Psychrometrics & HVAC — Cheat Sheet
Moist-air relations, coil loads, duct and ventilation sizing, refrigeration metrics.
Moist air basics
| Humidity ratio | W = 0.622 p_w / (p − p_w) [kg/kg dry air] |
| Relative humidity | φ = p_w / p_ws |
| Enthalpy | h = 1.006t + W(2501 + 1.86t) [kJ/kg dry air] |
| Specific volume | v = 0.287(t+273.15)(1+1.608W) / p [m³/kg dry air] |
| Key point | h and v are per kg of DRY air, not per kg of mixture |
The three temperatures
| Dry bulb | What a thermometer reads |
| Dew point | Cool at constant W until saturated — predicts condensation |
| Wet bulb | Evaporatively cooled; sits between the other two |
| At 100% RH | All three are equal |
| Heating air | W and dew point unchanged; RH falls (why winter feels dry) |
Coil loads
| Sensible | Q_s = ṁ_da · c_p · Δt |
| Latent | Q_l = ṁ_da · ΔW · h_fg |
| Total | Q_t = ṁ_da · Δh |
| Sensible heat ratio | SHR = Q_s / Q_t; comfort cooling 0.65–0.80 |
| Shortcut (SI, std air) | Q_s(kW) ≈ 1.23 × L/s × Δt |
Duct sizing
| Equal friction | Size everything to one Pa/m; 0.8–1.0 Pa/m typical |
| Velocity pressure | p_v = ½ρv² (60 Pa at 10 m/s) |
| Equivalent round | D_e = 1.30(ab)^0.625 / (a+b)^0.25 |
| Velocity limits | branch < 5 m/s, main 8–10 m/s — noise governs |
| Aspect ratio | Keep under 4:1 |
Ventilation (ASHRAE 62.1)
| Breathing zone | V_bz = R_p·P_z + R_a·A_z |
| Zone outdoor air | V_oz = V_bz / E_z |
| Office | R_p = 2.5 L/s·person, R_a = 0.3 L/s·m² |
| CO₂ rise | ≈650 ppm at 8 L/s per person |
| Note | E_z < 1 raises what you SUPPLY, not what arrives |
Refrigeration
| COP | cooling capacity / power input |
| EER | EER = 3.412 × COP |
| kW per ton | kW/ton = 12 / EER = 3.517 / COP |
| 1 ton | 12 000 BTU/h = 3.517 kW |
| Carnot limit | COP_max = T_e / (T_c − T_e) [kelvin] |
| Heat rejected | capacity + compressor power |
Building envelope
| Assembly R | R = Σ(t/k) + R_si + R_se |
| Surface films (ISO 6946) | R_si = 0.13, R_se = 0.04 m²·K/W |
| U-value | U = 1/R (lower is better) |
| Unit trap | R(imperial) = 5.678 × R(SI) |
| Inside surface temp | T_si = T_i − U·ΔT·R_si |
| Mould risk | f_Rsi = (T_si − T_o)/ΔT; below ~0.75 is a problem |
Formula reference — verify against the governing standard. Not a substitute for engineering judgment.