Air Density Formula
Do you know a formula that I could use to calculate air density
using the 3 inputs from the instruments I have:
Temperture in Celsius?
Rh - relative humidity?
Barometric pressure ( from my barometer in inches of Mercury)?
I would like to put the formula in my programmable calculator to
track changes in daily Air density. I know you have to allow for
saturation pressure and water vapour pressure but I'm not sure how
to go about it.
There are a number of websites that treat the properties of the
atmosphere. They vary in complexity, because the atmosphere is a
dynamic mixture of gases that is not constant. Some of the
treatments get rather involved because of the intended applications
of engine design and aircraft behavior. The most direct source I
found for your needs is: http://www.aeromech.usyd.edu.au/aero/atmos/atmos.html
It may require some "number crunching" on your part to write an
algorithm for a programmable calculator but I do not think it is out of reach.
It requires some equations, but it can be done.
First we need to convert your pressure (P) into
P(kPa) = P(in. Hg)*3.3864
Next we need to determine the vapor pressure (VP)
in kPa. To do this we first calculate the saturation
vapor pressure (SVP) in kPa from the temperature (T):
SVP = 0.61121*e^[17.67*T/(T+243.5)],
where e means exponential.
Then we can calculate VP from RH and SVP:
VP = RH*SVP/100
Now we calculate the mixing ratio (XM):
XM = 0.622*VP/(P-VP)
Finally, we calculate moist air density (RHO):
RHO = [P*(1+XM)]/[0.28703*(T+273.16)*(1+1.16078*XM)],
where the T+273.16 puts the temperature into Kelvin
So, if T=26 deg. C, P=29.23 in. Hg (99 kPa), and
RH=40%, we get SVP=3.3615 kPa, VP=1.345 kPa,
XM=0.008564, and RHO=1.1514 kg m^-3
(or 1.1514 x 10^-3 g cm^-3).
David R. Cook
Climate Research Section
Environmental Science Division
Argonne National Laboratory
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Update: June 2012