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# Moist Air - Relative Humidity

## Relative humidity in moist air is the ratio of partial vapor pressure to air pressure.

Humidity is the quantity of water vapor present in air. It can be expressed as an absolute, specific or relative value.

Relative humidity is expressed by

• partial vapor and air pressure,
• density of the vapor and air, or
• by the actual mass of the vapor and air

Relative humidity is usually expressed in per cent and abbreviated by φ or RH.

### Relative Humidity and Vapor Partial Pressure

Relative humidity as the ratio of vapor partial pressure in the air - to the saturation vapor partial pressure if the air at the actual dry bulb temperature.

φ = pw / pws 100%                            (1)

where

φ = relative humidity [%]

pw = vapor partial pressure [mbar]

pws = saturation vapor partial pressure at the actual dry bulb temperature [mbar]. This is the vapour pressure at maximum content of water gas in air, before it starts to condense out as liquid water.

Vapor saturation pressures at different temperatures:

TemperatureSaturation Vapor Pressure
[10-3 bar]
[oC][oF]
-18 0 1.5
-15 5 1.9
-12 10 2.4
-9 15 3.0
-7 20 3.7
-4 25 4.6
-1 30 5.6
2 35 6.9
4 40 8.4
7 45 10.3
10 50 12.3
13 55 14.8
16 60 17.7
18 65 21.0
21 70 25.0
24 75 29.6
27 80 35.0
29 85 41.0
32 90 48.1
35 95 56.2
38 100 65.6
41 105 76.2
43 110 87.8
46 115 101.4
49 120 116.8
52 125 134.2
• 10-3 bar = 1 millibar
• 1 bar = 1000 mbar = 105 Pa (N/m2) = 0.1 N/mm2 = 10,197 kp/m2 = 10.20 m H2O = 0.9869 atm = 14.50 psi (lbf/in2) = 106 dyn/cm2 = 750 mmHg

If the water vapor pressure in the air is 10.3 mbar, the vapor saturates on a surface with 45oF (7oC).

Note! The atmospheric pressure of air is 1013 mbar (101.325 kPa, 760 mmHg). As we can see the maximum water vapor pressure - the saturation pressure - is relatively small.

Example:
Relative Humidity and Vapor Pressure

From the table above the saturation pressure at 70oF (21oC) is 25.0 mbar. If the vapor pressure in the actual air is 10.3 mbar the relative humidity can be calculated as:

φ = 10.2 [mbar] / 25.0 [mbar]* 100[%]

= 41[%]

### Relative Humidity and Vapor Density

Relative humidity can also be expressed as the ratio of the vapor density of the air - to the saturation vapor density at the the actual dry bulb temperature.

Relative humidity by density:

φ = ρw / ρws 100%                               (2b)

where

φ = relative humidity [%]

ρw = vapor density [kg/m3]

ρws = vapor density at saturation at actual dry bulb temperature [kg/m3]

A common unit for vapor density is g/m3.

Example: Relative humidity at a given temperature and known vapor density and saturation density

If the actual vapor density at 20oC (68oF) is 10 g/m3 and the saturation vapor density at this temperature is 17.3 g/m3, the relative humidity can be calculated as

φ = 10 [g/m3] / 17.3 [g/m3] *100 [%]

= 57.8 [%]

### Relative Humidity and Vapor Mass

Relative humidity can also be expressed as the ratio at actual mass of water vapor in a given air volume - to the mass of water vapor required to saturate at this volume.

Relative humidity can be expressed as:

φ = mw / mws 100%                            (2c)

where

φ = relative humidity [%]

mw = mass of water vapor in the given air volume [kg]

mws = mass of water vapor required to saturate at this volume [kg]

### Altitude and Correction Factors

Barometric Altitude
[mbar]
Abs. AltitudeCorrection Factor for
φ
[m][ft]
1013 0 0 1.000
1000 108 354 0.987
989 200 656 0.976
966 400 1312 0.953
943 600 1996 0.931
921 800 2624 0.909
899 1000 3281 0.887
842 1500 4922 0.831
795 2000 6562 0.785

## Related Topics

• Air Psychrometrics - Moist and humid air - psychrometric charts, Mollier diagrams, air-condition temperatures and absolute and relative humidity and moisture content.

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