So Im in the last year of my degree, and I thought about this idea for a long time, why is it not possible to increase the power output of a hydro electric dam by stacking Archimedes screws in the way depicted in my sketch. Instead of having each set of water molecules entering the system power a single turbine, you could have each water particle move all other water particles along the vector - through all of the turbines.


I have also proven that this allows to infinitely extend the power output of a dam by a multiple only limited by how many turbines you can set up. And the reason is that water atoms interacts with gravity on a global level but interact with other water particles on a local level - so if you construct a system where a liquid is forced to move linearly localy, but non linearly globally ( through the system from start to finish is non linear), you actually get to leverage the second law of thermo dynamics - conservation of linear momentum, because you can effectively separate the global state ( where all water particles begin in the system and where they finish) vs the local state which dictates for each molecule where it should go ( which is where linear momentum points it).