Osmosis (excluded volume dynamics)
Initial upstream salt concentration is not nil (and arbitrary chosen). Downstream compartment contains pure water. Given upstream pressure is applied. Water molecules throw the membrane to downstream until an equilibrium situation occurs. On have the relation P = A * DS1 / DS2 * C1e where P is the upstream applied pressure, DS1 and DS2 are the solution densities on upstream and downstream and C1e is the equilibrium upstream salt concentration which may be different than the initial upstream salt concentration. A is the proportionality coefficient according to Vant Hoff law. Usually DS1 / DS2 is taken equal to 1 in water if the pressure P is law.
Example 4, reverse osmosis :