Re: [Phys-l] Definition of upthrust or buoyancy

[John Denker <jsd@av8n.com>]

On 10/19/2010 08:19 PM, M. Horton wrote:

> Where does the buoyant force come from?  Or to ask it in a slightly 
> different way, what causes the buoyant force on an object and how?  I've 
> seen answers such as "The difference in density between the liquid at the 
> bottom of the object versus the top," "The differnce between the pressure at 
> the bottom of the object and the top," "the now-elevated water level pushing 
> back," "the displaced water trying to get back in," and other equally 
> non-convincing arguments.

As Jeffrey Schnick hinted:  It helps to think about the microscopic
physics.  At the end of the day, the only thing that is going on is
molecules of the fluid colliding with the surface of the object.

1) When we consider a large number of microscopic collisions and 
summarize them in macroscopic terms, this is what we call "pressure".  
So at the end of the day, the buoyant force on the object is due to 
differences in pressure.

  We are making a number of conventional assumptions, notably that
  neither the object nor the fluid is in motion.

  Also:  It is not just the topmost top and the bottommost bottom that
  are acted upon by the pressure;  the sides count also, if there is
  any slope to the sides.  There are scads of classic exam problems
  that revolve around odd-shaped buoyant objects.

2) Differences in density have got nothing to do with any of this.  
An incompressible fluid would exhibit no differences in density, but 
would still produce buoyancy in the usual way.

3) The /total/ density matters indirectly, because it is what produces 
the differences in pressure required by item (1).  This is easy to
understand in terms of force balance (aka momentum budget).  The
gravitational force on each parcel of fluid has to be balanced by
something ... and in fact it is balanced by delta pressure.

It is an interesting exercise to calculate the pressure profile of
the entire atmosphere by integrating the weight (per unit area) of 
the air column.
  http://www.av8n.com/physics/altimetry.htm