All properties are computed at the local total pressure \(P\), determined from elevation \(z\) (m) using the barometric formula:
\[ P(z) = 101.325\left(1 - 2.25577\times10^{-5}\,z\right)^{5.25588} \ \text{kPa} \]
Saturation vapor pressure
A Tetens-type correlation is used for dry-bulb temperature \(T\) in \(^{\circ}\text{C}\):
\[ p_{sat}(T) = 0.61078\,\exp\!\left(\dfrac{17.27\,T}{T+237.3}\right)\ \text{kPa}, \quad T \ge 0^{\circ}\text{C} \]
\[ p_{sat}(T) = 0.61078\,\exp\!\left(\dfrac{21.875\,T}{T+265.5}\right)\ \text{kPa}, \quad T < 0^{\circ}\text{C (over ice)} \]
Humidity ratio and vapor pressure
\[ W = 0.62198\,\dfrac{p_w}{P-p_w} \qquad\Longleftrightarrow\qquad p_w = \dfrac{P\,W}{0.62198+W} \]
Relative humidity
\[ \text{RH} = \dfrac{p_w}{p_{sat}(T_{db})}\times 100\% \]
Dew point temperature
Found by inverting the Tetens correlation for the vapor pressure \(p_w\):
\[ T_{dp} = \dfrac{237.3\,\ln\!\left(p_w/0.61078\right)}{17.27-\ln\!\left(p_w/0.61078\right)} \]
Enthalpy of moist air
\[ h = 1.006\,T_{db} + W\left(2501.0+1.86\,T_{db}\right)\ \text{kJ/kg dry air} \]
Specific volume
\[ v = \dfrac{R_{da}\,(T_{db}+273.15)\,(1+1.6078\,W)}{P}, \qquad R_{da}=0.287055\ \text{kJ/(kg}\cdot\text{K)} \]
Thermodynamic wet-bulb temperature
\(T_{wb}\) is solved iteratively (bisection) from the adiabatic-saturation energy balance:
\[ h(T_{db},W) = h_{sat}(T_{wb}) - \left(W_{s}(T_{wb})-W\right)c_{p,w}\,T_{wb} \]
where \(W_s(T_{wb})\) is the saturation humidity ratio at \(T_{wb}\) and \(c_{p,w}=4.186\ \text{kJ/(kg}\cdot\text{K)}\) is the specific heat of liquid water.
Adiabatic mixing of two streams
Conservation of dry-air mass and energy for streams 1 and 2 combining into stream 3 (with mass fractions \(r_1+r_2=1\)):
\[ T_{db,3}=r_1T_{db,1}+r_2T_{db,2}, \qquad W_3=r_1W_1+r_2W_2 \]
Symbols
| Symbol | Meaning | Units (SI) |
|---|
| \(T_{db}\) | Dry-bulb temperature | °C |
| \(T_{wb}\) | Thermodynamic wet-bulb temperature | °C |
| \(T_{dp}\) | Dew-point temperature | °C |
| RH | Relative humidity | % |
| \(W\) | Humidity ratio | kg water / kg dry air |
| \(h\) | Specific enthalpy (per kg dry air) | kJ/kg |
| \(v\) | Specific volume (per kg dry air) | m³/kg |
| \(P\) | Total (atmospheric) pressure | kPa |
| \(p_{sat}\) | Saturation vapor pressure at \(T_{db}\) | kPa |
| \(p_w\) | Partial (vapor) pressure of water | kPa |
| \(z\) | Elevation above sea level | m |
| \(r_1, r_2\) | Mass fraction of mixing stream 1, 2 | — |