What is the formula for calculating air convection velocity?

[andytinker]

Hi
I'm trying to workout the velocity of air inside a pipe that's sealed and ten meters long.
I've found this Air Velocity

vc = 0.65 [g l dt / (273 + te)]1/2 (1)
where
vc = velocity in center of airflow (m/s)
g = 9.81 - acceleration of gravity (m/s2)
l = vertical distance from bottom of the surface (m)
dt = te - ts= temperature differanse between surface and room environment
ts = temperature surface (oC)
te = temperature surrounding environment (oC)

The pipe would be on the same level, would 10meters be for the vertical distance or 0meters.
Thanks

 

[mfb]

If the pipe is sealed, how can it have air flow?
In a horizontal pipe, the mechanism which is used in the formula (temperature difference inside/outside) does not work (vertical distance 0) and you get a flow of 0, unless you have other ways to generate a flow inside (wind, fan, ...).

 

[andytinker]

Thanks
If I had a temperature difference, what formula will give the gas velocity from hot to cold. If I have a fire on one side and water flow on the other to cool it. Would makeing the pipe large diameter at the hot end have any effect.

 

[mfb]

I am not sure how your setup is supposed to look like. If you connect a hot and a cold thing with a horizontal pipe, I would not expect a large net flow of air. Some convection inside (hot air on the upper side, cold air at the bottom, flowing towards the other side), but that is tricky to evaluate. The diameter of your pipe would be important, too, in this case.

 

[andytinker]

The pipe would be a circle joined at both ends, with one side being hot the other cool. I'm trying to workout the air velocity inside the pipe.

How would the diameter of the pipe effect the velocity? What would be the best way to get fast flow of air inside?
Cheers

 

[haruspex]

If the pipe's axis is literally a circle (i.e., it forms a torus), what portion of it is exposed to the heat source on one side and sink on the other? The whole semicircle in each case? Or do you mean it's more rectangular in form? Either way, please state all the dimensions involved.
I don't understand the references to 'surface' temperature in such a set-up. It sounds more like we need to know the temperature difference between the hot side and the cold side, and the thickness and conductivity of the pipe.

 

[andytinker]

The temperature on the hot side is 600C and 100C on the cold side. It is more a rectangle 1m by 5m. The hot and cold sides are in the 1m sides. The pipe is 2cm diameter and 3mm thick.
I thought that the ideal gas formula might come into it.
V = RT/P 345.7 * 600/101000 = 2.05 m3/kg

 

[mfb]

I think, you can use your formula here:

vc = 0.65 [g l dt / (273 + te)]1/2 (1)

l is the vertical distance => 1m
dt is 500 (K)
te is the cold side => 100.

 

[haruspex]

I think, you can use your formula here:


l is the vertical distance => 1m
dt is 500 (K)
te is the cold side => 100.

I'd be surprised if it's that simple. Where does this formula come from, Andy?
The horizontal distance will slow things a bit. The faster the air moves, the less time it has to come up to temperature in the vertical, and 1m is not very far to pick up such a big temperature swing.

 

[andytinker]

haruspex
The formula was from http://www.engineeringtoolbox.com/convective-air-flow-d_1006.html
The speed isn't much, but was thinking if you have a coil type shape with one side getting heated and the other cold, each turn in theory should add a couple m/sec?

Thanks for your help

 

[mfb]

Hmm... after a closer look at the formula, I think it neglects (internal) friction, but requires to have open ends. In this case, you cannot use it.

New approach: Calculate the driving force (coming from the different density at the vertical sides), assume constant mass flow everywhere, evaluate friction force and set both equal. Find some estimates for the 90°-turns or try to simulate them.
In any case, it gets more complicated than your simple formula.

 

[CWatters]

If you know the power transfer (eg the amount of energy being transported from the hot end to te cold end) you can probably work out the air velocity using the specific heat capacity of air...

For example if you know the energy flow and the temperature differential of the air you can work out the amount of mass transfer around the loop (Kg/sec). Then knowing the rough density of the air you can work out the flow rate in cubic meters per second. The average air velocity follows from the pipe dimensions.

 

[AlephZero]

I'm not convinced you will get any flow at all.

A thermosiphon works with a liquid (like water) because liquids are almost incompressible, so to a good approximation the density is only a function of temperature. But gases are compressible, so if your pipe system is a sealed loop with a hot side and a cold side, the pressure all the way round will just equalize and there will be no flow.

If you look at something like a Stirling engine, where the working fluid is air and the heat transfer is through "hot" and "cold" parts of the system similar to your loop of pipe, there is a mechanical device (a piston) to move the air where you want it to go. It doesn't just circulate on its own.

 

[haruspex]

I'm not convinced you will get any flow at all.

A thermosiphon works with a liquid (like water) because liquids are almost incompressible, so to a good approximation the density is only a function of temperature. But gases are compressible, so if your pipe system is a sealed loop with a hot side and a cold side, the pressure all the way round will just equalize and there will be no flow.

No, there will be flow. The hot side will be less dense. This is just normal convection.

 

[mfb]

A thermosiphon works with a liquid (like water) because liquids are almost incompressible, so to a good approximation the density is only a function of temperature. But gases are compressible, so if your pipe system is a sealed loop with a hot side and a cold side, the pressure all the way round will just equalize and there will be no flow.

The pressure cannot be equal everywhere, you need a pressure gradient at the vertical parts, otherwise the air would "drop down" due to gravity. However, the gradients are different at both sides (as the density is different), therefore you cannot get an equilibrium without other forces (here: friction as the air is moving).