## AIR AND WATER SYSTEMS HEAT TRANSFER EQUATIONS BASICS

AIR SYSTEMS - SENSIBLE HEAT TRANSFER EQUATION
Btuh = cfm × 1.08 × TD

Where:

Btuh = Btu per hour (sensible heat) also written Btuhs
cfm = volume of airflow, cubic feet per minute
1.08 = constant:
60 min/hr × 0.075 lb/cf (density of air) × 0.24 Btu/lb°F (specific heat of air)
TD = dry bulb temperature difference of the air entering and leaving a coil EAT – LAT or LAT – EAT (Entering Air Temperature and Leaving Air Temperature).

TD (temperature difference) is often written as delta T or ΔT. In applications where cfm to the conditioned space needs to be calculated, the TD is the difference between the supply air temperature dry bulb and the room temperature dry bulb.

To find volume: cfm = Btuh ÷ (1.08 × TD)
To find temperature difference: TD = Btuh ÷ (1.08 × cfm)

AIR SYSTEMS - TOTAL HEAT TRANSFER EQUATION
Btuh = cfm × 4.5 × Δh

Where:
Btuh = Btu per hour (total heat) also written Btuht
cfm = volume of airflow, cubic feet per minute
4.5 = constant: 60 min/hr × 0.075 lb/cf
Δh = Btu/lb change in total heat content (enthalpy) of the air

The total heat content of the air is determined from a wet bulb and dry bulb temperature, and a psychrometric chart. For example, the air temperature leaving a typical commercial cooling coil might be 55°Fdb and 54°Fwb.

Plotting these temperatures on a psychrometric chart gives an enthalpy (total heat content) of the air at 22.627 Btu/lb.

To find volume: cfm = Btuh ÷ (4.5 × Δh)
To find enthalpy difference: Δh = Btuh ÷ (4.5 × cfm)

WATER SYSTEMS-HEAT TRANSFER EQUATION
Btuh = gpm × 500 × TD

Where:
Btuh = Btu per hour
gpm = volume of water flow, gallons per minute
500 = constant:
60 min/hr × 8.33 lb/gal (weight of water) × 1 Btu/lb°F (specific heat of water).
TD = temperature difference of the water entering and leaving a coil EWT – LWT or LWT – EWT (Entering Water Temperature and Leaving Water Temperature).

TD can also be expressed as ΔT.

To find volume: gpm = Btuh ÷ (500 × TD)
To find temperature difference: TD = Btuh ÷ (500 × gpm)

WATER SYSTEMS — PRESSURES AND BOILING TEMPERATURES
The boiling point or boiling temperature of water can be changed by changing the pressure on the water. In the case of water in a heating system if the pressure is to be changed, the water must be in a boiler and then the water can be boiled at a temperature of 212°F or 250°F or any other temperature.

The only requirement is that the pressure in the boiler is changed to the one corresponding to the desired boiling point. If the pressure is 14.7 psia the boiling temperature is 212°F. A common low pressure HVAC steam heating system, for instance, operates at 15 pounds per square inch gage pressure (psig), which is an absolute pressure of 30 psia and a temperature of 250°F.

Sea Level Barometric Pressure is 14.7 pounds per square inch absolute (psia)
Sea Level Barometric Pressure is 0 pounds per square inch gage (psig) psia = psig + 14.7 pounds per square inch absolute = pounds per square inch gage + 14.7

As a hint for calculations psia can stand for “psi add 14.7” to gage pressure.

Sea Level Barometric Pressure is 29.92 inches of mercury (“Hg)

Sometimes sea level barometric pressure, for estimation purposes only, is rounded off to 15 psia and 30 inches of mercury.

1 psi equals 2.04” Hg (sometimes, for estimation purposes only, rounded to
1 psi = 2” Hg)
1” Hg equals 0.49 psi (sometimes, for estimation purposes only, rounded to
1” Hg = 0.5 psi)