1065.645—Amount of water in an ideal gas.
This section describes how to determine the amount of water in an ideal gas, which you need for various performance verifications and emission calculations. Use the equation for the vapor pressure of water in paragraph (a) of this section or another appropriate equation and, depending on whether you measure dewpoint or relative humidity, perform one of the calculations in paragraph (b) or (c) of this section.
(a) Vapor pressure of water.
Calculate the vapor pressure of water for a given saturation temperature condition, T
sat, as follows, or use good engineering judgment to use a different relationship of the vapor pressure of water to a given saturation temperature condition:
(1)
For humidity measurements made at ambient temperatures from (0 to 100) °C, or for humidity measurements made over super-cooled water at ambient temperatures from (−50 to 0) °C, use the following equation:
Where:
pH20 = vapor pressure of water at saturation temperature condition, kPa.
Tsat = saturation temperature of water at measured conditions, K.
Example:
Tsat = 9.5 °C
Tdsat = 9.5 273.15 = 282.65 K
log10(pH20) = 0.074297
pH20 = 100.074297 = 1.186581 kPa
(2)
For humidity measurements over ice at ambient temperatures from (−100 to 0) °C, use the following equation:
Example:
Tice = −15.4 °C
Tice = −15.4 273.15 = 257.75 K
log10(pH20) = −0.798207
pH20 = 10 0.79821 = 0.159145 kPa
(b) Dewpoint.
If you measure humidity as a dewpoint, determine the amount of water in an ideal gas, x
H20, as follows:
Where:
xH20 = amount of water in an ideal gas.
pH20 = water vapor pressure at the measured dewpoint, Tsat = Tdew.
pabs = wet static absolute pressure at the location of your dewpoint measurement.
Example::
pabs = 99.980 kPa
Tsat = Tdew = 9.5 °C
Using Eq. 1065.645-1,
pH20 = 1.186581 kPa
xH2O = 1.186581/99.980
xH2O = 0.011868 mol/mol
(c) Relative humidity.
If you measure humidity as a relative humidity, RH %, determine the amount of water in an ideal gas, x
H2O, as follows:
Where:
xH20 = amount of water in an ideal gas.
RH% = relative humidity.
pH20 = water vapor pressure at 100% relative humidity at the location of your relative humidity measurement, Tsat = Tamb.
pabs = wet static absolute pressure at the location of your relative humidity measurement.
Example:
RH% = 50.77%
pabs = 99.980 kPa
Tsat = Tamb = 20 °C
Using Eq. 1065.645-1,
pH20 = 2.3371 kPa
xH2O = (50.77% · 2.3371)/99.980
xH2O = 0.011868 mol/mol