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A fascinating challenge! Mariotte's Bottle is new to me. I found this
simpler version of it for constant flow:
http://en.wikipedia.org/wiki/Mariotte%27s_bottle

However, you can't have more water flowing into the main tank during
operation. So I've a feeling that a closed system might not be what you
want.

If not, here's another solution. The classical way to achieve gravity-fed
constant flow is a constant-head tank, with extra water continuously running
to waste through an overflow pipe. I'm guessing that you aren't doing this
because you don't want to waste water.

You say that you must drain water at a constant rate from the bottom of your
tank, whose water level varies. I suggest that you drain this water into a
separate constant-head tank, allowing it to overflow from there, not to
waste but into a third, lower tank. This third tank has a simple
float-switch actuated electric pump returning the overflow water to your
original tank.

The second, constant-head tank will then deliver a gravity-fed flow which is
perfectly constant. I hope this description is clear enough.

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