# In a column of rising hot air, is the velocity higher at the top?

Since the movement of the air is induced by buoyancy, i. e. there's a constant force acting on the air, so I would expect the velocity to increase during ascent, much like an object falling down due to gravity accelerates.

But wouldn't a velocity gradient tear the column apart along the axis? Or would it just lead to a corresponding pressure gradient and a deformation of the column (thinner at the top)?

If there is acceleration, there's probably a terminal velocity, just like with objects falling down through the atmosphere. What would that be limited by?

There's two effects that I would like to neglect for the purpose of this question, if possible, the dissipation of the warmer air into surrounding air and the cooling of the air as it rises. I suspect with a high enough $\Delta T$ and a column that is wide enough and not too tall, we can ignore those (for a bit, anyway)?

And just for context, what brought me to this was the idea of having hot air rising through a chimney to act as a pump via a constriction in the chimney that creates a Venturi effect. I was wondering whether it would be better to put that constriction further up in the chimney, so I get a higher pressure difference because of a higher velocity.

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I think it's better to understand what air actually does. It does not rise in a column. It rises in a toroidal vortex or "mushroom cloud". What's more, there is in-flow of air beneath it, and out-flow above, both rotating by coriolis effect (angular momentum). Its energy and momentum are the energy and momentum of that complex. –  Mike Dunlavey Feb 20 '13 at 15:14