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As we all know the Earth is flat. Once upon a time a group of explorers set off with the idea of proving that the world was round and that there was a route to the spice islands the other way, but the few survivors came back screaming about seeing ships falling off the edge of the world and something about dragons.

  • Some sort of "universal down" keeps everything on the top of the planet.
  • Anything underneath falls away (no turtles this time).
  • We're not sure how the atmosphere stays in place.
  • The Earth's crust varies between 5km (Oceanic) and 50km (Continental) thick.
  • The planet runs from Pacific to Atlantic, no Americas, no Antarctic, no Antipodes (sorry Cobbers).

The world's water levels seem to run down slowly but every 12 hours or so they're topped back up again. Nobody knows how this works or where the water comes from, apparently arrangements are made. What this means is that that there's an apparent infinite supply of water and the edge of the world consists of a constant waterfall.

How long would such a planet continue to exist if subjected to normal erosion from said rimfall?

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  • $\begingroup$ I think it's going to be difficult to get a good answer here. How much water goes over the edge? Is it a super-Niagara or is there kind of a lip that is just barely overflowing? What's the earth made of? Mostly sand? Rock? Adamantite? (I know you said "crust" but I'm not sure what that means in this world.) It sounds as if you have gravity that's not like ours. I'm guessing there's no chance the whole thing will buckle and try to collapse into a spheroid but... it's kind of hard to tell. $\endgroup$ – Hugh Meyers Dec 7 '18 at 14:23
  • $\begingroup$ For reference Rate Of Erosion Of Niagara Falls. $\endgroup$ – Theraot Dec 7 '18 at 14:27
  • $\begingroup$ @HughMeyers, everything is Earth-like unless otherwise defined. Does the depth at the lip of the waterfall matter or is it only a boundary conditions thing? Geography wasn't my subject, but I can set rules if needs be. There's no chance of it becoming a spheroid. $\endgroup$ – Separatrix Dec 7 '18 at 14:28
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    $\begingroup$ The more water going over the edge, the faster the erosion. If nothing flows over the edge, then there's very little erosion (but some from ocean currents and maybe tides if you have those). Maybe it's a bit like a bathtub filled up to the brim and you only get overflow if you toss something into the ocean. But the lower the lip, the faster the flow, the more erosion which further lowers the lip. $\endgroup$ – Hugh Meyers Dec 7 '18 at 14:38
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    $\begingroup$ Due to nature of the flat earth the rim is unable to erode. $\endgroup$ – SZCZERZO KŁY Dec 7 '18 at 14:48
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The main problem is that there is bound to be at least one section of the rim that gets eroded slightly faster than its surroundings. This explains the horseshoe shape of Niagara falls.

enter image description here

However if this erosion happens to the rim it will be like breaching a dam. There will be a catastrophic failure at some point and the ocean will drain at that one point. The effect will spread sideways and towards the centre of the planet until the ocean is emptying faster than the mysterious supply of new water can keep up with.

It is difficult to predict when a catastrophic failure will occur but I imagine it would take only hundreds of years. Maybe a few thousand.

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Waterfall erosion happens in two ways:

  1. undercutting, where the rock at the base of the waterfall is slowly cut away until the rock above collapse (which can't happen in your scenario).

  2. Erosion at the lip of the waterfall where the water going over the edge gradually wears down the rock.

Assuming the rim is of a uniform rock type and starts off just a few meters under sea level (so near 50km thick), it will quickly wear flat. The erosion rate will depend on the force of the water going over the rock, and you have essentially described the pressure of whole oceans bearing down on this rim.

Assuming the water is topped up daily to the same amount, the amount of water going over the edge gets more and more as the rim erodes, exponentially increasing the erosion.

How long the rim lasts depends on it's width, as it will erode quickest at the very edge where the water speeds up, but once it has gone you are going to be left with a river world. This will cause more problems, as all that water is now eroding much smaller areas of crust and will erode through completely very quickly leaving essentially hundreds of bottomless chasms.

Once enough of these bottomless chasms form, you are back to the erosion rates that are more in line with known waterfalls, so the chasms will widen at approximately a km per millennium each (this would vary wildly depending on rock type).

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