The original problem was as follows:
Closed-loop system, with complete isolation.
Salt water is green, fresh water blue,
porous plug (AB) is red.
Fresh water spills into the salt water column
at C if the fresh water is lifted
higher than the salt water,
maintaining continuous flow.
Can this really happen?
The theory that i worked out is that the pressure in the bottom of any of the columns is Pressure = density x constant of gravity x height
The density of pure water is 1000 kg/m^3, while the density of salt water is 1025 kg/m^3. This means that the pressure at the bottom of a salt water column is 2.5% higher than the fresh water.
The osmotic pressure needed to drive water from the salty side to the fresh side is 1450kPa, or around 14.5 bar.
If both columns are around 6km high, the osmotic pressure at the bottom of:
the salt water tank is 1025 * 9.8 * 6000 = 60.27 MPa, or 602.7 bar
the fresh water tank is 1000 * 9.8 * 6000 = 58.8 MPa, or 588 bar
The difference in pressure is 14.7 bar, enough to counter the 14.5bar requirement for reverse osmosis. The salt column's pressure now pumps fresh water into the fresh water column.
If the freshwater feeds back into the saltwater column, after perhaps passing a waterwheel that generates power, this becomes a perpetual motion machine.
some considerations noted: the saltwater will not become diluted by the fresh water pouring over at the top since the salt never leaves the column through the semi-permeable membrane
I know it doesn't really work due to thermodynamics, but i can't figure out why in terms of fluid dynamics and statics. Please tell me why it doesn't work, i cant figure it out.