View or download waterVapor.frink in plain text format
/*
This file is a library containing functions for calculating properties
of water vapor in air (e.g. absolute humidity, relative humidity,
partial vapor pressure of water.)
There are a lot of equations that could be used. See the survey:
http://faculty.eas.ualberta.ca/jdwilson/EAS372_13/Vomel_CIRES_satvpformulae.html
Most of the equations in this library are taken from the reversible
equations cited in:
Buck, A. L. (1981), "New equations for computing vapor pressure and enhancement factor", J. Appl. Meteorol. 20: 1527–1532
http://ams.allenpress.com/perlserv/?request=get-pdf&doi=10.1175%2F1520-0450%281981%29020%3C1527%3ANEFCVP%3E2.0.CO%3B2
This is further corrected in
Buck (1996), Buck Research CR-1A User's Manual, Appendix 1.
http://www.hygrometers.com/wp-content/uploads/CR-1A-users-manual-2009-12.pdf
The equations in this library are for water vapor pressure over water (there
are similar equations for over ice) and represent the corrected Buck
equations (1996).
A sample usage of this library might be to find how much water you need to
vaporize to bring your house to 100% relative humidity. (Assuming that the
contents of your house don't re-absorb any water.) This requires you to
know your true atmospheric pressure (not re-corrected for altitude.
Usually on weather sites, your atmospheric pressure is re-corrected as if
it were at sea level, even if you live at a high altitude. If you live at
5500 feet, and your weather site tells you that your pressure is 1000
millibars, it's definitely re-corrected. You can obtain a good estimate of
true atmospheric pressure for any altitude by running
StandardAtmosphereTest.frink and giving it your altitude.)
For example, true atmospheric pressure at my location (elevation 5500 feet
above sea level) is around 0.816 atmosphere, which is used below.
density = absoluteHumidity[F[68], 0.816 atm, 100 percent]
housevolume = 53 feet 28 feet 20 feet
density housevolume / water -> gallons
which yields
3.85 gallons
or, to obtain the mass of water to be vaporized:
density housevolume
which yields
14.8 kg
Again, all the stuff in your house is going to re-absorb water, so the true
amount of water that you'll have to evaporate will be more than this.
Also, in wintertime, if you have a window open, the air coming in will be
almost completely dry (especially if the outside air is near freezing or
below) and will force you to vaporize much more water to maintain humidity
(if you can keep up at all.)
*/
/*
Returns *saturation* vapor pressure of water at the specified temperature.
This is the maximum vapor pressure of water at the specified temperature
over water.
*/
saturationVaporPressure[temp is temperature] :=
{
t = C[temp]
return 6.1121 hPa exp[(18.678 - t/234.5) t / (257.14 + t)]
}
// Calculate the vapor pressure given temperature, pressure,
// and relative humidity (a number between 0 and 1, or, say, "30 percent")
vaporPressure[temp is temperature, p is pressure, relativeHumidity is dimensionless] :=
{
return relativeHumidity * buckF1[temp, p]
}
// Returns absolute humidity as a mass density (e.g. g/m^3)
// T is the temperature,
// relativeHumidity is a number between 0 and 1, or "30 percent"
absoluteHumidity[temp is temperature, p is pressure, relativeHumidity is dimensionless] :=
{
e = vaporPressure[temp, p, relativeHumidity] / millibars
return 216.7 g/m^3 * e / (temp/K)
}
/*
Returns absolute humidity as a mass density (e.g. g/m^3) for water vapor
over water. (As opposed to over ice, which has different equations.)
T is the temperature,
vaporPressure is the partial pressure of water vapor
It's much more likely that you'll use the function above, though, which
calculates the partial vapor pressure of water for you, which is nonlinear
and hard to measure directly.
*/
absoluteHumidity[temp is temperature, vaporPressure is pressure] :=
{
return 216.7 g/m^3 (vaporPressure/millibar)/(temp/K)
}
////////////////////////////////////////////////////////////////////
//
// You probably don't want to call functions below here directly,
// but use the friendlier functions above.
//
////////////////////////////////////////////////////////////////////
/* Calculates equation F1 from Buck (1996) for partial vapor pressure over
water (there are other equations for water over ice.)
Results are the partial vapor pressure of water.
temp is the temperature.
p is the total atmospheric pressure.
*/
buckF1[temp is temperature, p is pressure] :=
{
T = C[temp]
return EFw[temp, p] * 6.1121 * exp[(18.678 - T/234.5) * T/(T+257.14)] millibars
}
/* Calculates the "enhancement factor" due to water vapor not behaving
like an ideal gas in air. See Buck (1996).
This is for water vapor over water. There is a different equation for
water vapor over ice.
Result is a dimensionless number.
*/
EFw[temp is temperature, p is pressure] :=
{
P = p / millibars
T = C[temp]
return (1 + 10^-4 (7.2 + P (0.0320 + 5.9e-6 T^2)))
}
View or download waterVapor.frink in plain text format
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