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Re: Air in Water




brian whatcott writes:
Thanks to some delightful observations by Bill Beaty on another list
I have been considering the implications of an air bubble rising
through a long water column. If it were 34 feet high, we would
expect the diameter of such a bubble to increase by 59%
If this is the case, would you expect such a bubble to
1) Maintain constant speed?
2) Accelerate towards the surface?
3) Slow down towards the surface?

The answer would depend on whether or not the water column was sealed at
the top. As the bubble rises, the pressure of the water above decreases
and the bubble becomes larger, displacing more and more water. In
accordance with Archimedes' principle, buoyancy depends on the volume of
water displaced. Therefore the bubble would rise faster and faster as it
is accelerated by an increasing buoyant force.

If the top of the water column is open (as it is in a geyser) the
bubble's rise is not only affected by an increasing buoyant force but
there is another factor that accelerates its rate of acceleration. In a
narrow column, as the bubble rises it pushes water out the top of the
column, reducing the pressure of the water that presses on the bubble.

The combination of increased buoyancy coupled with reduced water pressure
work together increasing the rising speed of the bubble until it reaches
the surface. This acceleration could be called a "positive" acceleration
because the speed is continually increasing ....or it could be called a
"negative" acceleration by those who consider the downward acceleration
of gravity to be positive.

Herb Gottlieb from New York City
(Where upward accelerations are positive)