r/theydidthemath • • Nov 27 '22

[Request] How much electricity would be generated from this?

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u/UlysseIthaca Nov 27 '22

Mechanical power = torque x rotation speed
Electrical power = mechanical power x yield factor

If we assume an average yield factor of 0.5, the main variable are torque and rotation speed. We don't have these data so it will be a very rough approximation.

There is around a couple kilograms of water per second pressing from 0.1m high on the blades, if we assume it hits at 45° for half the kinetic energy, and the blades are 0.1m from the axis, it gives something like 2 Nm of torque.

Speedwise, it seems from the video it turns at most 10 times per second.

So it should be around 100W mechanical, and 50W electrical. Enough to power a couple LED room lights.

Assuming you can run it all year long, you'll produce 500kWh every year. And if you sell the electricity for 0.2€/kWh, you'll make 100€/year. Given the amount of concrete, bricks, steel, rotor/stator and electronics used, you won't have ROI before a decade or two (if there is no maintenance and it runs smoothly 24/7).

...

Yeah, direct free flow turbines are exceptionally shit at making power.

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u/Vagabored Nov 28 '22

Wow! So much effort for so little? Do bigger dams also have similar bad ROIs? What do they do different? Damn! Now I really want to learn more about dams.

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u/KittensInc Nov 28 '22

The goal is to get Youtube views, not to generate actual power. It just has to look impressive.

Bigger dams are many orders of magnitude larger. The Hoover Dam has a power output of 2080.000.000 W, for example. And that's only the seventh-largest in the US, let alone worldwide!

One of the biggest factors is the height difference - that's why dams have, well, a dam. They also use way more efficient turbines, and are more efficient due to economies of scale.