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Moist Air - Relative Humidity

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 = (p_w/ p_ws) 100% (1)

where

φ = relative humidity (%)

p_w = vapor partial pressure (mbar)

p_ws = 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:

Moist Air - Saturation Vapor Pressure

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^-3bar = 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 (lb_f/in²) = 10⁶ dyn/cm² = 750 mmHg

Air - Saturation Vapor Pressure - (Celcius and milibar) (pdf)

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

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 70 ^oF (21 ^oC) 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 = (ρ_w/ ρ_ws) 100% (2b)

where

φ = relative humidity (%)

ρ_w = vapor density (kg/m³)

ρ_ws = 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 20 ^oC (68 ^oF) 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 = (m_w/ m_ws) 100% (2c)

where

φ = relative humidity (%)

m_w = mass of water vapor in the given air volume (kg)

m_ws = mass of water vapor required to saturate at this volume (kg)