Fluid dynamics: emptying a chasm

Deep underground, there's a huge limestone cavern, roughly 50m x 100m. It's 250m deep, and completely filled with still water. There is a very small inlet, but the system is now effectively closed, so it appears to be a vast underground lake.

Now down at the bottom, there's an ancient stone door, 4m on a side. Using a magical bomb of sorts, the heroes blow this door off its hinges. On the other side is nothing to speak of -- the water can flow out freely and descend well below the bottom of the chasm/lake.

1) How long will it take for the lake to empty?

2) Will the emptying process accelerate over time, building up an increasing vortex, or remain basically steady? The water can tear the door-frames to bits as it races by.

3) What will this all look like, seen from the shore of the lake above?

4) The walls of the cavern are dressed elaborately -- think of the great gate of Petra, all the way around, halfway up the sides. What will happen to these sculptures as the water races out down below?

Note: If this belongs in some sort of fluid-dynamics SE, please direct me there. I figured it's such a broad hypothetical, especially the part about the Petra-like carved facades, that it belongs here.

posted over 8 years ago

CAgrippa‭

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