The area of the membrane matters
One more thing, before we get too enthusiastic about our new equations. We can imagine a litre of salt water and a litre of distilled water with a membrane (the partially permeable kind) between them, and we know that the thickness of the membrane is taken care of as a part of P … but how wide and how tall is the membrane?? It will make a big difference if the membrane is 1 square centimetre or 1 square metre in area!! In fact, I would be willing to take bets that if the membrane has 10 times the area, it will let 10 times more stuff through (that would be a linear relationship).
This issue becomes pretty important when we start thinking about scaling and things like the surface area of the lungs.
Small Membrane to left
Large Membrane on right