Atmospheric moisture content
is a useful value to monitor for a variety of HVAC control applications,
including basic humidity monitoring and control and automation of free cooling
processes. This note defines fundamental
expressions of atmospheric moisture content and gives calculations that can be
used in H I Solutions PC Central software.
Moisture content is often calculated given two commonly measured values—air
temperature and relative humidity—and can be expressed in several ways.
Humidity is the
general term for the concentration of atmospheric water vapor.
Vapor pressure
is the pressure contribution of water vapor to the total atmospheric pressure,
reported in millibars [mb]
or pascals [Pa] (1 mb = 100
Pa = 100 N/m^{2}). According to Dalton’s Law, the total
pressure of a mixture of gases is equal to the sum of the partial pressures of
each gas. At a gas’s saturation vapor
pressure, the rate of evaporation of molecules equals the rate of condensation. For a given temperature, a gas’s vapor
pressure cannot exceed its saturation vapor pressure. At a higher temperature, the rate of
evaporation increases, increasing the air’s humidity until a higher equilibrium
saturation vapor pressure is reached. In
this way, the saturation vapor pressure depends on the rate of evaporation,
which in turn depends on temperature.
Saturation vapor pressure vs. temperature
Mixing ratio
is the mass of water vapor per mass of dry air [g water/kg dry air].
Specific humidity is the mass of water vapor per mass of the air containing (and
including) the water vapor [g water/ kg moist air].
Absolute humidity is the mass of water vapor per volume of dry air [g/m^{3}]. Absolute humidity is less useful because it’s
value can change with a change in air volume, without a corresponding change in
vapor content.
Relative humidity is a common way to report atmospheric moisture content, and is defined
as
RH = 100 * e/e_{s}
Where e = actual water vapor
pressure and e_{s} = saturation vapor
pressure.
Because e_{s}
is dependent on air temperature, it is possible to change the relative humidity
of a body of air without changing its
moisture content.
Dew point temperature is another way of reporting the water vapor content
of air, and is based on the onetoone relationship between temperature and
saturation vapor pressure. At the dew
point temperature, the vapor pressure is equal to the saturation vapor
pressure. If air is cooled to its dew
point temperature, the air becomes saturated with water vapor; further cooling will result in condensation
or deposition.
Lawrence (2005) presents several ways to estimate dew point
temperature with various degrees of accuracy, given temperature and relative
humidity. One of the more accurate
expressions for dew point temperature (Lawrence’s
equation 8) is:
t_{d}
= B_{1} [ln
(RH/100) + A_{1}t / (B_{1} + t)]
A1 – ln(RH/100)
– A_{1}t / (B_{1} + t)
Where
t_{d} = dew point temperature [ºC]
A_{1}
= 17.625
B_{1}
= 243.04 ºC
RH =
relative humidity
Monitors for Calculating Dew Point Temperature in PC
Central
Both of the following
monitors are based on Lawrence’s
equation 8.
An expression for calculating t_{d} in ºF
given t in ºF:
1 @ ~ (32 +
437.47 * ( LOG((RH / 100)) + 17.63 * 5 / 9 * (T  32) / (243.04 + 5 / 9 * (T 
32))) / (17.63  LOG((RH / 100))  17.63
* 5 / 9 * (T  32) / (243.04 + 5 / 9 * (T  32))))
An expression for calculating t_{d} in ºC
given t in ºC:
1 @ ~ (243.04 *
( LOG((RH / 100)) + 17.63 * TC / (243.04 + TC)) / (17.63  LOG((RH / 100))  17.63 * TC / (243.04 +
TC)))
Simpler approximations for roughly calculating dew
point temperature are given in Lawrence
(2005). Some approximations are more
accurate for certain ranges of temperature and relative humidity.
Reference:
Lawrence, Mark G. (2005) The relationship between relative
humidity and the dewpoint temperature in moist air: a
simple conversion and applications.
Bulletin of the American Meteorological Society, 86 (2): 225233.
