Undergrad Calculating the rate of rise of air

[Gavin Sweeten]

I know there are many factors that affect this question, such as altitude etc, but in its simplest form...

- How fast does a parcel of air rise if, say, the parcel of air is at 5 degrees centigrade in a room filled with air at 0 degrees C. (Maybe I should be using Kelvin?). Just need to get an approximate figure in m per second.

 

[Nidum]

Just to get a general idea of this think about a balloon filled with air . Assume that the balloon itself weighs nothing and that it always holds the same volume of air .

If you fill your balloon with hot air then seal it and release it in a room full of cold air what forces do you think would be acting on the balloon that would cause it to rise ?

 

[sophiecentaur]

There is a simple experiment you could carry out to get an idea about rate of movement. Shine a torch through the air above a hot object (say an electric hob plate or a clothes iron. In a dark room, you will see the dust being carried up by the convection currents at a similar speed to your "parcel". Check the temperature of the rising air and of the room.
Yes - Kelvin temperature would perhaps be better as the density will be pretty well inversely proportional to the air temperature in K. (Charles' Law, I think.)
A calculation would be harder than an experiment because it would depend on the size of the parcel, I think. This would be because the friction against the ambient air would be proportional to area (r²) and the buoyant force would be proportional to the volume (r³).

 

[JRMichler]

What Nidum said. Here is a good description of how to estimate the rate of rise for a massless spherical balloon: https://www.grc.nasa.gov/www/k-12/airplane/dragsphere.html. It's an iterative calculation because you need the velocity to get the drag coefficient to get the velocity. That's after you calculate the lifting force from the density difference.

For a better estimate, find a meteorology forum. Meteorologists do this type of calculation all the time, although on a much larger scale.

 

[sophiecentaur]

Meteorologists do this type of calculation all the time, although on a much larger scale.

Very different. I wonder whether extrapolating on Cloud - sized parcels would work?

 

[anorlunda]

Glider pilots live or die on that number. They actively seek "thermals" to gain altitude. I'm not an expert, but I have seen 100 meters/minute and I suspect that three times that rate is possible.

Do you live in a place where you see flocks of soaring birds flying tight circles in the sky? They are riding thermals up. If you're clever, you can measure their rate of climb using trigonometry.

Near mountains, much higher vertical rates are found, but there is more than temperature at play.

 

[CWatters]

Glider climbing at 14kts for awhile. That's 16mph or 7m/S upwards.