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**posted on**

- junkhunter

January 21, 2006, 4:46 pm

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]

where...

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]

where...

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.

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