Calculating Moist Air Density 1

[sloth4z]

I am trying to find the density of air going into a fan system based on Dry and Wet Bulb Temperatures and Pressure. AMCA Publication 203 says to use the spychometric chart. Is a chart really the best way to go? All of the lines in the chart are straight which leads me to believe that there should be a simple formula to calculate it. Can someone enlighten me as to why a chart is used to calculate moist air density?

I've seen a calculator on the internet that calculates it for you. Do calculators like this contain tabulated data that is interpolated, or do they use the formula I am looking for?

 

[KernOily]

Psych chart is the shortcut. It gives you relative humidity and humidity ratio starting with Tdb and Twb. From those you determine the partial pressure of water vapor (and as you recall from Thermo II, partial pressure = mole fraction) in the air. Then you can calculate the air-water vapor mixture density.

The calcs themselves are found in any thermo text. The procedure is given in there.



Thanks!
Pete

 

[Yorkman]

Although the lines look staight the Db temperature lines on the A.S.H.R.A.E. Psychrometric chart do not run perpendicular to the base line or (0% humidity line) and the Wb temerature lines do not run parallel to the enthalpy lines. The humidity lines are almost exponential in nature, because of these issues I'm not sure there is a "simple" formula to calculate density changes to moist air.
I'm with 74Elsinore the Psychrometric chart is the down and dirty "simple" method to finding any changes in moist air. After plotting your Db and Wb values you can locate the specific volume of the air, taking its reciprocal will get you the density.

I'm not a real engineer, but I play one on T.V.
A.J. Gest, York Int./JCI

 

[quark]

The preference to a psychro chart seems to be due to nostalgia rather than simplicity, when you have such cute and spreadsheets like,

http://www.hvacware.net/engrproj.html

However, for a person who never bothers to check even the spelling of a psychrometric chart, the chart itself is a good starting point.

sloth4z,

If you google with the tag 'psychrometric equations' you will come across many links.

 

[25362]

There are formulas such as the complicated CIPM-81/91 and simpler. Their accuracy depends on the uncertainties of the basic measurements.

You may visit the following link and go to formula (2.8) and following paragraphs:

http://www.ce.utwente.nl/rtweb/publications/MSC2006/pdf-files/001CE2006_Mocking.pdf

It took me quite a while to convince a colleague that moist air has a lower density than dry air at equal T,P.

 

[Cockroach]

Yeah, thermodynamic tables on Saturated Air ought to cover it. You need to determine quality based on start and end states of the working fluid.

Try the various textbooks, there are several examples of this used in the HVAC industry.

Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada

 

[25362]

A simple formula for atmospheric air from Google:

[ρ]_moist = [ρ]_dry (1+x)[÷](1+1.608x)​

where x is the specific humidity in mass per mass units

 

[katmar]

Sloth4z,

There are fundamental formulas for all of this, and the better programs should be based on them. However, I would not be surprised if some of the programs and spreadsheets that float around the internet are actually based on tables of data read off a psychrometric chart! But even if they are not rigorously correct they are probably good enough for most work.

Once you have the temperature, pressure and moisture content of the air it is a simple matter to calculate the density using the CIPM-81/91 formula referenced above. For normal air conditioning work you can safely assume that Z (gas compressibility) is 1.00.

The tricky part is to calculate the composition from the wet and dry bulb temperatures. This topic was discussed in thread724-129442

Harvey

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[KernOily]

"For normal air conditioning work you can safely assume that Z (gas compressibility) is 1.00."

Not to hijack this thread, but as a practical matter, you can use z=1.0 (ideal gas assumption) for pressures up to about 60 psig for engineering work with very good accuracy, certainly at least as good accuracy as any end device you are using to take your measurements...




Thanks!
Pete

 

[sloth4z]

I continued to read the your replies and the AMCA publications. AMCA publications 210 and 203 actually have a method to calculate density from Wet Bulb Temperature (Tw), Dry Bulb Temperature (Td), and Absolute Pressure (Pb). It makes sense now why people like to use the chart. They first calculate the Saturated Vapor Pressure (Pe) at Tw using a table (I can't fit a good regression line to it without using a higher order polynomial), and then calculate Partial Vapor Pressure (Pp) using the formula...

Pp = Pe - Pb * ((Td-Tw)/2700)

and finally calculate the density (rho) using the formula...

rho = 70.73 * (Pb - 0.378 * Pp) / R / (td + 459.67)

R is the gas constant (53.35 ft*lbf/lbm*R).

Quark: I was very impressed with the spreadsheet, and I appreciate you sharing it with me. One thing I was concerned about is that in the worksheet the Saturated Vapor Pressure is based off of the Dry Bulb Temperature, but the VBA formulas base it off of the Wetbulb Temperature. AMCA publications 210 and 203 both base it off of the Wet Bulb Temperature. Is this a simple mistake, or was this done on purpose?

 

[quark]

sloth,

At saturation, dry bulb temperature is equal to wet bulb temperature. So, you can calculate saturation vapor pressure if you know the dry bulb temperature.

But, somehow, I feel that you may be asking for something else. I am sorry if I couldn't grab it.

 

[sloth4z]

I wanted to know why you would need the saturation pressure at the dry bulb temperature, but I figured out later that you use this value to calculate the relative humidity. It's been too long since I took thermodynamics. Thanks again.