# Air Density Calculation

#### moust  Could someone please benice and tell me how to find the air density when the temperature is 18 degrees celsuis and the atmospheric pressurew is 782 mm HG.

thanks a lot Related Mechanical Engineering News on Phys.org

#### FredGarvin

Neglecting humidity, $$\rho = \frac{P}{RT}$$

Remember pressure is in absolute units as well as temperature (kelvine or rankine).

#### TexanJohn

Is the calculation for total density including humidity something like:

D = [ Pd / (Rd * T)] + [Pv / (Rv * T)]

Pd - pressure dry air (Pascals)
Pd - pressure water vapor (Pascals)
Rd - gas constant for dry air ~ 287.05 (J/kg*K)
Rv - gas constant for water vapor ~ 461.495 (J/kg*K)

I have always been curious about the affect of water/water vapor on the overall density. I found the above formula on the internet so I have no idea if it is correct. I don't think I fully understand the relationship between vapor pressure and the more common weather term humidity. How much does the overall density change when humidity changes from 30% to 90%. Does the vapor pressure change as well?

#### Gokul43201

Staff Emeritus
Gold Member
Neglecting humidity, $$\rho = \frac{P}{RT}$$

Remember pressure is in absolute units as well as temperature (kelvine or rankine).
I believe that should be $$\rho = \frac{MP}{RT}$$
where M is the average molar mass (approx 0.029kg/mol) and R is the molar gas constant.

Edit: ...unless R is the normalized gas constant for air, in units of J/K-kg (not the molar gas constant), in which case, Fred's equation is correct.

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#### Astronuc

Staff Emeritus
I have always been curious about the affect of water/water vapor on the overall density. I found the above formula on the internet so I have no idea if it is correct. I don't think I fully understand the relationship between vapor pressure and the more common weather term humidity. How much does the overall density change when humidity changes from 30% to 90%. Does the vapor pressure change as well?
Relative Humidity
A dimensionless ratio, expressed in percent, of the amount of atmospheric moisture present relative to the amount that would be present if the air were saturated. Since the latter amount is dependent on temperature, relative humidity is a function of both moisture content and temperature. As such, relative humidity by itself does not directly indicate the actual amount of atmospheric moisture present. See dew point.
from - http://www.weather.gov/glossary/

Humidity
Generally, a measure of the water vapor content of the air. Popularly, it is used synonymously with relative humidity. - NWS glossary

Dew Point
(Abbrev. DWPT) - A measure of atmospheric moisture. It is the temperature to which air must be cooled in order to reach saturation (assuming air pressure and moisture content are constant). A higher dew point indicates more moisture present in the air. It is sometimes referred to as Dew Point Temperature, and sometimes written as one word (Dewpoint). - NWS glossary

Both density and vapor pressure are related to the mole fraction of water vapor in the gas. The water molecule has a molecular mass of 18, as compared to N2 = 28 and O2 = 32, so moist air is lighter since the mean molecular mass is less.

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#### TexanJohn

Relative Humidity

from - http://www.weather.gov/glossary/

Humidity
Generally, a measure of the water vapor content of the air. Popularly, it is used synonymously with relative humidity. - NWS glossary

Dew Point
(Abbrev. DWPT) - A measure of atmospheric moisture. It is the temperature to which air must be cooled in order to reach saturation (assuming air pressure and moisture content are constant). A higher dew point indicates more moisture present in the air. It is sometimes referred to as Dew Point Temperature, and sometimes written as one word (Dewpoint). - NWS glossary

Both density and vapor pressure are related to the mole fraction of water vapor in the gas. The water molecule has a molecular mass of 18, as compared to N2 = 28 and O2 = 32, so moist air is lighter since the mean molecular mass is less.
Thanks. I have been reading some definitions of weather terms. I have always used this http://wahiduddin.net/calc/calc_da.htm" [Broken].

Using the calculator above, I enter:

Altitude = 0
Air Temp = 58.7
Altimeter = 29.921
Dew Point = 0 (I don't know if this is a reasonable value)

The results are

Density Altitude = 0
Absolute Pressure = 29.921
Relative Density = 100 %

If I change the Dew Point to 40* (F), the results are

Density Altitude = 88
Absolute Pressure = 29.921
Relative Density = 99.74

If I change Dew Point to 58.7*, the results are

Density Altitude = 196
Absolute Pressure = 29.921
Relative Density = 99.43

I find this a little confusing. I would have thought a dew point being equal to the air temp would have indicated a much higher presence of water and thus a much lower Relative Density.

I am at 600' elevation, and my current conditions are 47.1* (F) air temp, dew point 28* (F), pressure 29.93 inHg. It is indicated that the 'Humidity' is 46%. Can the 'humidity' increase and all other variables remain constant? The above definition indicates that Dew Point is determined assuming Pressure and 'moisture content' are kept constant. So, I assume the answer to my question is 'No' as humidity is 'moisture content'.

I had always heard that humidity affected density more. So, I am trying to work a few real examples to confirm/deny.

Thanks. :)

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#### FredGarvin

...unless R is the normalized gas constant for air, in units of J/K-kg (not the molar gas constant), in which case, Fred's equation is correct.
That's the way I always do it. I'm so used to using
$$R = 53.35 \frac{ft-Lb_f}{R-Lb_m}$$ for air that it didn't even cross my mind to mention that. Good catch.

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#### Sjeanh

Air density percent

I think I now understand how to get the raw air density in kg/m^3; can someone help me with a formula to convert this to air density percent with 100 as the standard density? I would also like to know how to account for altitude - I'm trying to write a calculator where I can have floor techs enter the temperature, humidity, and barometric pressure and print out what an air density gauge should read for the location of my manufacturing plant, for calibration purposes. Thanks for your help...

#### stewartcs

I think I now understand how to get the raw air density in kg/m^3; can someone help me with a formula to convert this to air density percent with 100 as the standard density?
If I understand what you are asking correctly, then the measured density divided by the standard (referenced) density will give you the ratio you are looking for. Both units must be the same.

For example, if you measure the density to be 80 kg/m^3, then simply divide by your reference of 100 kg/m^3 to find that your measurement is 80% of the referenced.

CS

#### Sjeanh

That would seem to be the logical solution, however, with the density calculator I found online (which does not give the underlying formulae) the % does not appear to be a direct calculation. Example: Temp = 75 F; Humidity = 30%, Barometric pressure = 29.29; Altitude = 755 --> Air density = 1.126 Kg/m^3; corrected (std = 100) = 91.892. If I make the altitude = 0, I get AD = 1.164; corrected to 100 Std = 94.964. I think I'm missing something, or the program is missing something, but I can't find a formula for what is going on. I'm about 25 years past college and I've not used this much, but I need to figure out what the full formula is (including altitude and humidity) to calibrate gauges to measure air density percent... I don't really want to trust the program I found online to calibrate unless I can verify that it is working correctly....

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#### engware

Hi there:

Here is another online calculator that provides gas and/or air density based upon the ideal state equation.

URL is as follows:
http://members.aol.com/engware/calc7.htm [Broken]

In general, the state equation is given as:

pv = RT

density = 1/v

Thanks,

Gordan

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