Water moisture content of humid air calculator
When analysing HVAC or other thermal applications, and the humidity of air needs to be modelled, some kind of multiphase flow calculation is chosen. In many cases the fraction of water in the air is required as input variable for the CFD algorithm. The calculator below calculates the different mass fractions of O2, N2 and H2O in air.
Specific and Relative Humidity: Understanding and Calculating Water Vapor in Air
Humidity plays a crucial role in atmospheric and environmental conditions, affecting everything from weather patterns to human comfort. Humidity refers to the amount of water vapor present in the air and can be described in terms of specific and relative humidity.
Specific Humidity
Specific humidity (also known as the humidity ratio) is the mass of water vapor per unit mass of dry air. It is an absolute measure that quantifies the actual amount of moisture in the air, independent of temperature or pressure conditions. Mathematically, it can be expressed as:
$$\omega = \frac{{m_v}}{{m_a}} \quad \left(\text{kg of water vapor per kg of dry air}\right)$$
where \(m_v\) is the mass of water vapor and \(m_a\) is the mass of dry air. Alternatively, in terms of pressure, the specific humidity can be calculated using the equation:
$$\omega = \frac{{0.622 P_v}}{{P - P_v}}$$
In this equation, \(P_v\) is the partial pressure of water vapor, and \(P\) is the total pressure of the air mixture. The constant 0.622 comes from the ratio of the gas constant for dry air to the gas constant for water vapor.
Relative Humidity
While specific humidity gives an absolute measure, relative humidity (\(\phi\)) is a more common metric that expresses how much moisture the air contains compared to the maximum amount it can hold at the same temperature. Relative humidity is the ratio of the actual water vapor present to the maximum amount of water vapor the air can hold at saturation:
$$\phi = \frac{{P_v}}{{P_{g}}}$$
where $P_v$ is the partial pressure of water vapor, and $P_g$ is the saturation pressure of water at the given temperature. The saturation pressure of water at a given the temperature (between 0 °C and 100 °C) can be found (or interpolated) in the table below.
Relative humidity ranges from 0% (dry air) to 100% (saturated air) and varies with temperature. Warm air can hold more moisture than cold air, meaning that for the same specific humidity, the relative humidity will be lower at higher temperatures.
Calculation of Water Vapor in Humid Air
To calculate the amount of water vapor in the air, the partial pressure of the water vapor must first be determined. If the temperature and relative humidity are known, the partial pressure \(P_v\) can be calculated using:
$$P_v = \phi \times P_{g}$$
where $P_g$ is the saturation pressure of water vapor at the given temperature. After determining $P_v$, the specific humidity can be calculated using the formula for $\omega$ given earlier.
For example, let’s calculate the amount of water vapor in a room where the air is at 25°C, 65% relative humidity, and 101325 Pa (101.325 kPa) total pressure. The saturation pressure of water at 25°C is 3.1697 kPa. Using the formula:
$$P_v = 0.65 \times 3.1697 \, \text{kPa} = 2.060 \, \text{kPa}$$
Now, the specific humidity \(\omega\) can be calculated:
$$\omega = \frac{{0.622 \times 2.060}}{{100 - 2.060}} = 0.0129 \, \text{kg of water vapor per kg of dry air}$$
Thus, for every kilogram of dry air, 0.0129 kg of water vapor is present.
Saturation pressure (Pg) of water
| Temperature [°C] | Saturation Pressure Pg [kPa] |
|---|---|
| 0.00 | 0.6112 |
| 0.01 | 0.6117 |
| 5.00 | 0.8726 |
| 10.00 | 1.2282 |
| 15.00 | 1.7057 |
| 20.00 | 2.3392 |
| 25.00 | 3.1697 |
| 30.00 | 4.2467 |
| 35.00 | 5.6286 |
| 40.00 | 7.3844 |
| 45.00 | 9.5944 |
| 50.00 | 12.351 |
| 55.00 | 15.761 |
| 60.00 | 19.946 |
| 65.00 | 25.041 |
| 70.00 | 31.201 |
| 75.00 | 38.595 |
| 80.00 | 47.415 |
| 85.00 | 57.867 |
| 90.00 | 70.182 |
| 95.00 | 84.609 |
| 100.00 | 101.42 |
Humidity calculator
Calculate the fractions of O2, N2 and H2O in humid air for a given temperature and relative humidity.
The calculation is only valid for temperatures between 0 and 100 °C.
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