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Bottle Shape and Failure
Name: Selden
Status: educator
Grade: N/A
Location: CA
Country: N/A
Date: 1/1/2006
Question:
I am an English teacher but like to talk science
sometimes. Some years ago, I had an air-pump wine bottle opener
that with a needle into the cork pumped air into the bottle and
popped the cork out. I liked using it because it was innovative
and very cool. Once, I used it on a triangular-shaped bottle of
sangria from Spain and the bottle exploded, which in retrospect
seemed logical, and I learned a lesson: "science is everywhere,"
my scientist colleague used to say. Recently, I got in a rather
in-depth argument with one of my students. We both agreed that
the non-circular bottle shape caused the problem, and would every
time. I said the bottle exploded because the triangular shape
caused there to be different pressure at different points on the
bottle surface area. He said that pressure was distributed
equally to all points by the liquid, but the bottle exploded
because the glass at different points was weaker than at others.
Who was right?
Replies:
Hi Selden
The pressure within the bottle will be close to the same everywhere
(it will increase a bit more as you approach the bottom as the weight
of the wine will contribute to the pressure). I believe what you
experienced was an uneven distribution of strain within the glass.
The discussion that follows assumes uniform strength. If the glass
was, in fact, weaker in some places, the problem would be further
compounded.
Consider the cross-section of your bottles sliced radially. When you
pressurize a glass cylinder, the resulting strain (deformation) on
the glass is confined to a direction tangent to the glass and will be
uniform within the glass cross-section. That is, the glass wants to
become a larger diameter. When you pressurized the triangular
bottle, the sides wanted to become more cylinder-like. Consequently,
the strain will have a component in the direction perpendicular to
the side of the bottle. This puts a lot of stress on the corners
since deformation at those points will have contributions from the
two adjacent walls. Since glass breaks in tension, not in
compression, it is likely your triangular bottle initially broke on a
corner starting from the inside.
Hope this helps.
Robert Froehlich
I am afraid I will have to give credit to your student on this one.
The pressure is (or rather WAS) equally distributed throughout the bottle.
However, due to the non-circular shape, the structure of the bottle itself
was not equally strong everywhere.
Ryan Belscamper
This sounds like a classical example of fracture of a brittle object.
First some basics: a material will fail whenever the mechanical stress at
some point exceeds the strength of the material. Glass is fairly strong,
but brittle. When a triangular-shaped bottle is pressurized, the pressure
will push against all of the internal walls. The resulting forces will
cause stresses in the glass. In a triangular bottle, comparatively large
bending stresses will be generated at the triangular apexes, and a crack in
the glass might open up, which then propagates through the glass, and it
explodes. A square bottle would be expected to fail at a low pressure too.
A cylindrical or spherical bottle will experience tensile stresses and some
bending stresses, but the stresses will be smaller than in the triangular
bottle under pressure, everything else being equal. Thus, industrial
pressure vessels tend to be cylindrical or spherical, regardless of the
material that they are made of. Airplanes are nearly cylindrical, so that
they can resist the internal air pressure.
As to which one of you was correct, neither and both. The internal pressure
was uniform against all the glass surfaces. But the resulting forces built
up large stresses in certain parts of the bottle.
It would be possible to make a stronger triangular bottle (if that was
required) by wisely making the bottle thicker in the parts that experience
the greatest stress. It would still not be as good as a cylindrical bottle
at resisting pressure.
Bob Erck
Dear Selden,
One thing that is definitely true is that the pressure exerted on the inner
wall of the bottle is everywhere the same. So the force per unit area is
everywhere the same whether it is a circular or triangular bottle or any
other shape.
The bottle may just have been defective; I am surprised that the bottle
exploded. If that were common, they would certainly have difficulty selling
bottle openers of that type, which I also often use (so far without breaking
any bottles).
It is true, though, that a cylindrical bottle (especially with a rounded
bottom) is intrinsically stronger that a bottle with flat sides. With a
cylindrical bottle, the walls are under tension -- trying to stretch the
walls. With flat walls, however, the pressure is also trying to bend the
flat walls, which makes it easier to break the glass. To convince yourself,
try to break a plate of glass by stretching it (impossible!) and then by
bending it (easy!).
Best, Dick Plano,
Professor of Physics emeritus, Rutgers University
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Update: June 2012
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