Relative Humidity
The definition of Relative Humidity can be expressed as the System Water Vapor Pressure divided by the Saturation Water Vapor Pressure. Unfortunately neither of these parameters are easy to measure directly. Fortunately, the saturation vapor pressure of a given system is only a function of the temperature of the system. This fact has many repercussions, but for the researcher, this simply means that we can calculate the relative humidity of the system if we know the system temperature and the system dewpoint.
Vapor Pressure Calculations
To calculate the Saturation Water Vapor pressure for a given temperature we refer to the The International Association for the Properties of Water and Steam. In particular we look to their Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam. Notice that the dewpoint of a gas is the condition when a system is at its Saturation Water Vapor Pressure
Dewpoint to Saturation Vapor Pressure
These equations came from reducing the equations listed on page 33
- A= T^2 + 1,713 * T - 330,882
- B = -17.07 * T^2 +2,694 * T - 1,222,898
- C = 14.9 * T^2 +3,325 * T +200,461
- Saturation Pressure = ( 11.247 * C/(-B + Sqrt(B^2 - 4 * A * C)))^4
Vapor Pressure Backward to Dewpoint
Using backward equations from page 34 in above mentioned release.
- E = 0.0316 *Ps^0.5 - 3.036 * Ps^0.25 +14.915
- F = 36.9 * Ps^0.5 + 2,137.8 * Ps^0.25 - 4,823.3
- G = -22,901 * Ps^0.5 -574,881 * Ps^0.25 + 405113
- D = 2 * G / (-F - Sqrt(F^2 - 4 * E * G))
- Ts = 51.94 + D / 2 - Sqrt( 0.25 * D^2 - 325.09 * D + 105,682)