# Air Humidity Ratio

## The ratio between the mass of water vapor present in moist air - to the mass of dry air

The **humidity ratio** of moist air can be expressed with

- the mass of water vapor in the humid air - to the mass of dry air, or by
- the partial pressure of vapor in the air - to the partial pressure of the dry air

### Humidity Ratio by Mass

Humidity ratio by mass can be expressed as

- the ratio between the actual mass of water vapor present in moist air - to the mass of the dry air

Humidity ratio is normally expressed in kilograms (or pounds) of water vapor per kilogram (or pound) of dry air.

Humidity ratio expressed by mass:

x = m_{w}/ m_{a}(1)

where

x = humidity ratio (kg_{water}/kg_{dry_air}, lb_{water}/lb_{dry_air})

m_{w}= mass of water vapor (kg, lb)

m_{a}= mass of dry air (kg, lb)

### Humidity Ratio by Vapor Partial Pressure

Based on the Ideal Gas Law the humidity ratio can be expressed as

x = 0.62198 p_{w}/ (p_{a}- p_{w}) (2)

where

p_{w}= partial pressure of water vapor in moist air (Pa, psi)

p_{a}= atmospheric pressure of moist air (Pa, psi)

The maximum amount of water vapor in the air is achieved when *p _{w} =*

*p*the saturation pressure of water vapor at the actual temperature. (2) can be modified to:

_{ws }

x_{s}= 0.62198 p_{ws}/ (p_{a}- p_{ws}) (3)

where

x_{s}= maximum saturation humidity ratio of air (kg_{water}/kg_{air}, lb_{water}/lb_{dry_air})

p_{ws}= saturation pressure of water vapor

The water vapor pressure is small regarding to the atmospheric pressure and the relation between the humidity ratio and the saturation pressure is almost linear.

Note! - be careful with these equations at higher temperatures - as indicated in Temperature and Moisture Holding Capacity of Air.

Maximum specific humidity at some common temperatures:

Temperature ( )^{o}C | Water Vapor Saturation Pressure ( Pa) | Maximum Saturation Humidity Ratio of Air - x -( kg)_{w}/kg_{a} |
---|---|---|

0 | 609.9 | 0.003767 |

5 | 870 | 0.005387 |

10 | 1225 | 0.007612 |

15 | 1701 | 0.01062 |

20 | 2333 | 0.014659 |

25 | 3130 | 0.019826 |

30 | 4234 | 0.027125 |

**Note **that the saturation pressure of water vapor, - and the maximum humidity ratio, increases dramatically with air temperature. This important for the capacity of drying processes.

### Example - Humidity Ratio of Moist Air

The humidity ratio for saturated moist air at *20 ^{o}C* with water vapor partial pressure

*2333 Pa*at atmospheric pressure of

*101325 Pa*(

*1013 mbar, 760 mmHg*) can be calculated as:

x =0.62198(2333 Pa) / ((101325 Pa) - (2333 Pa))

= 0.0147 (kg/kg)

= 14.7 (g/kg)

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