Here is a video of Julius Sumner Miller's show illustrating Pascal's principle: https://www.youtube.com/watch?v=8ma4kW3xVT0
At 12:31, he states (but only sort of demonstrates) that a glass bottle completely filled with water would be able to act as a hammer, meaning he could hit the screw and the bottle would not break.
My confusion is that, according to Pascal's principle, hitting a glass bottle with a nail like Julius did would essentially be equivalent to hitting the bottle with the same nail everywhere from the inside. That would certainly shatter the bottle.
I'll provide my explanation of this (I'm probably wrong): The internal pressure of water at ~20 degrees Celsius is much less than atmospheric pressure. This means that a closed, glass bottle filled completely with water has a net force going inwards. Water can not compress, and so the pressure the water exerts on the glass bottle increases until it is not enough to deform the glass bottle. Thus there is a net force inwards on the glass bottle system which is the very lowest amount at which glass will deform.
When the glass bottle is hit by a nail, it deforms, applies a force to the water over some area, and by pascal's principle, this same pressure is applied everywhere throughout the glass bottle. However, because there is already net force inwards from the atmosphere and the water's pressure, the glass bottle does not feel a sufficient net force outwards to shatter it. Essentially, the atmosphere cushions the blow outwards that the glass bottle would otherwise feel from the water's application of outwards pressure.
Is this correct, or grossly misguided?
Edit: Another explanation I can think of is based on how the glass deforms. If, for example, the glass deformed by having the half of the surface of its cylinder deforming inward, then this would imply a relatively large force over a relatively large area, which diminishes the pressure exerted by the water outwards greatly.
Answer
Glass breaks because it is brittle instead of flexible; this means that if the shape of the glass deforms enough, if a surface bends just a little, it breaks. If the shape of the bottle doesn't change, then it won't break, no matter what forces are applied to it.
In the case of a bottle that is full of water with no air, the force of the impact with the nail causes one side of the bottle to deform. But, water is incompressible, so the water stops the side of the bottle from bending more than a negligible amount in order to keep the water volume constant (this is what "incompressible" means). Now, pressure is force divided by area, so the force driving the nail is spread out over the entire interior of the bottle by the water, so no part of the glass bends enough to break. That's why the bottle would survive.
In the case where the bottle has a bubble in it, the story would be different. Air and all other gases are very compressible. So, upon impact with the nail, the side of the bottle impacting the nail would deform. The gas would compress from the transmitted water pressure, allowing the water to move out of the way of the deforming side of the glass bottle into the volume formerly occupied by the bubble. This allows the glass to bend more, resulting in it breaking.
To compare, imagine the result of the virtual experiment with the corked bottle full of water with no bubbles at 11:44. If the professor had hit the top of the cork, the bottle would have shattered. Why? In order to stop the cork from entering the bottle (to keep the volume of water from compressing), the water would have to deliver a large force to the cork to stop it. This requires a large pressure since the area of the cork face is small ($Force = Pressure \times Area$). This pressure is transmitted to all sides of the bottle, generating an enormous force since the bottle interior has a much larger area. Air pressure outside the bottle is far too weak to prevent the bottle's sides from bowing outward and breaking. This is the basis behind the hydraulic press seen from 4:37 to 7:20.
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