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 Click here to return to the Engineering Archives

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