 psi 250 lbs. Systems 125225 psi

3.23 Air Balance Equations

SA Supply AirRA Return AirOA Outside AirEA Exhaust AirRFA Relief AirSA RA OA RA EA RFA

32 PART 3

If minimum OA (ventilation air) is greater than EA, then

OA EA RFA

If EA is greater than minimum OA (ventilation air), then

OA EA RFA 0

For Economizer Cycle:

OA SA EA RFA RA 0

3.24 Efficiencies

COPBTU OUTPUT

BTU INPUT

EER 3 413.

EERBTU OUTPUT

WATTS INPUT

KW TON12,000 BTU HRTON

COP BTU / HR/

/

,

r 3 517 KKW

Turndown Ratio = Maximum Firing Rate: Minimum Firing Rate (e.g., 5:1, 10:1, 25:1)

OVERALL THERMAL EFFGROSS BTU OUTPUT

GROSS.

BBTU INPUTr100%

COMBUSTION EFFBTU INPUT BTU STACK LOSS

BTU.

INPUTr100%

Overall Thermal Efficiency Range 7590%

Combustion Efficiency Range 8595%

3.25 Cooling Towers and Heat Exchangers

APPROACHCT'S LWT AWB

APPROACHHE'S EWTHS LWTCSRANGE EWT LWT

EWT Entering Water Temperature (F)LWT Leaving Water Temperature (F)AWB Ambient Wet Bulb Temperature (Design WB F)HS Hot SideCS Cold Side

3.26 Cooling Tower/Evaporative Cooler Blowdown Equations

CE D B

D B

BE C D

C

r

1

1

Equations 33

E GPMCOND. r R r 0.0008

D GPMCOND. r 0.0002

R EWT LWT

B Blowdown, GPMC Cycles of ConcentrationD Drift, GPME Evaporation, GPMEWT Entering Water Temperature, FLWT Leaving Water Temperature, FR Range, F

3.27 Electricity

A. General

KVA KW KVAR

B. Single-Phase Power

KWV A PF

1 1000F r r

KVAV A

1 1000F r

BHPV A PF DEVICEEFF.

1 746F

r r r

MHPBHP

M / DEFF.1

1F

F

C. Three-Phase Power

KWV A PF

3

3

1000F r r r

KVAV A

3

3

1000F r r

BHPV A PF DEVICEEFF.

3

3

746F

r r r r

MHPBHP

M / DEFF.3

3

FF

KVA Total Power (Kilovolt Amps)KW Real Power, Electrical Energy (Kilowatts)KVAR Reactive Power or Imaginary Power (Kilovolt Amps Reactive)V Voltage (Volts)A Current (Amps)PF Power Factor (0.750.95)BHP Break HorsepowerMHP Motor Horsepower

34 PART 3

EFF EfficiencyM/D Motor Drive

3.28 Moisture Condensation on Glass

T TR

R(T TGLASS ROOM

IA

GLASSROOM OA r

)

T TU

UT TGLASS ROOM

GLASS

IAROOM OA r

( )

If condensation occursT DPGLASS ROOM

T Temperature (F)R R-Value (hr. sq.ft. F/Btu)U U-Value (Btu./hr. sq.ft. F)IA Inside AirfilmOA Design Outside Air TemperatureDP Dewpoint

3.29 Calculating Heating Loads for Loading Docks, Heavily Used Vestibules and Similar Spaces

A. Find volume of space to be heated (cu.ft.).

B. Determine acceptable warm-up time for space (min.).

C. Divide volume by time (CFM).

D. Determine inside and outside design temperaturesassume inside space tem-perature has dropped to the outside design temperature because doors havebeen open for an extended period of time.

E. Use sensible heat equation to determine heating requirement using CFM andinside and outside design temperatures determined earlier in this Part.

3.30 Ventilation of Mechanical Rooms with Refrigeration Equipment

A. For a more detailed description of ventilation requirements for mechanical roomswith refrigeration equipment, see ASHRAE Standard 15 and Part 8.

B. Completely Enclosed Equipment Rooms

CFM 100 r G0.5

CFM Exhaust Air Flow Rate Required (cu.ft./minute)G Mass of Refrigerant of Largest System (pounds)

C. Partially Enclosed Equipment Rooms

FA G 0.5

FA Ventilation Free Opening Area (sq.ft.)G Mass of Refrigerant of Largest System (Pounds)

Equations 35

3.31 Pipe Expansion Equations

A. L-Bends

L D r6 225. $

F 500 LB. / PIPE DIA. r PIPE DIA.

L Length of Leg Required to Accommodate Thermal Expansion or Contraction, Feet$ Thermal Expansion or Contraction of Long Leg, InchesD Pipe Outside Diameter, InchesF Force Exerted by Pipe Expansion or Contraction on Anchors and Supports, lbs. See Tables

in Part 18 for solved equations.

B. Z-Bends

L D r4 $

F 200 500 LB. / PIPE DIA. r PIPE DIA.

L Length of Offset Leg Required to Accommodate Thermal Expansion or Contraction, Feet$ Anchor to Anchor Expansion or Contraction, InchesD Pipe Outside Diameter, InchesF Force Exerted by Pipe Expansion or Contraction on Anchors and Supports, lbs. See Tables

in Part 18 for solved equations.

C. U-Bends or Expansion Loops

36 PART 3

L D r6 225. $F 200 LB. / PIPE DIA. r PIPE DIA.

L 2HW

H 2W

L 5W

L Length of Loop Required to Accommodate Thermal Expansion or Contraction, ft.$ Anchor to Anchor Expansion or Contraction, in.D Pipe Outside Diameter, in.F Force Exerted by Pipe Expansion or Contraction on Anchors and Supports, lbs.

3.32 Relief Valve Vent Line Maximum Length

LP D

C

P D

C

r r

r rr

9 9

1612 5

222 5

2

P PRESSURE SETTING1 0 25 1 1 14 7 r r . . .

P PRESSURE SETTING2 1 1 14 7 r . .

L Maximum Length of Relief Vent Line in FeetD Inside Diameter of Pipe in InchesC Minimum Discharge of Air in lbs./min.

3.33 Relief Valve Sizing

A. Liquid System Relief ValvesSpring-Style Relief Valves

AGPM G

K K PB V r

r r r28 14. $

B. Liquid System Relief ValvesPilot-Operated Relief Valves

AGPM G

K PV r

r r36 81. $

C. Steam System Relief Valves

AW

K P K K KSH N B

r r r r r51 5.

D. Gas and Vapor System Relief Valveslbs./hr.

AW TZ

C K P K MB r

r r r r

E. Gas and Vapor System Relief ValvesSCFM

ASCFM TGZ

C K P K B

rr r r r1 175.

Equations 37

F. Relief Valve Equation Definitions

1. A Minimum required effective relief valve discharge area (sq.in.)2. GPM Required relieving capacity at flow conditions (gal./min.)3. W Required relieving capacity at flow conditions (lbs./hr.)4. SCFM Required relieving capacity at flow conditions (standard cu.ft./min.)5. G Specific gravity of liquid, gas, or vapor at flow conditions

Water 1.0 for most HVAC applications Air 1.0

6. C Coefficient determined from expression of ratio of specific heatsC 315 if value is unknown

7. K Effective coefficient of discharge K 0.975

8. KB Capacity correction factor due to back pressure KB 1.0 for atmospheric discharge systems

9. KV Flow correction factor due to viscosity KV 0.9 to 1.0 for most HVAC applications with water

10. KN Capacity correction factor for dry saturated steam at set pressures above 1500 psia and up to 3200 psiaKN 1.0 for most HVAC applications

11. KSH Capacity correction factor due to the degree of superheat KSH 1.0 for saturated steam

12. Z Compressibility factor Z 1.0 if value is unknown

13. P Relieving pressure (psia) P Set pressure (psig) over pressure (10% psig) atmospheric pressure

(14.7 psia)14. $P Differential pressure (psig)

$P Set pressure (psig) over pressure (10% psig) back pressure (psig)15. T Absolute temperature (R F 460)16. M Molecular weight of the gas or vapor

G. Relief Valve Sizing Notes

1. When multiple relief valves are used, one valve shall be set at or below the maximum allowable working pressure, and the remaining valves may be set up to 5 percent over the maximum allowable working pressure.

2. When sizing multiple relief valves, the total area required is calculated on an over pres-sure of 16 percent or 4 psi, whichever is greater.

3. For superheated steam, the following correction factor values may be used:a. Superheat up to 400F: 0.97 (range 0.9790.998)b. Superheat up to 450F: 0.95 (range 0.9570.977)c. Superheat up to 500F: 0.93 (range 0.9300.968)d. Superheat up to 550F: 0.90 (range 0.9050.974)e. Superheat up to 600F: 0.88 (range 0.8820.993)f. Superheat up to 650F: 0.86 (range 0.8610.988)g. Superheat up to 700F: 0.84 (range 0.8410.963)h. Superheat up to 750F: 0.82 (range 0.8230.903)i. Superheat up to 800F: 0.80 (range 0.8050.863)j. Superheat up to 850F: 0.78 (range 0.7860.836)

k. Superheat up to 900F: 0.75 (range 0.7530.813)l. Superheat up to 950F: 0.72 (range 0.7260.792)

m. Superheat up to 1000F: 0.70 (range 0.7040.774)4. Gas and vapor properties:

38 PART 3

Gas or VaporMolecular

WeightRatio of Specific

HeatsCoefficient

CSpecificGravity

AcetyleneAirAmmonia (R-717)ArgonBenzene

26.0428.9717.0339.9478.11

1.251.401.301.661.12

342356347377329

0.8991.0000.5881.3792.696

N-ButaneIso-ButaneCarbon DioxideCarbon DisulphideCarbon Monoxide

58.1258.1244.0176.1328.01

1.181.191.291.211.40

335336346338356

2.0062.0061.5192.6280.967

ChlorineCyclohexaneEthaneEthyl AlcoholEthyl Chloride

70.9084.1630.0746.0764.52

1.351.081.191.131.19

352325336330336

2.4472.9051.0381.5902.227

EthyleneHeliumN-HeptaneHexaneHydrochloric Acid

28.034.02

100.2086.1736.47

1.241.661.051.061.41

341377321322357

0.9680.1393.4592.9741.259

HydrogenHydrogen ChlorideHydrogen SulphideMethaneMethyl Alcohol

2.0236.4734.0816.0432.04

1.411.411.321.311.20

357357349348337

0.0701.2591.1760.5541.106

Methyl ButaneMethyl ChlorideNatural GasNitric OxideNitrogen

72.1550.4919.0030.0028.02

1.081.201.271.401.40

325337344356356

2.4911.7430.6561.0360.967

Nitrous OxideN-OctaneOxygenN-PentaneIso-Pentane

44.02114.2232.0072.1572.15

1.311.051.401.081.08

348321356325325

1.5203.9431.1052.4912.491

PropaneR-11R-12R-22R-114

44.09137.37120.9286.48

170.93

1.131.141.141.181.09

330331331335326

1.5224.7424.1742.9855.900

R-123R-134aSulfur DioxideToluene

152.93102.0364.0492.13

1.101.201.271.09

327337344326

5.2793.5222.2113.180

GAS AND VAPOR PROPERTIES

3.34 Motor Drive Formulas

DFP r RPMFP = DMP r RPMMPBL [(DFP DMP) r 1.5708] (2 r L)

DFP Fan Pulley DiameterDMP Motor Pulley DiameterRPMFP Fan Pulley RPMRPMMP Motor Pulley RPMBL Belt LengthL Center to Center Distance of Fan and Motor Pulleys

Equations 39

3.35 Domestic Water Heater Sizing

H GPH LBS GAL TOUTPUT r r r8 34 1 0. . / . .$

HGPH LBS GAL T

%EFFICIENCYINPUT r r8 34. . / . $

GPHH EFFICIENCY

T LBS GAL

KWINPUTr

r

%

$ 8 34. . / .rrr

3413

8 34

BTU KW

T LBS GAL

/

. . / .$

$TH EFFICIENCY

GPH LBS GAL

KWINPUTrr

r%

. . / .8 34

33413

8 34

BTU KW

GPH LBS GAL

/

. . / .r

KWGPH LBS GAL T

BTU KW r r r8 34 1 0

3413

. . / . .

/

$

%COLDWATERT T

T THOT MIX

HOT COLD

%HOT WATERT T

T TMIX COLD

HOT COLD

HOUTPUT Heating Capacity OutputHINPUT Heating Capacity InputGPH Recovery Rate Gallons per Hour$T Temperature Rise FkW KilowattsTCOLD Temperature Cold Water FTHOT Temperature Hot Water FTMIX Temperature Mixed Water F

3.36 Domestic Hot Water Recirculation Pump/Supply Sizing

A. Determine the approximate total length of all hot water supply and return piping.

B. Multiply this total length by 30 Btu/ft. for insulated pipe and 60 Btu/ft. for uninsu-lated pipe to obtain the approximate heat loss.

C. Divide the total heat loss by 10,000 to obtain the total pump capacity in GPM.

D. Select a circulating pump to provide the total required GPM and obtain the headcreated at this flow.

E. Multiply the head by 100 and divide by the total length of the longest run of the hotwater return piping to determine the allowable friction loss per 100 feet of pipe.

F. Determine the required GPM in each circulating loop and size the hot water returnpipe based on this GPM and the allowable friction loss as determined earlier.

3.37 Swimming Pools

A. Sizing Outdoor Pool Heater

1. Determine pool capacity in gallons obtain from Architect if available. Length r Width r Depth r 7.5 gal./cu.ft. (If depth is not known, assume an average

depth of 5.5 feet.)

40 PART 3

2. Determine heat pick-up time in hours from Owner. 3. Determine pool water temperature in degrees F from the Owner. If Owner does not

specify temperature, assume 80F. 4. Determine the average air temperature on the coldest month in which the pool will

be used. 5. Determine the average wind velocity in miles per hour. For pools less than 900 square

feet and where the pool is sheltered by nearby buildings, fences, shrubs, etc. from the prevailing wind, an average wind velocity of less than 3.5 mph may be assumed. The surface heat loss factor of 5.5 Btuh/sq.ft. F in the following equation assumes a wind velocity of 3.5 mph. If a wind velocity of less than 3.5 mph is used, multiply the equa-tion by 0.75; for 5.0 mph, multiply the equation by 1.25; and for 10 mph, multiply the equation by 2.0.

6. Pool heater equations:

H H HPOOLHEATER HEAT UP SURFACE LOSS

HGAL LBS GAL T BT

HEAT UPWATER

r r r. . . / . .8 34 1 0$ UU LBS F

HEAT PICK UP TIME

/ .

H BTU HR SQ. FT. F TSURFACE LOSS WATER/ A r5 5. / $ IIR POOL AREAr

$T T TWATER FINAL INITIAL

T POOL WATERTEMPERATUREFINAL

T FINITIAL 50

$T T TWATER / AIR FINAL AVERAGE AIR

H Heating capacity (Btu/hr.) $T Temperature difference (F)

Front MatterTable of ContentsPart I. IntroductionPart II. DefinitionsPart III. Equations3.01 Airside System Equations and Derivations3.02 Waterside System Equations and Derivations3.03 Air Change Rate Equations3.04 English/Metric Airside System Equations Comparison3.05 English/Metric Waterside System Equation Comparison3.06 English/Metric Air Change Rate Equation Comparison3.07 English/Metric Temperature and other Conversions3.08 Steam and Condensate Equations3.09 Building Envelope Heating Equation and R-Values/U-Values3.10 Fan Laws3.11 Pump Laws3.12 Pump Net Positive Suction Head (NPSH) Calculations3.13 Mixed Air Temperature3.14 Psychrometric Equations3.15 Ductwork Equations3.16 Equations for Flat Oval Ductwork3.17 Steel Pipe Equations3.18 Steam and Steam Condensate Pipe Sizing Equations3.19 Air Conditioning Condensate3.20 Humidification3.21 Humidifier Sensible Heat Gain3.22 Expansion Tanks3.23 Air Balance Equations3.24 Efficiencies3.25 Cooling Towers and Heat Exchangers3.26 Cooling Tower/Evaporative Cooler Blowdown Equations3.27 Electricity3.28 Moisture Condensation on Glass3.29 Calculating Heating Loads for Loading Docks, Heavily Used Vestibules and Similar Spaces3.30 Ventilation of Mechanical Rooms with Refrigeration Equipment3.31 Pipe Expansion Equations3.32 Relief Valve Vent Line Maximum Length3.33 Relief Valve Sizing3.34 Motor Drive Formulas3.35 Domestic Water Heater Sizing3.36 Domestic Hot Water Recirculation Pump/Supply Sizing3.37 Swimming PoolsPart IV. Conversion FactorsPart V. Cooling Load Rules of ThumbPart VI. Heating Load Rules of ThumbPart VII. Infiltration Rules of ThumbPart VIII. Ventilation Rules of ThumbPart IX. Humidification Rules of ThumbPart X. People/Occupancy Rules of ThumbPart XI. Lighting Rules of ThumbPart XII. Appliance/Equipment Rules of ThumbPart XIII. Cooling Load FactorsPart XIV. Heating Load FactorsPart XV. Design Conditions and Energy ConservationPart XVI. HVAC System Selection CriteriaPart XVII. Air Distribution SystemsPart XVIII. Piping Systems, GeneralPart XIX. Hydronic (Water) Piping SystemsPart XX. Glycol Piping SystemsPart XXI. Steam Piping SystemsPart XXII. Steam Condensate Piping SystemsPart XXIII. AC Condensate PipingPart XXIV. Refrigerant Piping SystemsPart XXV. Air Handling UnitsPart XXVI. FansPart XXVII. PumpsPart XXVIII. ChillersPart XXIX. Cooling Towers and CondensersPart XXX. Heat ExchangersPart XXXI. BoilersPart XXXII. Motors and Motor ControllersPart XXXIII. HumidifiersPart XXXIV. FiltersPart XXXV. InsulationPart XXXVI. Fire-Stopping and Through-Penetration SystemsPart XXXVII. Makeup WaterPart XXXVIII. Water Treatment and Chemical Feed SystemsPart XXXIX. Automatic Controls Building Automation SystemsPart XL. Equipment SchedulesPart XLI. Equipment ManufacturersPart XLII. Building Construction Business FundamentalsPart XLIII. Architectural, Structural, and Electrical InformationPart XLIV. Properties of AirPart XLV. Properties of WaterPart XLVI. Cleanroom CriteriaPart XLVII. Wind Chill and Heat IndexPart XLVIII. MiscellaneousPart XLIX. General NotesPart L. Designer's ChecklistPart LI. Professional Societies and Trade OrganizationsPart LII. References and Design Manuals