The Romans figured out that an overshot wheel is many, many times more efficient than an undershot wheel. The falling water contains way more energy than water just poking along under the wheel… of course, making an overshot wheel would require at least partially damming up a water source and creating a sluice to dump the water over the wheel. But it can be done.
Thing is, there’s a max RPM when dealing with an overshot wheel, which means you will need to build some sort of step-up transmission to spin your generator at anything approaching a useful velocity.
Much more efficient would be to combine the two – make your dam and sluice but use a turbine like 74 said. If you design the turbine correctly, the water will “pull” the turbine instead of “push” it…. think if each blade as an airplane wing. Water hits the blade and creates a pulling effect instead of a “normal” pushing effect… you can get a turbine going really, really fast that way… but you’ll still need some type of gearing to spin the genny (which should be out of the water stream)…
Good stuff! I give it two thumbs way, way up…
The wicked flee when none pursueth..." - Proverbs 28:1