Will a tightly sealed Cannonball that contains a small amount of water, when frozen, break apart? If so what are the limits to force of expansion of freezing water?
No
Next question?
…what are the limits to force of expansion of freezing water?
In all fairness that’s a pretty poorly worded question.
If the cannonball is nothing but a very thin shell of iron…then maybe. Freezing water will burst a plastic bottle. I’ve never tried to see if it will burst a glass bottle, but if the glass were quite thin, I’m sure it could happen.
When you say “a small amount” of water, this tilts the likelihood the other way. It would take something like 98% water, 2% iron shell (by weight) for the expansion of freezing to break through the iron.
For the force freezing water exerts you can start here, but it’s a bit of a trip down a rabbit hole.
Only grammatically - it’s very clear what the OP wants to know.
I saw pictures of a demonstration once in which a spherical cast-iron bomb, roughly the size of a cannonball and with walls perhaps 3/4" thick, had been filled with water, sealed, and then placed in a pile of dry ice (-110F). After some time had passed, the bomb shattered to pieces.
So my answer to the OP’s first question is yes.
Doesn’t have to be particularly thin either, reports the disgruntled cook who has more than once nearly-filled a sturdy quart mason jar with what she was SURE was a safe level of lovely homemade soup, only to find a frozen shattered mass the next time she opened the freezer. :mad:
According to the phase diagram of ice, the lowest temperature at which water can remain liquid is about 251 Kelvin, at a pressure of just over 200 megapascals (2000 atmospheres, or over 29,000 pounds per square inch, at about -20 C). So conversely freezing water could exert that much pressure at 20 below C.
Sure. If it’s made of rubber instead of iron.
Or, as noted above, a really really thin layer of iron.
Or if you just leave it a million years until it’s all rust.
The capacity of the iron shell to withstand a given force from inside would also be highly variable, depending on many factors, including the temperature that the iron itself had been reduced to by the process of freezing the internal water. Also, the temper of the iron itself, would depend on the casting conditions, how quickly the molten iron was cooled, impurities in the iron, etc.
So, while the force of the expanding water can be easily calculated, the resistance of the iron shell cannot be, and that is where the variable lies.
You forget that the soup mostly freezes outward, not upward, and that Mason jars are relatively thin. Old milk bottles were much thicker and could constrain the freezing milk better, so you would sometimes get a column of frozen milk rising out of the bottle. I don’t know how or if the rate of freezing affects anything, or if the screw-on cap of your well-sealed Mason jar vs the Pogs that sealed the milk bottles has anything to do with it.
Freezing water can burst copper pipes. They’re not as strong as a cannonball, but they’re up above plastic and glass.
Freezing water can crack iron pipes also, and engine blocks.
I should have made my question clearer. I am assuming a more or less “normal” cannonball. 4" to say 8" dia solid cast iron except for a hollow core say 25% of diameter. Tripolar reminded us that a frozen engine block can crack but the cast iron there is a minimum of maybe 1/4". Lumpy said that from the phase diagram of water that the force could be around 29,000 lbs/sq in. That is somewhat above the tensile strength of cast iron but below most steels. Question answered maybe?
I’m not sure about the tensile strength of cast iron being effective here. Cast iron is notoriously brittle due to it’s high carbon content, and if I understand it correctly, cannon balls are made from very low grade iron to reduce costs. Given a perfectly spherical cast iron cannon ball with a perfectly sperical hollow core for the water maybe the brittleness of cast iron wouldn’t come into play, but cast iron certainly doesn’t have the ductile quality of steel that would allow it to deform before breaking.
ETA: Cast iron engine blocks are definitely made from from either actual steel, or an iron alloy with much greater strength than the iron cannonballs would be made from.
You could use the equations for a thick-walled pressure vessel to calculate the stresses. The two equations there have constants that you can figure out from your particular situation. In this case, radial stress is maximum at the inner surface (29,000 psi), and zero at the outer surface. Now you can solve for constants A and B, plug them into the equation for tangential stress, and then evaluate that to see whether the tangential stress exceeds the yield stress for the material anywhere in the cannonball.