Hydroelectricity is another term for power generated by harnessing the power of moving water. Not necessarily falling water, just moving water. There are many famous such generating stations in the world, not the least of them at Niagara Falls, Grand Coulee and Boulder Dam.
These are just a few of the many examples of energy produced by falling water. On the other hand, a small mill set in the rapids of a fast-moving stream is also an example of it in action, on a lesser scale. The truth is that any steady current of flowing water from a river or other waterway can be converted to power.