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Full Bottle, Hole, NO Leak
Name: Bob
Status: student
Grade: 9-12
Location: PA
Country: N/A
Date: 5/31/2005
Question:
Why does water not leak out of a closed plastic bottle
(cap tightly secured on top) with a hole poked in it?
Replies:
That is because the surface tension of water makes a rather good seal if the
hole is small enough. Water molecules attract one another, which is the
cause of surface tension. Thus molecules in the middle of the hole feel a
force pulling them back into the bottle from molecules inside the bottle.
There are obviously no molecules outside the bottle to exert a balancing
force by attempting to pull the surface molecules out. This is why surface
tension is apparent mostly at surfaces. If the hole is large enough, the
pressure pushing the molecules out overcomes the surface tension forces
holding them in.
Having the bottle tightly sealed except for the small hole means that if the
water bulges out even slightly, the pressure inside the bottle decreases so
the force pushing the water out decreases. Notice that if you squeeze the
plastic bottle, you can quite easily push the water out (unless the hole is
very small so the surface tension effects are very large).
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
The reason (answer) is one of two, depending upon the configuration.
If the hole is in the "top" with a bit of air space between the water
level and the cap, the water can only escape by diffusion through the small
hole in the cap. This is a very slow process, which would appear negligible
on any reasonable time scale (hours to days).
If the bottle is inverted so that the hole is located beneath the water
level there is a balance of pressure between the outside atmosphere and the
air "pocket" inside the plastic bottle. The pressure difference is just the
height of the water inside the plastic bottle. After a few drops of water
"dribble" out of the hole, the pressure of the trapped air space + the
height of the water inside the plastic bottle will equal the outside
atmospheric pressure, and no further flow of water from the plastic bottle
will take place. You probably would not even notice the loss of that small
amount of water. You recognized the key factor: (cap tightly secured on
top).
Vince Calder
Bob-
There are two forces helping hold the water in the bottle:
the atmospheric pressure from the air outside, and
the surface tension of the water at the hole.
When you first poke the hole or fill and cap the bottle, I would
expect a little water does try to dribble out of the tiny hole. When it
is finished, it leaves a partial vacuum inside the bottle, just enough to
hold back the water pressure inside.
The larger the air volume at the top of the water, the more water will
need to dribble out to build up this partial vacuum. So as a
demonstration it probably works best with the bottle as full of water as
you can get it, only tiny air bubbles at the top.
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Such partial vacuums only hold back water up to about 30 feet
high. Water deeper than that has water pressure higher than one
atmosphere, so it pushes right out through the hole until it is only 30
feet higher than the hole. No air bubbles need to go
back in through the hole. The newly emptied space at the top of the water
would be a vacuum, not air, with only a little water vapor pressure in it,
which is only about 1/50 of an atmosphere at room temperature.
Your bottle, of course, is maybe 1 foot high, so you will not need to
think about that.
Surface tension tends to hold back water pressure equivalent to 0.05
to 2 inches of water depth.
It only has effect if the water is trying to inflate one small round
droplet at a time, which then detaches and falls away.
The smaller the hole, the larger the pressure required to squeeze out a
small round droplet of water.
Once there is a continuously connected stream of water outside the bottle,
surface tension can't create much back-pressure.
So water can "wick" or "wet" or "seep" past this barrier if the material
of the bottle is very wettable.
On the other hand, if it is a very water-repellent plastic such as
poly-ethylene (often abbreviated "PE"), or DuPont's Teflon (TM),
surface tension will cause the most back-pressure. Then there will be
some excess water depth required to start a flow of droplets or a stream
of water. Soft-drink bottles are "PETE" (poly-ethylene-ter-ephthalate),
and it tends to act somewhat
water-repellent too, when it is clean and smooth.
You can see that atmospheric pressure is the much stronger force.
But surface tension is why flow of only one direction (water going out, or
air going in) usually happens at a small hole.
If both directions could flow simultaneously, air bubbles going in would
fill the partial vacuum inside, and water would keep leaking out.
I guess that is why it takes two holes to let the water out. One can be
"outbound" and the other can be "inbound".
Try to guess how the holes choose which to be...
Jim Swenson
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Update: June 2012
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