Air heat loads
Latent heat from a moisture content difference
- where
- latent heat (kW)
- air density (kg/m³)
- air volume flow rate (m³/s)
- moisture content of entering or room air (g/kg)
- moisture content of leaving or supply air (g/kg)
- latent heat of vaporisation of water (kJ/kg)
- latent heat (W)
Explain this equation
Works out the heat tied up in moisture added to or removed from air. Use it for the dehumidifying part of a cooling coil's duty, or the energy a humidifier must supply.
ρ V̇ is the mass flow of air. W₁ and W₂ are moisture contents in grams of water per kilogram of dry air, so their difference divided by 1000 is kilograms of water per kilogram of air. hfg is the energy needed to evaporate (or released when condensing) one kilogram of water. The bars mean the size of the difference, whichever way it goes.
Each kilogram of water condensed on a coil gives up about 2450 kJ, so latent load is simply water mass rate times that latent heat.
Sense check: 0.5 m³/s dried by 2 g/kg is about 2.9 kW of latent load and 4.3 kg/h of condensate. Double the moisture drop and both double.
Watch out: use moisture content, not relative humidity, which changes with temperature even when no water is added or removed.
Works out the latent heat removed (dehumidifying) or added (humidifying) when air changes moisture content. Use it with coil on and off conditions or with room and supply air.
Enter your values to see the result.
Good to know
Moisture content (humidity ratio) is in grams of water per kilogram of dry air; get it from a psychrometric chart or the moisture content calculator. hfg = 2454 kJ/kg is the value at about 20 °C; ASHRAE’s 3010 factor corresponds to about 2508 kJ/kg with ρ = 1.2. The third output is the condensate (or humidifier water) rate.
Common mistake
Using relative humidity difference instead of moisture content difference. Two air states can have the same RH but very different moisture contents.
Limits
Steady flow; air density treated as constant. The result is the rate of latent heat, not including any sensible cooling of the condensate.
Sources
- ASHRAE Handbook — Fundamentals (2017), chapter 18 Nonresidential cooling and heating load calculations, Table 1 heat gain from occupants (moderately active office work: 75 W sensible, 55 W latent); simplified air equations qs = 1.23 Q Δt and ql = 3010 Q ΔW (Q in L/s)
- CIBSE Guide C: Reference data (2007), chapter 1 (properties of humid air) and chapter 4 (flow of fluids in pipes and ducts)
- IAPWS-IF97 steam tables: latent heat of vaporisation of water 2453.5 kJ/kg at 20 °C
Results are calculations from the published methods and figures shown, and depend on the data you enter. Follow the equipment manufacturer’s data, CIBSE guidance, BS EN 378, the F-gas Regulations and your company procedures. Refrigerant work needs the correct F-gas certification.