Re: [Phys-l] Buoyancy again

["Robert Cohen" <Robert.Cohen@po-box.esu.edu>]

This is the way I look at it and am curious to see if it passes muster
(whatever that means).

1. The pressure in the warm blob increases due to the increase in
temperature.

2. The warm blob pushes against the cool surrounding air and expands.

3. Basically, it will expand on top and contract on the bottom (leading
to your rising bubble) and, with a lower density (having expanded) it
will continue to rise.  One way to see why is to break down the process
as follows:

3a. First let the warm blob only expand vertically until the pressure at
the surface of the warm block is the same as the pressure of the cool
surrounding air at the surface.

3b. In hydrostatic balance, if the pressure between cool and warm is the
same at the bottom then the pressure cannot be the same above the
surface, since the the densities are different (dP/dz is proportional to
rho*g).  That means the pressure at the top of the warm blob is greater
than the pressure of the cool surrounding air (at the same height).

3c. Due to the pressure difference at the top (greater pressure in the
warm blob), the top of the blob expands sideways.

3d. The increased air on the sides increases the pressure near the
surface in the cool air.

3e. Due to the pressure difference at the bottom (greater pressure in
the cool surrounding air), the bottom of the blob contracts.

----------------------------------------------------------
Robert A. Cohen, Department of Physics, East Stroudsburg University 
570.422.3428   rcohen@po-box.esu.edu    http://www.esu.edu/~bbq 

> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu 
> [mailto:phys-l-bounces@carnot.physics.buffalo.edu] On Behalf 
> Of LaMontagne, Bob
> Sent: Tuesday, January 04, 2011 6:47 PM
> To: Forum for Physics Educators
> Subject: [Phys-l] Buoyancy again
>
> I would like to return to the informative discussion we had 
> about buoyancy. If my memory serves me correctly, we seemed 
> to agree that a wooden post that was less dense than water, 
> driven vertically into a lake bottom such that its top was 
> submerged, would actually be under compression (with no net 
> upward buoyant force acting). This brought into question the 
> interpretation of the common mantra: "the buoyant force 
> acting on an object is equal to the weight of the water it 
> displaces."  I don't wish to revisit that problem and please 
> forgive me if my summary is not exactly correct - I realize 
> there was some dissention on the conclusion and the mantra.
>
> One aspect of the problem was the idea that if an object less 
> dense than water was submerged on the bottom of a beaker in 
> such a way to exclude all water beneath it, the net force 
> acting on it would not be upward. An argument was made that 
> if a little water was allowed to seep under a portion of the 
> bottom of the object, there is a point where the ratio of the 
> area of the wetted bottom to that of the non-wetted bottom 
> can become large enough so the net vertical force on the 
> object is zero. If the ratio increases, the object will rise.
>
> My question involves a blob of air in contact with an asphalt 
> parking lot. That blob of air will attain a significantly 
> higher temperature (and lower density) than the surrounding 
> air. Why does it rise? It is in intimate contact with the 
> asphalt and none of the denser air has seeped under it (or 
> perhaps it has?) to mimic the case mentioned above of the 
> object at the bottom of a beaker. 
>
> These bubbles certainly do rise - I have used them often as a 
> glider pilot.
>
> Bob at PC
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