- posted 14 years ago
This will be about 20-times more information than most of you want to know about the engineering mechanics of this question, so feel free to stop reading at any time, lest you fall asleep.
For the purposes of answering this question, the bottle can pretty much be "idealized" as a cylinder. Imagine two types of tensile stresses in the wall of a cylinder. One type of tensile stress goes circumferentially around the walls of the cylinder. These are called "hoop stresses", I think. The other type of tensile stress runs parallel to the longitudinal axis of the cylinder. I don't know if this type has a common name, but I will call them "longitudinal tensile stresses".
The value of the hoop tensile stresses are equal to the following:
fh = (Pf * D) / (2 * t) [formula F1]
fh = the hoop tensile stress, in psi Pf = the pressure of the fluid or gas inside the bottle, in psi D = the diameter of the bottle, in inches t = the thickness of the wall of the bottle, in inches
The value of the longitudinal tensile stresses are equal to the following:
fl = (Pf * D) / (4 * t) [formula F2]
fl = the longitudinal tensile stress, in psi
while all other terms are the same as defined above.
One thing that you will note is that the hoop tensile stresses are twice as large as the longitudinal stresses. (The formula for hoop stress has a "2" in the denominator, while the other formula has a "4" in the denominator.) This means that if a bottle fails due to internal pressure, it will likely fail due to hoop stress rather than the other kind. So, let's ignore the longitudinal stresses, [F2], because the hoop stresses are the likely failure mode.
Let's take the hoop stress formula, [F1], and solve it for Pf which is the fluid pressure inside the bottle:
Pf = (2 * t * fh) / (D) [F3]
Let's set the value of "fh" at 6,000 psi, which apparently is the stress at which common glass ruptures under tensile forces. (It looks like this property is called the "modulus of rupture".)
Let set "t" equal to 1/8 of an inch, the approximate wall thickness of a beer bottle.
Let's set "D" equal to 2.5 inches, the approximate diameter of a "long neck" bottle.
If we solve for "Pf" (the internal pressure in the bottle) it comes out to 600 psi, given the values above. That's the approximate pressure at which a 2.5" diameter glass bottle will break, if it has a 1/8" thick wall.
How a plastic bottle of the same size will perform, I'm not certain. However, I saw an episode of Mythbusters in which they "exploded" a two-liter soda bottle at a pressure of about 140 psi. This suggests to me that a smaller plastic bottle, about the size of a beer bottle, would rupture at some pressure between 300psi and 400psi.
Let's think about these for a moment. The breaking pressure value for a 2.5" glass bottle (600psi) and the approximate breaking pressure for a 2.5" plastic bottle (maybe 400psi) are probably both larger than you would be able to get by vigorously shaking up the bottles. Much, much larger. That's a heck of a lot of pressure.
Plus, if I am a glass bottle manufacturer, I definitely don't want my bottles to rupture under pressure. That would earn me a bunch of lawsuits. So, I expect that the caps of glass bottles are engineered to pop off long before the internal pressure of the liquid reaches the pressure that will rupture the glass. The cap, then, probably serves as a "safety valve", even though we don't think of it that way. If my bottle breaks at 600 psi, then I probably will engineer my caps to pop off at 60 psi or less, which would give me a ten-fold factor of safety against the rupturing of the bottle.
So, in terms of pressure, both the glass bottles and the plastic bottles are pretty safe, provided that both were manufactured to hold contents under pressure. (A plastic water bottle probably doesn't fall in that category.)
For me, I will probably use plastic bottles most of the time. This is because the most likely way that I would break a glass bottle would be to drop it, either during washing, filling, storing or whatever. And plastic bottles survive being dropped better than the glass.