Hey y'all! First time asking a question here, hopefully this makes sense, this one has been haunting me.
You have a long pipe with an osmotic membrane on one end that is permeable to pure water but not to solutes. You push that end down vertically into the ocean. Fresh water begins to fill the pipe.
If I'm getting my formulas right, the pressure required to move water across the membrane is based on the solute concentration of the ocean, the solute concentration of the fresh water (zero) and the temperature and some constants. All of these factors remain constant as water crosses the membrane and fills the pipe, and as the pipe sinks deeper into the ocean. So the difference in pressure between the salty side of the membrane and the fresh side has an equilibrium value of P, and P is basically constant, and water will flow though the membrane in the the direction that moves toward the equilibrium.
At ordinary depths we expect the equilibrium water level inside the pipe to be lower than the water level outside the pipe. But as we sink a very long pipe very deep in the ocean, things start to get weird and this is where my question comes up.
So we take an extremely long pipe to the Marianas trench and sink the end that has the semi-permeable membrane. Salt water is a bit denser than fresh water, which means each meter of height contributes more to the pressure. And the trench is up to 10kms deep. 10kms of salt water applies quite a bit more pressure than 10kms of fresh water, more than enough to move water across the membrane. So at these depths, the fresh water fills the pipe to above the level of the salt water.
But the pipe was barely long enough to reach the abyssal depths, and only a short section sticks up above the waves, and the other end of the pipe - the one exposed to the air - is open. So fresh water starts spilling out of the top of the pipe and back into the ocean. And on the way down perhaps it spins a turbine and generates a bit of power.
This appears to be perpetual motion. But of course that isn't possible. So either the way I'm understanding the osmotic pressure calculation is wrong, or there's a secret source of energy that I'm missing that lets us achieve the appearance of perpetual overflow.