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Name: Scott
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Question:
Hi there, 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.


Replies:
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.

Vince Calder


Scott,

It requires some equations, but it can be done.

First we need to convert your pressure (P) into
kPa (kiloPascals):

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 degrees.

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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