HVAC FORMULAS

Dewpoint and Wetbulb Temperature

The following equations are used to calculate the wetbulb temperature of air given the drybulb temperature and relative humidity %. The equation assumes that the ambient barometric pressure is constant at a value of 29.15 "Hg since the change in wetbulb temperature is very insignificant with changes in the ambient barometric pressure.

Input Variables		System Variables		Output Variables
RH	Relative Humidity %	e	Ambient vapor pressure in kPa	Td	Dewpoint temperature in degrees C
T	Drybulb temperature in degrees C	GAMMA	Constant based upon ambient barometric pressure	Tw	Wetbulb temperature
		DELTA	Constant
Equations
e	(RH / 100) * 0.611*EXP(17.27*T/(T+237.3))
Td	[116.9 + 237.3 ln(e)] / [16.78 – ln(e)]
GAMMA	0.00066*P (Use P = 98.642 kPa. This is equal to 29.15 "Hg… about the pressure we normally experience.)
DELTA	4098*(e / Td + 237.3)^2
Wetbulb Temperature in Degrees F Equals:
Tw	1.8 * [[(GAMMA*T) + (DELTA*Td)] / (GAMMA + DELTA)] + 32
Dewpoint Temperature in Degrees F Equals:
Td	1.8 * [[116.9 + 237.3 ln(e)] / [16.78 – ln(e)]] + 32

Air Handling Unit Tonnage Output

The following equation calculates the refrigeration output in Tonns of a coil.

Input Variables		Output Variables
T1	Entering air temperature of the coil in degrees F	TONNS	Dewpoint temperature in degrees F
T2	Leaving air temperature of the coil in degrees F
CFM	Volume of air passing through the coil
Equation
TONNS	1.08*(T1 – T2)*CFM

Chiller Tonnage Output

The following equation calculates the refrigeration output in Tonns of a chiller.

Input Variables		Output Variables
T1	Chilled water return temperature in degrees F	TONNS	Energy output of the chiller
T2	Chilled water supply temperature in degrees F
GPM	Volume of water passing through the chiller
Equation
TONNS	GPM*(T1 – T2) / 24

Chiller Coefficient of Performance

The following equation calculates the ratio of energy used to the energy output of a chiller.

Input Variables
T1	Chilled water return temperature in degrees F
T2	Chilled water supply temperature in degrees F
GPM	Volume of water passing through the chiller
KW	Kilowatts

Output Variables
COP	Energy output of the chiller

Equation
COP	(T1 – T2) * GPM * 0.0417 / (0.28433 * KW)

VAV Box Air Flow Rate (CFM)

Input Variables
A	Duct area in sq. ft
Pv	Pressure in inches of H2O from PV3

Output Variables
V	Velocity of the air
CFM	Cubic feet of air per minute

Equation
Q	AV
0.0763 is the density of dry air at 60o F The duct diameter units are in ft.
CFM	1096(Duct Diameter/2)2(√(Pv/.0763))

Heat Index Calculation

The following equation calculates the heat index of the outside air.

Input Variables
Tf	Outside air temperature in degrees F
RH	Outside air relative humidity % (enter 50 for 50%, etc.)

Output Variables
HI	Heat index

Equation

HI

HI = -42.379 + 2.04901523T + 10.14333127R - 0.22475541TR - 6.83783x10-3T2 - 5.481717x10-2R2 + 1.22874x10-3T2R + 8.5282x10-4TR2 - 1.99x10-6T2R2 where T = ambient dry bulb temperature (°F) R = relative humidity (integer percentage). Because this equation is obtained by multiple regression analysis, the heat index value (HI) has an error of ±1.3°F. Even though temperature and relative humidity are the only two variables in the equation, all the variables on the lists above are implied.

Wind Chill Temperature Calculation

The following equation calculates the wind chill temperature of the outside air.

Input Variables
V	Outside air velocity in Miles per Hour
T	Outside air temperature in degrees F

Output Variables
WC	Wind chill temperature

Equation
WC	0.0817(3.71(V)^0.5 + 5.81 - 0.25V)(T - 91.4) + 91.4

Pressure Measurement

Velocity Pressure
Where V = Air Velocity (FPM) Pv = Velocity Pressure (in. w.g.)

Equivalent Measures of Pressure
1lb. per square inch	= 144lbs. per sq. ft. = 2.036in. Mercury at 32°F = 2.311ft. Water at 70°F = 27.74in. Water at 70°F
1 inch Water at 70°F	= .03609lb. per sq. in. = .5774oz. per sq. in. = 5774oz. per sq. in. = 5.196lbs. per sq. ft.
1 ounce per sq. in.	= 1272in. Mercury at 32°F = 1.733in. Water at 70°F
1ft. Water at 70°F	= .433lbs. per sq. in. = 62.31lbs. sq. ft.
1 Atmosphere	= 14.696lbs. per sq. in. = 2116.3lbs. per sq. ft. = 33.96ft. Water at 70°F = 29.92in. Mercury at 32°F
1in. Mercury at 32°F	= .491lbs. per sq. in. = 7.86oz. per sq. in. = 1.136ft. Water at 70°F = 13.63in. Water at 70°F

Compression Ratio
Compression Ratio	= Absolute Discharge Pressure / Absolute Suction Pressure
Absolute Discharge Pressure	= gauge reading + 15psi
Absolute Suction Pressure	= gauge reading + 15psi

Refrigerant Mass Flow Rate
Mass Flow Rate (Pounds/Minute)	= Piston Displacement X Refrigerant Density = (Cubic Feet/Minute) X (Pounds/Cubic Feet)