AVR-Chat

--- In AVR-Chat@yahoogroups.com, "Brian" <blue_eagle74@...> wrote:
>
> I know pressure is equal on all sides.

Hmm.  This depends what you mean by "sides".  If you're counting the top and the bottom, then no.  Imaging a cube instead of the ball and imagine that it is oriented with one face parallel to the water surface.  Label the sides P, Q, R and S, going around, and the top and bottom T and B.  By symmetry, the pressure on P balances the pressure on R and Q balances S, so the cube does not move sideways.  Or, strictly, I should say the forces balance, but the force equals the pressure times the area and the area of all faces of a cube is the same.  How about the pressure on T and B?  Well, the bottom is deeper in the water than the top, so the pressure on B will be greater than the pressure on T.  The cube is being pushed up from the bottom with a greater force than it is being pushed down from the top.  That, in a nutshell, is bouyancy.  With a cube, it's almost trivial to caculate the net force, but Archimedes showed that the same rule applies to all objects, whatever their shape.  The force of bouyancy is equal to the weight of fluid displaced.

> So as the ball desends in the water
> the point of Bouyancy would raise
> from the center of the ball.

I'm not sure what you mean by "the point of Bouyancy".

> Would this cause it to rise faster
> at deaper depths?

If the ball and the water are considered incompressible, no.  As I hope we've shown, the force of bouyancy is constant with depth, so the force tending to make the ball rise is constant.  If the viscosity of the fluid is also constant, for example the temperature is constant, then the ball will rise at constant speed.

If the ball is compressible, perhaps a basketball, then as it rises and the pressure decreases it will expand.  As it expands it will displace more water and the force of bouyancy will increase.  So, it will rise slower at greater depth than near the surface.

If the ball is not compressible and the fluid is, perhaps airated water, then at greater depth the constant volume of the ball displaces a greater weight of the fluid and it will rise faster.  It would be possible to reach a point of stable equilibrium in which the force of bouyancy is exactly equal to the weight of the ball and it remains at some constant depth.  If it rises, the fluid density decreases and bouyancy is lost so it sinks again.  If it sinks too far, the fluid density increases and the additional bouyancy causes it to rise.

Graham.