waross said:
When that cubic foot accelerates, it doesn't leave behind a vacuum.
An expanding cone of water behind the subject cubic foot also accelerates, at a reduced rate, depending on the distance from the breach.
Correct - but at the depth we're talking about, the amount of energy available to feed the collapse - basically 100% of the potential energy of the water column above the sub - is hundreds or thousands of times larger than the amount of energy it takes to accelerate the volume of water required to close the bubble. In simplest terms, you're talking about a reservoir of potential energy 3800m tall, which only 'falls' 1.5-2m. There's a large amount of energy consumed in the collapse, but that large amount of energy is still a tiny percentage of the energy available.
Point is, yes- there's energy required to 'backfill' the volume of the collapsing hull - but the energy required is coming from an infinite reservoir.
waross said:
The bubble from an explosion will be many times the volume of the hull, and will be at a pressure above the pressure of the surrounding water.
It would be at standard temperature and pressure. But we aren't talking about standard temperature and pressure - we're talking about a 6000 psi environment.
When an explosion happens underwater, the explosive becomes a cloud of gas, rapidly expanding. At some point, assuming the explosion is deep enough to not breach the surface, the expanding gas bubble reaches a point where the gas pressure and surrounding water pressure are equalized, at which point the gas bubble stops expanding and the water causes it to collapse. When the bubble collapses, effectively all that water slams together at the center point of the explosion, creating an extremely powerful shock wave.
This collapse would have involved the same interaction - surrounding water accelerating to fill the void at extremely high speed. Imagine a scenario where instead of imploding, we stopped time and just waved our magic wand and caused the sub to cease to exist, leaving behind a Cyclops II shaped hole in the water, filled with air, at 3800m. If that bubble of air was preserved and allowed to float to the surface, its volume would expand by your 400x multiplier.
If you make the analogy to an explosion, the upper limit of the energy involved in the collapse of the sub is exactly the same as the explosive energy it would take to create a gas bubble of the exact same volume as the sub,
at 6000 psi ambient pressure.
Alternatively, the energy involved in the explosion would be the amount of explosive energy required to create a gas bubble 400 times the volume of the pressure hull
at standard pressure.
We can actually calc this out. On average, TNT produces roughly 1 liter of gas at standard pressure, per gram. The approximate volume of the hull of the sub is/was 8.1m
3
8.1m
3 = 8100L
8100L gas = 8100g TNT at standard pressure, or 8.1kg of TNT.
If you assume 400 bar pressure environment for the 'explosion', to create a gas bubble of 8.1m
3 volume, you would need 3,240kg of TNT.
That's not a nuclear level of explosive energy.. but 3 tons of TNT is a LOT of energy.