Humidity Ratio Calculator: Water-Vapour Mass Fraction in Humid Air

Specific Humidity (Humidity Ratio)

Specific humidity (also called the humidity ratio) is the mass of water vapour per unit mass of dry air. It is an absolute measure of the moisture content, independent of temperature or pressure. Mathematically:

$$\omega = \frac{m_v}{m_a} \quad \left(\text{kg of water vapour per kg of dry air}\right)$$

where \(m_v\) is the mass of water vapour and \(m_a\) is the mass of dry air. In terms of partial pressures, the same quantity can be expressed as:

$$\omega = \frac{0.622 \, P_v}{P - P_v}$$

Here \(P_v\) is the partial pressure of water vapour and \(P\) is the total (atmospheric) pressure. The constant 0.622 is the ratio of the molar mass of water (18.015 g/mol) to the effective molar mass of dry air (28.964 g/mol).

Relative Humidity

While specific humidity gives an absolute measure, relative humidity (\(\phi\)) expresses how close the air is to saturation at the current temperature:

$$\phi = \frac{P_v}{P_g}$$

where \(P_g\) is the saturation pressure of water at the given temperature. Relative humidity ranges from 0 % (completely dry) to 100 % (saturated). Because warm air can hold more moisture than cold air, the same specific humidity corresponds to a lower relative humidity at higher temperatures. The saturation pressure \(P_g\) for temperatures between 0 °C and 100 °C can be found in Table 1 below.

Calculating the Water-Vapour Mass Fraction

To determine the mass fractions needed for a CFD simulation, the partial pressure of water vapour is first calculated from the known relative humidity and saturation pressure:

$$P_v = \phi \times P_g$$

The specific humidity then follows from the formula for \(\omega\) given above. Finally, the mass fractions of the three species in simplified moist air are:

$$\text{mf}_{H_2O} = \frac{\omega}{1 + \omega}$$

$$\text{mf}_{O_2} = (1 - \text{mf}_{H_2O}) \times 0.23$$

$$\text{mf}_{N_2} = (1 - \text{mf}_{H_2O}) \times 0.77$$

Worked example

Consider a room at 25 °C, 65 % relative humidity and 101 325 Pa total pressure. From Table 1, the saturation pressure at 25 °C is \(P_g\) = 3.1697 kPa. The partial pressure of water vapour becomes:

$$P_v = 0.65 \times 3.1697 = 2.060 \; \text{kPa}$$

The specific humidity is then:

$$\omega = \frac{0.622 \times 2.060}{101.325 - 2.060} = 0.01290 \; \text{kg/kg}$$

In other words, every kilogram of dry air contains 12.9 g of water vapour. The corresponding mass fraction for the CFD input is mf_H₂O = 0.01274.

Saturation Pressure of Water (P_g)

Humidity Ratio Calculator

Calculate the mass fractions of H₂O, O₂ and N₂ in humid air for a given temperature and relative humidity. The calculation is valid for temperatures between 0 and 100 °C.

For projects involving complex moisture transport, condensation modelling or multi-zone HVAC simulations, our CFD team can set up and run the full analysis. Thermal comfort in the occupied zone can then be evaluated using the PMV and PPD method. To learn more about the fundamentals, see our course Introduction to Computational Fluid Dynamics.