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:
| Temperature | Saturation 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]
Relative Humidity Chart - degrees Fahrenheit
Relative Humidity Chart - degrees Celsius
Altitude and Correction Factors
| Barometric Altitude [mbar] | Abs. Altitude | Correction 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 |