[Phys-L] Re: Help with Fluids....

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

At 12:09 AM 12/2/2005, Ralph v. Philp,  you wrote:
> Okay....
> Imagine 3 vessels filled with water to the same height resting on a table.
> One vessel is a vertical cylinder, one is shaped like a "V", and one is
> shaped like an "A".  They all have the same area for the base.  You've see
> the situation before....Pascal's Vases?
>
> Now, I understand that the pressure on each base would be the same, and
> therefore the total force on each base would be the same.
>
> I also understand that the "V" shape would contain more total water, and
> therefore would weight more, and therefore would exert more total force on
> the table.
>
> What I don't understand is how the force on each base is the same, but the
> force on the table is not.  Is the additional weight of the water
> transmitted through the walls of the container to the table via the "edges"
> of the base, and that does not count as the force on the base due to the
> fluid pressure?
>
> What would be an effective way to explain this apparent paradox to students?
>
> Thanks for the help!
> ~ Ralph von Philp


A slightly more extreme case of this physics puzzle is the case of the
rose vase with a trumpet bell base, and a hemisphere sitting on a base
of equal area.   Both are naturally weghtless of themselves in the physics
  manner, and both filled to the same height with water.
  The pressure gradient with depth is identical in both of course.

In the rose vase, which tapers upwards, the water pressure on the base is
opposed by the water pressure on the concave outwards vase wall.
The total force due to the water weight is reacted through the base,
though the water is much less in quantity in this container.

In the bowl, the water pressure on the base is augmented by the
graduated pressure on the horizontal projection of its walls, still
  reacting its water weight.



Brian Whatcott    Altus OK    Eureka!
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