MadSci Network: Earth Sciences
Query:

Re: Where can I find the formula to create a psychrometric chart?

Date: Tue Mar 2 16:03:44 1999
Posted By: Allan Harvey, Staff,National Institute of Standards and Technology
Area of science: Earth Sciences
ID: 918221964.Es
Message:

There are lots of things that go (or potentially can go) on a 
psychrometric chart, so I'll have to make a guess as to which piece you 
are looking for.  I'll assume you know how to make the conversion between 
absolute and relative humidity, and that you have the pure-water 
properties you need (like vapor pressure and latent heat of water as a 
function of temperature).  If you do happen to need pure water properties, 
the keeper of the official standards (though you probably don't need such 
quality for psychrometric charts) is the International Association for the 
Properties of Water and Steam, which has a Website at
http://www.iapws.org

I should also mention up front that among the best places to find the 
basic equations of psychrometry are chemical engineering mass transfer 
textbooks.  For example, I'm getting most of my background for this answer 
from R.E. Treybal, Mass-Transfer Operations, 3rd ed., McGraw-Hill, 1980.  
Appropriate material is also in Perry's Chemical Engineers' Handbook, 
which should be in any decent technical library.

I assume what you want to be able to do is relate the wet-bulb temperature 
to the absolute humidity (given the dry-bulb temperature).  The 
relationship between these quantities is given by a mass/enthalpy balance 
around a liquid drop, and turns out to be:
TG-Tw = (LAMw(Yw-Y))/(hG/kY)
where:
TG is the dry-bulb (normal) temperature
Tw is the wet-bulb temperature
LAMw is the latent heat of water at the wet-bulb temperature
Yw is the absolute humidity (units like kg/kg air) of saturated air at the 
wet-bulb temperature
Y is the absolute humidity
hG is a heat-transfer coefficient
kY is a mass transfer coefficient
For water-air mixtures at normally encountered humidities and 
temperatures, the ratio hG/kY can be taken to be 950 N m / (kg K)

That should be all you need, but I'll mention that another concept you may 
run into is the adiabatic saturation temperature, which is basically the 
temperature of liquid required to bring a gas mixture to its dew point if 
they are brought into contact.  The equation for this is the same as for 
the wet-bulb temperature except that hG/kY is replaced by Cs, the so-
called "humid heat", which is the constant-pressure heat capacity of a 
unit mass of gas and its accompanying vapor.  For water in air at commonly 
encountered conditions, this happens to be very close to the ratio hG/kY, 
so the adiabatic saturation temperature and the wet-bulb temperature are 
essentially the same.  This equality won't be true in general for other 
liquid-gas mixtures.

Finally, I'll mention that there are a bunch of programs around that do 
these calculations, as you can see by doing a Web search on the word 
"psychrometric".  It looks like most of them cost money, but there 
appeared to be at least one or two free ones in my quick search.  Of 
course I can't vouch for the quality of these programs, so you should 
check any results against a trusted source like Perry's Handbook or the 
ASHRAE Handbook.

Dr. Allan H. Harvey, Phys. & Chem. Properties Div., NIST
"Don't blame the government for what I say, or vice-versa."


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