فرمولهای مهم

Equations 

 01-Cooling and Heating Equations

HS =1.08 ×CFM ×∆T
HS =1.1 ×CFM ×∆T
HL =0.68 ×CFM ×∆WGR.
HL =4840 ×CFM ×∆WLB.
HT =4.5 ×CFM ×∆h
HT =HS +HL
H =U ×A ×∆T
SHR = HS/HT=HS/(HS+HL)
LB. STM/HR = (BTU/HR )/HFG

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/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/Hr. Sq. Ft. °F.)

A = Area (Sq. Ft.) SHR = Sensible Heat Ratio
HFG = Latent Heat of Vaporization at Design Pressure (1989 ASHRAE Fundamentals) 

  02 R-Values/U-Values R = 1/C= (1/K)×Thickness
U=1/ΣR  
R = R-Value (Hr. Sq. Ft. °F./Btu.) 

U = U-Value (Btu./Hr. Sq. Ft. °F.) 

C = Conductance (Btu./Hr. Sq. Ft. °F.) 

K = Conductivity (Btu. In./Hr. Sq. Ft. °F.) 

ΣR = Sum of the Individual R-Values

03 Water System Equations

H =500 ×GPM ×∆T
GPMEVAP. =(TONS ×24)/∆T

GPMCOND. =(TONS ×30)/∆T   

H = Total Heat (Btu/Hr.) 

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)

04 Air Change Rate Equations
 
AC/HR=(CFM ×60)/VOLUME
CFM=((AC/HR )xVOLUME)/60

 AC/HR. = Air Change Rate per Hour 

CFM = Air Flow Rate (Cubic Feet per Minute) 

VOLUME = Space Volume (Cubic Feet)

05 Mixed Air Temperature

TMA =(TROOM ×(CFMRA/CFMOA))+(TOA ×(CFMOA /CFMSA ))

TMA =(TRA ×(CFM RA /CFMSA))+(TOAx(CFMOA /CFMSA ))

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)

06 Ductwork Equations

TP =SP +VP V 2(V)2

VP =(V^2/4005^2)

V = Q/A=(Qx144/WxH)

DEQ=(1.3 × (A × B)^0.625)/((A + B)^0.25)

TP = Total Pressure 

SP = Static Pressure, Friction Losses 

VP = Velocity Pressure, Dynamic Losses 

V = Velocity, Ft./Min. 

Q = Flow through Duct (CFM) 

A = Area of Duct (Sq. Ft.) 

W = Width of Duct (Inches) 

H = Height of Duct (Inches) 

DEQ = Equivalent Round Duct Size for Rectangular Duct (Inches) 

A = One Dimension of Rectangular Duct (Inches) 

B = Adjacent Side of Rectangular Duct (Inches)

07 Fan Laws

CFM2/CFM1 =RPM2/RPM1

SP2/SP1=(CFM2/CFM1)^2=(RPM2/RPM1)^2

  BHP2/BHP1=(CFM2/CFM!)^3=(RPM2/RPM1)^3=(SP2/SP1)^1.5

BHP = (CFM× SP × SP.GR.)/(6356 × FANEFF.)

MHP =BHP/(M/DEFF.)

CFM = Cubic Feet/Minute

RPM = Revolutions/Minute SP = In. W.G.

BHP = Break Horsepower

Fan Size = Constant Air Density = Constant

SP.GR. (Air) = 1.0

FANEFF. = 65–85% 

M/DEFF. = 80–95% 

M/D = Motor/Drive

08 Pump Laws

GPM2/GPM1=RPM2/RPM1

HD2/HD1=(GPM2/GPM1)^2=(RPM2/  RPM1)^2

BHP2/BHP1=(GPM2/GPM1)^3=(HD2/HD1)^1.5

BHP=( GPMx HD ×SP.GR.)/(3960 ×PUMPEFF.)

MHP =BHP/(M/DEFF.)

VH =V2/2g

HD =(P ×2.31)/SP.GR.

GPM = Gallons/Minute

RPM = Revolutions/Minute 

HD = Ft. H2O 

BHP = Break Horsepower 

Pump Size = Constant 

Water Density = Constant 

SP.GR. = Specific Gravity of Liquid with Respect to Water

SP.GR. (Water) = 1.0 

PUMPEFF. = 60–80% 

M/DEFF. = 85–95% 

M/D = Motor/Drive

P = Pressure in Psi 

VH = Velocity Head in Ft.

V = Velocity in Ft./Sec. g = Acceleration due to Gravity (32.16 Ft./Sec2)

09 Pump Net Positive Suction Head (NPSH) Calculations


NPSHavail >NPSHreq'd
NPSHavail =HA (+,-) HS(+,-)HF(+,-)HVP

NPSHavail = Net Positive Suction Available at Pump (Feet)
NPSHreq’d = 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—1989 ASHRAE Fundamentals)

10 Air Conditioning Condensate

GPMAC COND =(CFM ×∆WLB.)/SpV ×8.33
GPMAC COND =(CFM ×∆WGR.)/SpV ×8.33  ×7000
HD=(Px2.31)/SP.GR.

GPMAC COND = Air Conditioning Condensate Flow (Gallons/Minute)
CFM = Air Flow Rate (Cu.Ft./Minute)
SpV = Specific Volume of Air (Cu.Ft./Lb.DA)
∆WLB. = Specific Humidity (Lb.H2O/Lb.DA)
∆WGR. = Specific Humidity (Gr.H2O/Lb.DA)

11 Humidification

GRAINSREQ’D=(WGR./SpV )room air -(WGR./SpV )supply air
POUNDSREQ’D =(WLB./SpV )room air -(WLB./SpV )supply air
LB. STM/HR =(CFM × GRAINSREQ’D × 60)/7000= CFM × POUNDSREQ’D × 60

GRAINSREQ’D = Grains of Moisture Required (Gr.H2O/Cu.Ft.)
POUNDSREQ’D = Pounds of Moisture Required (Lb.H2O/Cu.Ft.)
CFM = Air Flow Rate (Cu.Ft./Minute) SpV = Specific Volume of Air (Cu.Ft./Lb.DA)
WGR. = Specific Humidity (Gr.H2O/Lb.DA) WLB. = Specific Humidity (Lb.H2O/Lb.DA)


12 Humidifier Sensible Heat Gain

HS = (0.244 × Q ×∆T) + (L × 380)

HS = Sensible Heat Gain (Btu/Hr.)
Q = Steam Flow (Lb.Steam/Hr.)
∆T = Steam Temperature − Supply Air Temperature (F.)
L = Length of Humidifier Manifold (Ft.)


13 Expansion Tanks


CLOSED VT =VS ×[ [(ν2/ν1)− 1]− 3α∆T]/[PA /P1-PA/P2]
OPEN  VT=2×{(VS ×[(ν2/ν1)-1])− 3α∆T}
DIAPHRAGM VT = VS ×{[(ν2/ν1)-1]-3α∆T}/[1-( P1/P2)

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 = 45–50°F 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 = 95°F 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./Lb.H2O) 1989 ASHRAE Fundamentals, Chapter 2,
Table 25 or Part 27, Properties of Air and Water
V2 = SpV of H2O at T2 (Cu. Ft./Lb.H2O) 1989 ASHRAE Fundamentals, Chapter 2, Table 26 or Part 27, Properties of Air and Water
α= Linear Coefficient of Expansion αSTEEL = 6.5 × 10−6 αCOPPER = 9.5 × 10−6
System Volume Estimate: 12 Gal./Ton 35 Gal./BHP
System Fill Pressure/Minimum System Pressure Estimate: Height of System +5 to 10 Psi OR 5–10 Psi, whichever is greater.
System Operating Pressure/Maximum Operating Pressure Estimate: 150 Lb. Systems 45–125 Psi 250 Lb. Systems 125–225 Psi


14 Air Balance Equations

SA = Supply Air
RA = Return Air
OA = Outside Air
EA = Exhaust Air
RFA = Relief Air
SA = RA + OA = RA + EA + RFA

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

15 Efficiencies

COP =BTU OUTPUT/BTU INPUT =EER/3.413
 EER =BTU OUTPUT /WATTS INPUT
 Turndown Ratio = Maximum Firing Rate: Minimum Firing Rate (i.e., 5:1, 10:1, 25:1)
OVERALL THERMAL EFF. =(GROSS BTU OUTPUT/GROSS BTU INPUT) × 100%
COMBUSTION EFF. =[(BTU INPUT − BTU STACK LOSS )/BTU INPUT] ×100%

Overall Thermal Efficiency Range 75%–90%
Combustion Efficiency Range 85%–95%

16 Cooling Towers and Heat Exchangers


APPROACHCT’S = LWT − AWB
APPROACHHE’S = EWTHS − LWTCS
RANGE = EWT − LWT

EWT = Entering Water Temperature (°F)
 LWT = Leaving Water Temperature (°F)
AWB = Ambient Wet Bulb Temperature (Design WB, °F)
HS = Hot Side
CS = Cold Side

17 Moisture Condensation on Glass

TGLASS = TROOM − [(RIA /RGLASS)× (TROOM − TOA)]
TGLASS = TROOM − [(UGLASS/UIA× (TROOM − TOA)]

 If TGLASS < DPROOM Condensation Occurs
T = Temperature (°F.)
R = R-Value (Hr. Sq.Ft. °F./Btu.)
U = U-Value (Btu./Hr. Sq.Ft. °F.)
IA = Inside Airfilm
OA = Design Outside Air Temperature
DP = Dew Point

18 Electricity

KVA = KW + KVAR

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 (0.75–0.95)
BHP = Break Horsepower
MHP = Motor Horsepower
EFF = Efficiency
M/D = Motor Drive

A. Single Phase Power:


KW1φ=(V × A × PF)/1000
KVA1φ= V × A/1000
BHP1φ=(V × A × PF × DEVICEEFF.)/746
MHP1φ= (BHP1φ)/M/DEFF.

B. 3-Phase Power:


KW3φ=V3× V × A × PF /1000
KVA3φ=V3× V × A/1000          V3=رادیکال3
BHP3φ= V3× V × A × PF × DEVICEEFF. /746        V3=رادیکال3
MHP3φ=BHP3φ/M/DEFF.



19 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 temperatures—assume inside space temperature has dropped to the outside design temperature because doors have been open for an extended period of time.
E. Use sensible heat equation to determine heating requirement using CFM and inside and outside design temperatures determined above.


20 Ventilation of Mechanical Rooms with Refrigeration Equipment


A. For a more detailed description of ventilation requirements for mechanical rooms with refrigeration equipment see ASHRAE Standard 15 and Part 9, Ventilation Rules of Thumb.
B. Completely Enclosed Equipment Rooms:
CFM =100 ×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 =G0.5
FA = Ventilation Free Opening Area (Sq.Ft.) G = Mass of Refrigerant of Largest System (Pounds)





21 Steam and Condensate Equations


A. General:


LBS. STM./HR. =(BTU/HR.)/960
LB. STM. COND./HR. =EDR/4
EDR = BTU/HR./240
LB. STM. COND./HR. =(GPM ×500 ×SP.GR. ×CP ×∆T)/L
 LB. STM. COND./HR. =(CFM ×60 ×D ×CP ×∆T)/L

B. Approximating Condensate Loads:


LB. STM. COND./HR. =(GPM(WATER) ×∆T)/2
LB. STM. COND./HR. =(GPM(FUEL OIL) ×∆T)/4
LB. STM. COND./HR. =[CFM(AIR) ×∆T]/900

STM. = Steam
GPM = Quantity of Liquid (Gallons per Minute)
CFM = Quantity of Gas or Air (Cubic Feet per Minute)
SP.GR. = Specific Gravity
 D = Density (Lbs./Cubic Feet)
CP = Specific Heat of Gas or Liquid (Btu/Lb)
Air CP =0.24 Btu/Lb
Water CP =1.00 Btu/Lb
L = Latent Heat of Steam (Btu/Lb. at Steam Design Pressure)
 ∆T = Final Temperature minus Initial Temperature
 EDR = Equivalent Direct Radiation


22 Swimming Pools

A. Sizing Outdoor Pool Heater:


Determine pool capacity in gallons. Obtain from Architect if available. Length ×Width ×Depth ×7.5 Gal/Cu.Ft. (If depth is not known assume an average depth 5.5 Feet)


Determine heat pick-up time in hours from Owner.


Determine pool water temperature in degrees F. from the Owner. If Owner does not specify assume 80°F.


Determine the average air temperature on the coldest month in which the pool will be used.


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 Btu/Hr/Sq.Ft.°F. in the equation below assumes a wind velocity of 3.5 mph. If a wind velocity of less than 3.5 mph is used, multiply equation by 0.75; for 5.0 mph multiply equation by 1.25; and for 10 mph multiply equation by 2.0.


Pool Heater Equations:




HPOOL HEATER =HHEAT-UP +HSURFACE LOSS
HHEAT-UP =[GALS. ×8.34 LBS./GAL. ×∆TWATER ×1.0 BTU/LB.°F.]/HEAT PICK-UP TIME
HSURFACE LOSS =5.5 BTU/HR. SQ. FT. °F. ×∆TWATER/AIR ×POOL AREA
∆TWATER =TFINAL −TINITIAL
TFINAL =POOL WATER TEMPERATURE
TINITIAL =50 °F
∆TWATER/AIR =TFINAL −TAVERAGE AIR

H = Heating Capacity (Btu/Hr.)
∆T = Temperature Difference (°F.)

23 Domestic Water Heater Sizing


HOUTPUT =GPH ×8.34 LBS./GAL. ×∆T ×1.0
HINPUT =[GPH ×8.34 LBS./GAL. ×∆T]/% EFFICIENCY
GPH =HINPUT ×% EFFICIENCY/∆T ×8.34 LBS./GAL.= KW ×3413 BTU/KW/∆T ×8.34 LBS./GAL.
∆T = HINPUT ×% EFFICIENCY /GPH ×8.34 LBS./GAL.=(KW ×3413 BTU/KW)/ GPH ×8.34LBS./GAL.
KW = GPH ×8.34 LBS./GAL. ×∆T ×1.0/3413 BTU/KW
% COLD WATER =(THOT −TMIX)/(THOT −TCOLD )
% HOT WATER =(TMIX −TCOLD)/(THOT −TCOLD )


HOUTPUT = Heating Capacity, Output
 HINPUT = Heating Capacity, Input
GPH = Recovery Rate (Gallons per Hour)
∆T = Temperature Rise (°F.)
KW = Kilowatts
TCOLD = Temperature, Cold Water (°F.)
THOT = Temperature, Hot Water (°F.)
 TMIX = Temperature, Mixed Water (°F.)





24 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 uninsulated 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 head created at this flow.
E. Multiply the head by 100 and divide by the total length of the longest run of the hot water 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 return pipe based on this GPM and the allowable friction loss as determined above.