>>2506626I'm about to dork out for a sec, sorry in advance. Yes, it's possible, but it would be very inefficient (in a colloquial sense, hydropower is actually very efficient going over 70%). Your idea is similar to what is known as "run-of-the-river" hydropower, where wheels are placed in rivers, often with small dams. The amount of power generated by the water is defined by the formula: P = ρ*G*h*g, where ρ is the density of water (about 1000 kg/m^3), G is the volumetric flow rate (m^3/s), h is the head (how far the water actually falls, in meters), g is gravity (9.81 m/s^2), and P is in watts.
Let's say you want to charge your phone, which requires about 5W. I'm going to make the generous assumption that you built this system with a head of about 8 meters (a little over a 2 story house). That would mean a value for G(volumetric flow rate) of about 0.000065 m^3/s is required, or about 1 gallon per minute (lots of estimations being made). Neglecting generator efficiency, you would be able to charge your phone if you manage to get a gallon of water per minute through your gutters.
This is an incredibly idealized scenario. In the video linked by someone else in the thread, the guy planned for a 2 watt system, but only ended up getting about 0.25 watts. You need to take into account actual head (in the drawing you posted, the head for each generator would be the distance from the gutter to the first wheel), generator efficiency, losses from storage (assuming you want to capture all of the energy and store it into batteries for later use), and frictional losses.
There are lithium batteries used to store energy with a capacity of 1200Wh, or 4.3 million joules. For the guy in the video, if the rain was generating 0.25 W like in his demo, he would be able to store 900 joules in an hour of rainfall. It would take 4800 hours of rainfall to charge that lithium battery.
You'd have to build many of these systems in parallel to capture a significant amount of energy.
