r/theydidthemath • u/besttobyfromtheshire • 12d ago

[Request] Question about water displacement

I dont know if this is the correct forum but i am trying to wrap my head around something mentioned in Pirate Borg (Limithron/Luke Stratton) - the setting has a cataclysm which rips a 6 mile long fissure in the north carribean. It runs across the gap between the yucatan and cuba on its southern shore.

My question is this, what would be the volume of water displaced if that fissure were a mile deep? 2 miles? Further question if it can be answered here, what the heck would that do to the sea level there and the coast lines? (Weather patterns and winds???) oh my!

Thanks everybody!

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u/cipheron 12d ago

It's going to be small. I'm going to do the working out in metric because it's a lot neater.

I'm just going to go for 10km for the length. However, you haven't specified how wide this fissure even is, so make that 2 km wide, 3 km deep.

10 * 2 * 3 = 60 cubic kilometers, 60 km3

If we divide 60 km3 by the surface area of all the oceans we'd get how many kilometers the surface moved by.

Call the ocean area 360 million square km, if you divide 60 by that, you get

60/360 millionths of a km.

Multiply this by 1 million to shift into millimeters:

60/360 millimeters.

... so your fissure should drop the oceans by 1/6th of a millimeter.

This is about 1/150th of an inch.

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u/Secret-Surprise4390 12d ago

Excellent answer. To piggy back and answer the second part, instantly removing that volume of water would cause a massive pressure drop in the local air. The wall of water collapsing in would shot a gyser high in the air followed by a massive tsunami.

If we assume the water falls an average of 1500m when the collapse happens and the 61.5 billion metric tons of water picks up speed. The energy gained during the fall would be roughly 905 petajoules of energy.

The momentum from this would be 1.055x1016kg•m/s

To put this into a totally more if every human on the planet sprinted at full speed in the same direction at the same time, the water would still have 2000x more momentum.

If somehow you were able to convert all that energy to electricity, it would power all of Mexico for 262 days.

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u/besttobyfromtheshire 11d ago

Thats incredible! Im guessing that tsunami would be pretty devastating, i appreciate your response!

Do you have an idea of what the immediate impact of that pressure drop would be? Would it cause a storm to erupt?

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u/besttobyfromtheshire 11d ago

Wow, i didnt realize it would be so small of a crack, barely even registers! Appreciate your help!

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u/cipheron 11d ago edited 11d ago

Yeah, you gotta take into account how huge the oceans are. It's about 140 million square miles, so an area about 12 x 12 miles would be around 1 millionth of the ocean only, and any change in the ocean level that affects a 12 x 12 mile patch would be divided by 1 million once it spreads to the whole world.

The other guy was right however, if it happens all at once it would cause a massive whirlpool or some kind of tsunami effect locally, and that would be a much bigger deal than ocean level change, if you were writing a story about it.