Bottle Shape and Failure
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?
In a liquid or any fluid at rest, the pressure is the same in all
directions. The failure of the bottle is due to stresses that remain in
the glass when the bottle is cast. These stresses tend to be greater in
places where the curvature of the bottle is greatest. If there were any
differences in the pressure in different regions of a fluid, gas or low
viscosity liquid, the fluid would move to equalize the pressure
Your student was partially correct. What most likely cause you explosion
was an increase in stress at the corners of the triangular bottle. A fluid
contained in a bottle will exert the same amount of force perpendicular to
the walls of the container at every point of the bottle. What caused the
problem was the fact that the angular shape of the container creates what is
know as stress intensities. The change in shape, i.e. the sharp corner of
the triangle, causes an increase in stress. This is a common problem in
mechanical behavior of materials in many contexts. For instance, a simple
hole in a plate will increase the stress around the hole by sometimes up to
a factor of 3. Once you increased the pressure of the bottle contents, you
increased the stress on the bottle. At the corners you probably increased
the stress by some multiplication factor that exceeded the yield strength of
the bottle. Also, with glass, slight flaws such as micro-cracks around a
corner (or anywhere for that matter) can be exacerbated by an increase in
stress. Throw in the multiplication factor of stress intensities, and you
get the explosion. That is the brittle nature of ceramics and glasses.
This is one of the reasons I still use a cork screw to release my bottle of
Christopher Murphy, P.E.
Air Force Research Laboratory
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Update: June 2012