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This write‑up explains the science behind psychrometric calculations, the mathematical formulas required, step‑by‑step construction of an Excel calculator, practical applications, and advanced automation techniques. Before building the calculator, we must define the key properties of moist air, treating it as a mixture of dry air and water vapor.
– solved iteratively from ( p_ws(T_dp) = p_w ).
[ RH = \fracp_wp_ws(T) \times 100% ]
=0.62198 * B6 / (B2 - B6) Cell B8:
For (pressure in kPa, temperature in K):
| Property | Symbol | Typical Units | Description | |----------|--------|---------------|-------------| | Dry‑bulb temperature | T | °C or °F | Ordinary air temperature measured by a standard thermometer | | Wet‑bulb temperature | T w | °C or °F | Temperature recorded by a thermometer with a wet wick; indicates cooling by evaporation | | Dew‑point temperature | T dp | °C or °F | Temperature at which condensation begins for a given moisture content | | Relative humidity | RH | % | Ratio of actual water vapor pressure to saturation pressure at same dry‑bulb | | Humidity ratio (mixing ratio) | W | kg water /kg dry air | Mass of water vapor per mass of dry air | | Enthalpy | h | kJ/kg dry air or Btu/lb dry air | Total heat content (sensible + latent) | | Specific volume | v | m³/kg dry air | Volume per unit mass of dry air | | Vapor pressure | p w | kPa or psi | Partial pressure exerted by water vapor in the mixture | Excel does not have built‑in psychrometric functions. Instead, we must implement empirical correlations from ASHRAE Handbook—Fundamentals. The most important is the saturation vapor pressure over liquid water (Hyland‑Wexler formulation, valid 0–200°C):
[ W = 0.62198 \cdot \fracp_wP - p_w ] where ( P ) is total atmospheric pressure (typically 101.325 kPa at sea level). The factor 0.62198 is the ratio of molecular weights of water (18.01528) to dry air (28.9645).
– requires iterative solution of the carrier equation:
[ \ln(p_ws) = \fracC_8T + C_9 + C_10 T + C_11 T^2 + C_12 T^3 + C_13 \ln(T) ]
[ v = \frac0.2871 \cdot (T_db + 273.15)P \cdot (1 + 1.6078 \cdot W) ] where 0.2871 = gas constant for dry air (kJ/kg·K), ( P ) in kPa.
=B5 * (B4/100) Cell B7:
=$B$2*0.62198*B6/($B$2-B6) Wait – careful: ( W = 0.62198 * p_w / (P - p_w) ). So correct formula:
[ p_ws = 0.61094 \cdot \exp\left( \frac17.625 \cdot T_dbT_db + 243.04 \right) ] where ( T_db ) is in °C, result in kPa. 1. Humidity ratio from vapor pressure