If you want to re-check my numbers, you are welcome. Engineering calculations have been a large part of my profession for 40 years – but errors can always creep in
If you compare the sitation to a hilly region, like the one where I live, then (historically) hydropower was very common. Water-powered textile mills were built all along the local valley – as this account, from 1841, of only a couple of the local neighborhoods shows.
In the production of these articles a very considerable power from water and steam is employed — there being in motion, in the two townships of Golcar and Longwood, twelve water wheels, of the united power of one hundred and seventy horses, and three steam engines, equal to the exertion of fifty-seven horses.
That is an average of 14 horsepower (10.5 kW) per wheel – and each one was expected to power a small factory. The steam engines were 1.3x as powerful, and gradually steam largely displaced water power in the area.
Interestingly, a (now derelict) mill near me (mentioned in this thread) installed a water turbine in 1920 – utilising a larger vertical fall of the river Colne than had previously been possible for thier old waterwheel. There is a recent photograph below (taken by some unrban explorers). The turbine produced 85 horsepower (63kW) which was a useful amount of power – but when you consider that it is about the same as available from a typical small (1.4 litre), normally aspirated, petrol car engine – then you can see why the relative capital cost of the earthworks, ducting, and turbine is now seen as excessive. However, if fossil fuel prices rise considerably, or people actually decide to stop burning coal/oil/gas to prevent a global catastophe, then the relative economics would certainly change.
But please, don’t give up your dream of using the power from rainwater captured by roofs. As you say, @donald , there can be applications for micro power sources – and using static pressure from the head of water, for actuation, is always a possibility.