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Plastic Bottles and Water Columns
Name: Margaret H.
Status: educator
Age: 30s
Location: N/A
Country: N/A
Date: 2000-2001
Question:
Plastic bottles are filled with water and holes are
punched in the bottle at various heights up its side. How far does the
water spurt from the bottle and how does the distance change according to
the height of the hole.Why they spurt at different angles?
Replies:
The higher the column of water (distance from the top of the water to the
hole), the higher the water pressure. The higher the pressure, the greater
the force pushing water out the hole.
Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
Margaret,
Air pressure at the top of the water pushes down on the entire top surface.
Air pressure at the hole pushes in on the side at about the same pressure.
Air pressure from the outside has little effect on the water.
Gravity pulls down on the water. The weight of all the water above the hole
pushes down on all the water at the height of the hole. It is easiest to
see through conservation of energy. If a little water flows out, some water
moves down. Gravitational potential energy stored within the water
decreases, and the water leaving the hole gets it as kinetic energy.
Originally, 1 gram of water is at the top. After, that 1 gram at the top is
not there. 1 gram of water is leaving the hole. Everything else is the
same. (1/2)mv^2 = mgh. The speed of the water is sqrt(2gh), where h is the
height from the hole to the top of the water. As for direction, that
depends on exactly how the hole is cut. In a perfect cut, the water will
leave along an almost perfectly horizontal path.
After leaving the bottle, the water acts as a stream of projectiles,
accelerating downward at g=9.8m/s^2.
If you have the bottle closed, so that pressure in the bottle may not be air
pressure, then you must use Bernoulli's equation from fluid dynamics.
Dr. Ken Mellendorf
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Update: June 2012
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