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Time to run out water (Posted on 2006-07-13) Difficulty: 3 of 5
Consider a solid sphere (capable of withstanding full vacuum) of 3m diameter filled completely with water resting at sea level. It has a 10cm hole at the bottom with a cork on it. If you open the cork, what is the time taken for water to completely drain out.

What happens for higher diameter spheres?

No Solution Yet Submitted by Salil    
Rating: 1.2500 (4 votes)

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The Bloop Factor; size matters | Comment 9 of 11 |
I believe that for smaller holes, the liquid will stay in the sphere since any fluid exiting the sphere will create a vacuum at the top inside of the sphere.  The downward hanging meniscus of water will be pulled downward by gravity, but upward from the adhesive force of the water above it, which is pulled upward by the suction from the tiny vacuum.  This depends somewhat on the viscosity of the fluid.  And probably surface tension plays a role. 
(There are glass vials of medication, partially filled:  you break off the top, invert it, and the liquid stops at the bottom of the glass. )

For a very large hole, say the diameter of the hole is the diameter of the sphere:  if you invert a bowl of water, all the water falls out immediately.

I suspect there is an intermediate size hole where the greater weight of the water bulging downward breaks the surface tension and a volume of air enters the sphere as a quatity of water exits, creating the "bloop, bloop, bloop" effect well known to anyone who has ever emptied out a large bottle.  Not sure if this is a break in the meniscus surface allowing a bubble to enter, or a vortex the dips down from the top inside of the sphere.

But the details of what creates the "bloop" activity, or what equations govern the bloop effect remain a mystery to me.

  Posted by Larry on 2006-07-14 17:16:25
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