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Wwyd if you were given a pocket dimension 3m cubed? (lemm.ee)

submitted 10 months ago* (last edited 10 months ago) by [email protected] to c/[email protected]

220 comments fedilink hide all child comments

Rules:

*You can teleport into and out of it at will

*It has a couple of plug sockets and can connect to internet from the region you teleported in from

*You can take objects and people with you

*As already stated, it is (3m)^3 (3m*3m*3m). The walls are plain plaster with a light in the middle of the ceiling. The pocket dimension is topologically toroidal, so if there weren't walls and a ceiling/floor (which you can actually destroy) you would loop if you went more than 3m in any direction. Gravity, then, is artificial and can be altered to anywhere from 0 to 2g from a dial on the wall.

Edit: additional specifications

*You can only teleport out to where you teleported in from.

*Time proceeds at the same rate inside the pocket dimension

*There is an eject button for those inside to get out if something happens to you

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[–] [email protected] 12 points 10 months ago* (last edited 10 months ago) (1 children)

I don't think the drag force due to air would work the same in a system with such a high concentration of rocks. It's not like one object falling through undisturbed fluid, which then has to get out of the way, in this case the air would gradually start to move along with the rocks.

This might be better modelled as turbulent flow of a mixed solid/air suspension. But there's no 'edges' to the flow due to the looped dimension, so the viscous forces are pretty uniform... There would still be a terminal velocity, but much much higher than a rock falling through an atmosphere

Also I imagine the rocks would quickly grind themselves to very fine dust, once they pick up a bit of kinetic energy, so then it would behave more like a fluid with uniform density... Could it even end up as laminar flow?

[–] [email protected] 3 points 10 months ago (1 children)

i don't think they would grind themselves to dust, as they're all moving in the same direction therefore their reaktive Velocity compared to each other would be (near) 0, not giving them much energy

[–] [email protected] 2 points 10 months ago* (last edited 10 months ago) (1 children)

It's a really interesting question, I would love it if someone who understands this kind of physics properly would chime in!

By my understanding of Reynolds number etc, the faster they go, the more turbulent the flow, so the rocks would be constantly hitting against each other sideways, and surely grind to dust in the constantly accelerating scenario.

But maybe the infinite (looped) nature of this 'dimension' means that this logic doesn't apply. What would even be the 'characteristic length'? Are we thinking about established flow at the centre of an infinitely wide pipe? Am I wrong to think of constantly accelerating rocks with air in between as a type of fluid flow?

[–] [email protected] 2 points 10 months ago (1 children)

No I think you're right about the fluid dynamics aspect, as we do have an indefinitely long pipe, but in the prompt the walls do still exist, so they'll probably do create some friction. The question is, would the rocks build up some sort of boundary layer of slower flowing particles near the wall, and how much do the boundary layer and "main" center flow mix?

Thinking about it, it isn't even an indefinitely long pipe really, as there are no "new" sections of wall coming up, instead it's constantly passing the same section of wall, and same section of boundary layer...

If someone knows how to simulate this in a physics engine or virtual air tunnel I'd be really interested in that!

[–] [email protected] 1 points 9 months ago* (last edited 9 months ago)

I guess I was imagining it with the walls torn out as well, but you're right the op (of this comment chain) said top and bottom broken. If the walls are somehow firmly fixed forever no matter how much force they experience, and are not subject to thermal degradation, then we have a square pipe with 3m sides and infinite length. If the walls break down then it's also infinite diameter.

In terms of modelling it there's a FOSS option openfoam.org but I don't know how to use it and don't have time to mess about with it right now.