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)

Plan for Sour Water

 Recycling Sour Water Stripper Bottoms for Cooling Towers, Boiler Feedwater

Oil refining is dependent on the use of the distillation process. However, in the course of this procedure, condensed water accumulates in the overheads of the extraction columns. While this water is essentially distilled, the soluble gases and soluble hydrocarbons remain entrained and are in equilibrium with ionic species in the water, depending on the pH.

In most refineries, the overheads send water to a central collection where it is stream-stripped for bulk removal of NH3 and H2S. There are other similar small-volume sources of water that are sent to the sour water stripper (SWS) as well. In medium-sized refineries, there are typically 30 sources feeding the stripper. Some of the SWS-treated water, or "Bottoms," is sent to the desalter as wash water and from there becomes wastewater. The excess of unused SWS Bottoms for desalting is transferred directly to the wastewater treatment plant (WWTP).

With appropriate treatment of the SWS Bottoms -- to the extent where NH3, H2S, short-chain light hydrocarbons, and amines are decreased to acceptable levels -- the value of the water increases and cannot be wasted on the lower-quality needs of desalter wash water. Under normal and proper operating conditions, the SWS water has no significant levels of calcium, magnesium or iron -- the primary scale-forming inorganic contaminants of concern in

After specific treatment of the SWS Bottoms for these contaminants, this water is not only considered a suitable quality for steam and cooling systems but actually becomes a superior quality similar to steam condensate. Further, this captured SWS-treated water produces substantial fuel value in the form of heat. Similar to steam condensate, this water can bypass normal boiler feedwater pretreatment systems such as ion exchange or reverse osmosis (RO) and can proceed directly to the boiler deaerator.

Occasionally, SWS units are not operated or maintained correctly. A system with a significant presence of the three aforementioned inorganic cations would be overlooked as a candidate for water reuse. Most commonly, these cations enter the SWS system either by cooling water intrusion from piping and condenser leaks or by using an unsuitable water injection source in the distillation column overheads for the forcing of the dewpoint to initiate condensation.

These two conditions ultimately cause major problems in the SWS units themselves, such as the deterioration of the SWS trays, which will cause serious SWS performance problems and will require repairs. These problems almost always are short term with respect to the presence of these inorganic cations in the Bottoms, as the SWS cannot operate very long under these conditions.

In addition to boiler feedwater supply, the same considerations regarding scale formation exist as the criteria for the justification of SWS water reuse as cooling tower supply water; this also has an attractive return on investment. The validation for this cooling tower make-up can be found in the increased cycles of concentration, which would be tolerable in the cooling towers with the treated SWS water. This translates to substantial reductions in the volume of supply water used, wastewater generated and cost of chemical treatment in cooling tower operations.

The economic basis for the justification of water reuse investment at the SWS is substantially more attractive for boiler feedwater than it is for cooling tower make-up water. The return on investment for SWS Bottoms reuse as boiler feedwater is based on the reduction in the cost of treating wastewater; the decrease in the cost of supply water pretreatment; and the capture of SWS heat, which reduces deaerator heating fuel costs.

Interestingly, for those plants required to meet selenium NPDES permit limits, the routing of the SWS Bottoms to the boilers inherently extracts more than 80 to 90 percent of the total selenium load to the wastewater treatment plant, thus eliminating any selenium removal needs in the facility in almost all cases.