Fluid Mechanics, HVAC & Refrigeration · The three air rules
Three constants, three questions
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Three constants, three questions

Every load an airstream carries is one of three things, and the trade has a one-line rule for each. American HVAC knows them as 1.08, 0.68 and 4.5. Those numbers are not physics — they are cfm, °F and BTU bookkeeping wearing a disguise. Underneath sit the density and specific heat of air, and in SI they hand you three cleaner siblings.

Sensible heat is the part you can feel on a thermometer. Q˙s=ρacaV˙ΔT\dot{Q}_s = \rho_a c_a \dot{V} \Delta T — read aloud Q-sensible equals rho-a c-a V-dot delta-T. Q˙s\dot{Q}_s is the sensible heat rate in watts; V˙\dot{V} — said V-dot, the dot meaning “per second” — is the airflow in litres per second; ΔT\Delta T is the dry-bulb temperature change in kelvins; and ρaca\rho_a c_a is standard air's density times its specific heat, 1.2014×1004.8=1207 J/(m3K)1.2014 \times 1004.8 = 1207\ \mathrm{J/(m^3 \cdot K)}. Feed it litres per second and it becomes 1.207 watts per kelvin. That is the only number to carry.

Latent heat is the part the thermometer never sees: the energy spent turning water vapour back into water. Q˙l=ρahfgV˙ΔW\dot{Q}_l = \rho_a h_{fg} \dot{V} \Delta W, where ΔW\Delta W is the change in humidity ratio — grams of water per kilogram of DRY air — and hfgh_{fg} is the latent heat of vaporisation. Multiplied out: 2.96 watts per litre per second per gram per kilogram. The subscript convention matters here and never changes: everything moist-air is quoted per kilogram of dry air, because the dry air is the only part that does not condense out on you.

Total heat is both at once, and it is the honest one: Q˙t=ρaV˙Δh\dot{Q}_t = \rho_a \dot{V} \Delta h, where Δh\Delta h is the change in enthalpy in kJ per kilogram of dry air, read straight off a psychrometric chart. With airflow in litres per second that is 1.201 watts per kJ/kg. Sensible plus latent equals total, always — and if your three numbers do not add up, one of the three is wrong, which is a check worth running every single time.