A scientific reconstruction, how the hydraulics of the water mills in Barbegal, France in the second century AD worked:
https://www.nature.com/articles/s41598-020-74900-5
I found this article quite interesting, because of the elbow-shaped gutters, and because the scientists found saw marks on the timber of the kinked inlet, which probably came from a with water power operating machine saw.
It would be one of the earliest ones.