# Density of moist air at high temperatures?

1. Dec 27, 2013

### jblc

I've spent hours trying to understand conceptually how to find the density of moist, hot air at high temperatures, eg at 600° C. Any help would be great. This is not a homework problem, but I'm preparing for a problem i will likely encounter shortly at work, and thermo is outside my specific expertise.
I'd like the density because i would like to find the Reynolds number of an air flow (i need Rey# to find air flow in a tube by two pressure measurements). I'm new to thermo and fluids, but am learning as fast as possible.

1. Generally, density of moist air is a simple equation
Density = Pdry / (Rdry*T) + Pwet / (Rwet*T)

Finding the water vapor pressure Pwet is proving tricky. Of course once I have Pwet I can find Pdry = P - Pwet, and evaluate the above equation. The system is near atmosphere, ~1000 hPa.

There are equations by Herman Wobus, and also the simplified version Pwet=c0*10(c1*T/(c2+T) ), but both equations break down for high temps.

How does one find the vapor pressure at high temperatures?

2. Complicating the above is that it's unclear how to find the Relative Humidity at these temps. Is it correct that the Dew Point is needed as the temp T inserted into the Wobus equation, which i tried using to find Pwet? My knowns are the amount of water removed from a mixture at a given temp, and hopefully also a given air flow.
To find the Dew Point i need to find the RH, which i tried using Psychrometric tables; none go to temps that high, nor are they accurate enough at high slopes.

Thoughts? Am I missing something fundamental here? I'm in a loop, with my goal being calculating an air flow of a known temp, with a known pressure drop. To find Density I need Dew Point, but to find Dew Point requires R.H., but to find RH I need gas flow, but to find the gas flow I need the Reynold's Number and thus Density.

2. Dec 27, 2013

### Simon Bridge

I'd ask the hot-air balloon people:
https://www.brisbanehotairballooning.com.au/faqs/education/116-calculate-air-density.html [Broken]

You should consider what you want to do the calculation for - so you don't break you brain trying to factor in every possible complication. The link starts with the same relation you do and discusses finding the different terms. i.e. finding $p_{wet}$ via the Wobus polynomial.

There are other ways, so that should provide a starting point if it's not good enough for your needs.

Last edited by a moderator: May 6, 2017
3. Dec 27, 2013

### jblc

Thanks, I actually started with that link when learning about this. I can't use their Moist Air Density calculators because they require either RH or Dew Point; and I can't find RH (or dew point) without air velocity, but I need Moist Air Density to find velocity in the first place.
Dry Air Density is easy, but i'd like to know how to find the Moist Air Density.

4. Dec 27, 2013

### Simon Bridge

By "air velocity" you mean the speed of sound in air?
http://www.sengpielaudio.com/calculator-airpressure.htm

To get the relative humidity you do need to know how much water is in the air.
No getting around that - it is something you measure as you can imagine, the same volume and temperature of air may have a wide range of humidities. You can probably get a ballpark figure from the circumstances.

Last edited: Dec 27, 2013
5. Dec 27, 2013

### jblc

By air velocity, I'm referring to the flow rate of a gas. For example, if V m3/hr of gas passes through an opening of area A, the gas velocity V = X / A.

Yes, to find RH I need to know water content, of course. I do know how much water is transferred the air, but I need to know how much air is picking up that water, in order to find the relative humidity of the resulting gas.
This is an evaporating system, where the water is transferred to the gas. Just to clarify what I'm referring to: if a small volume (very slow air flow rate) picks up the quantity of water, then it's a larger RH. If the flow rate is very large, then a larger volume of air will pick up that same amount of water, and thus have a lower RH. The temperature of the gas is assumed to be known.

6. Dec 27, 2013

### Simon Bridge

OK - then the flow rate is something else you need to measure - either directly or calculate from other things you know.
I am afraid that your descriptions are far too vague for anybody to be able to help you.

What is this all for?

7. Dec 27, 2013

### SteamKing

Staff Emeritus
At 600 C, you don't have moist air anymore: you have hot air mixed with superheated steam.

8. Dec 27, 2013

### Staff: Mentor

600 C is above the critical temperature of water, so speaking of the relative humidity (or of air saturated with water vapor) doesn't make any sense. Somehow, you need to know the mole fraction or partial pressure of the water in the air stream. This should arise from your processing. The average molecular weight of the gas is equal to the mole fraction of water times 18 plus the mole fraction of air times 29. You then use the ideal gas law with this molecular weight to get the density: ρ=PM/(RT), where P is the total pressure.

Chet

9. Dec 27, 2013

### jblc

Okay, let's say I have the flow, and this is superheated steam. How does someone calculate the density of superheated steam? When is something superheated steam, as opposed to just hot moist air? Is it above a certain temp, eg 150 C?

10. Dec 27, 2013

### AlephZero

"Superheated steam" means the conditions are such that the temperature can fall without and water condensation.

Since your OP said the pressure is approximately 1 atmosphere, that means any temperature above 100C.

The minimum temperature for superheated steam increases with pressure, in the same way that the boiling point of water increases with pressure.

Post #8 explains how to calculate the density (it was probably posted while you were typing #9)

11. Dec 28, 2013

### Simon Bridge

Oh good - someone beat me to it ... all the time I was out I had this nagging feeling I was missing something :)
It's not the balloon people you want - it's the steam engine people.

I think we need to know the exact situation to help you properly.
i.e. do you have very hot air from an oven vent bubbling through a water bath?
The specifics will change what you need.

12. Dec 28, 2013

### Staff: Mentor

You can determine the mole fraction of water in your gas stream by measuring the dew point.