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

[John Denker <jsd@av8n.com>]

On 10/21/2010 11:29 AM, Philip Keller wrote in part:
> 2.  The argument that "if you cut off the piling it floats so it
> must be in tension" had me convinced for a while.

That's a worthwhile Gedankenexperiment.  It has some simple
points and some tricky points, all of which are instructive.

> Or the reverse argument that if you wanted to add another layer to
> your piling, you would need glue.  But you wouldn't need glue -- you
> would just need to have smooth enough surfaces to push out all the
> water.....

But you would need glue, or chemical bonds, or a suction pump,
or something;  just setting the slice into place would not 
suffice, as we now discuss:

Scenario: We are working in deep water, where there is tremendous
pressure.  We are building a piling out of two slices, using the 
following fancy structure:

         XXXXXXX
         XXX XXX
         OXX XXO

         XXX XXX
         XXX XXX
         XXX  > 
         XXXXXXX

The piling material is buoyant, i.e. it wants to float up.
The bottom piece is anchored to the bottom somehow.  The
diagram is a slice along the axis of a cylinder.

Basic structure is indicated by X.  There is an O-ring seal 
at location O.  When we gently push the top slice into place
atop the bottom slice, at first it just sits there loosely, 
with water in the empty core region, and a thin film of water 
between the two slices.  We pump out the water using the pump 
at location >.

As we pump out the water, a tremendous suction-cup effect is 
created.  The top slice is no longer sitting there loosely;
it is firmly pressed down onto the lower piece.  The piling
as a whole is under tremendous compression.

Conversely, if we then switch off the pump and allow water 
to flow backwards through the pump, the suction-cup effect
will be released.  Water will weasel its way in and create
a thin film between the two slices.  The top slice will
float away, because it is buoyant.

So we see that both answers are possible:  For a piling
made of slices of buoyant material, each individual slice
is under compression, and:
  A) If water can get in between the slices, the structure 
   as a whole is under tension, in the sense that the 
   individual slices will float away, unless they are held 
   together by some explicit tensile force.  
  B) If water cannot get in between the slices, then a 
   suction-cup effect is produced, and the structure as a 
   whole is under compression.

Whether simply pushing two flat surfaces together suffices
to create the suction-cup effect is not clear.  I still 
consider this a pathological case.  It would not work easily 
or quickly (because of viscosity among other things) and it 
might not work at all.  It would raise all sorts of questions 
about the chemical nature of the surfaces, blah, blah, blah, 
and I don't want to get into it.

The two cases that arise in practice are relatively easy to
understand
 -- the "sitting there loosely" limit, and
 -- the "suction-cup" limit.