How fast does hot air rise and disperse?

[dBrandon/dC]

I know there have been some forums here about hot air rising, but I'm curious - how fast does hot air rise? Also, how fast does it disperse? If we consider steam, for example, rising and dispersing horizontally from a boiling pot of water. Does anyone know some (hopefully simple) equations to describe this?

 

[Gabe21]

to know how fast hot air will rise you would need to know the type of gas, how hot it is, elevation above sea level, whether it is rising in a tube or in the open, and the volume of hot gas. as you increase the temp and/or amount it will rise faster without dissipating. if you look at a video of a bomb exploding the hot gas rises in a ball that circulates. (http://www.youtube.com/watch?v=WwlNPhn64TA&feature=related)
hot air will dissipate fast unless it rises at a certain velocity allowing it to stay in ball form.

sorry but i don't have a simple equation for you.

 

[dBrandon/dC]

It seems to me the rising would be the easier one to figure out. I know some people haven't liked the description of hot air rising as a result of buoyancy, but considering that as an approximation, I can see the buoyant force decreasing as the body of air rises and/or changes (cools, diffuses, etc.). I think the speed of dispersion question is probably harder - a fluid flowing into/through another fluid. ...

 

[Gabe21]

if you take 1 cubic foot of gas at sea level and heat it up to a couple hundred degrees it will expand. so let's say it expands to 1 1/2 cubic feet. it will create lift because it displaces 1/2 cubic foot of cool air around it. so if atmospheric air weighs .005 grams per 1/2 cubic foot that's how much lift it will create. just like a hot air balloon. to figure out how fast it will rise you would have to assume gravity is non existent and figure out how fast .005 grams of thrust can accelerate a 1 1/2 cubic feet of air weighing .01 grams.

i didnt use the actual weight of the air just to keep it simple.

 

[dBrandon/dC]

Hmmm ... thrust. Not a bad idea. But what about the speed of expansion of a body of hot air?

 

[Gabe21]

that depends on how much heat u put into it over a certian time period

 

[dBrandon/dC]

Alright, let's assume the volume of air in question is saturated by steam rising off a boiling pot of water. Let's say the air is 0.1 x 0.1 x 0.01 m, or 10^-4 m^3, it's 100 degrees C, and it has a density of 58g/m^3. The ideal gas equation gives its initial pressure as about 100 mBars. If the ambient air is at standard temperature and pressure (about 15 degrees C and 1 Bar), how fast will the water-saturated air rise and expand?

 

[Gabe21]

in this case you would measure the expansion in reference to the water. so if you could boil off 1/2 cubic foot of water in one minute you would create 8000 cubic feet of steam. so the steam would expand at 16000 cfm(cubic feet a min). as far as the steams effect on the air around it, you would need to know how much the air expands when it goes from 15 degrees c to 100 degrees c and add it to the 16000 cfm.

 

[Gabe21]

in this case you would measure the expansion in reference to the water. so if you could boil off 1/2 cubic foot of water in one minute you would create 8000 cubic feet of steam. so the steam would expand at 16000 cfm(cubic feet a min). as far as the steams effect on the air around it, you would need to know how much the air expands when it goes from 15 degrees c to 100 degrees c and add it to the 16000 cfm.

it would expand at 8000 cfm, my bad

 

[hotvette]

I believe the general topic you refer to is called 'natural convection'.

http://en.wikipedia.org/wiki/Natural_convection

 

[Borek]

You will need viscosity to calculate anything IMHO.