Could You Build a Hydroelectric Dam in Your Home?

At What If?, webcomic artist Randall Munroe answers reader questions about scientific possibilities. He draws stick figures at xkcd, but he's also a scientist and roboticist. So he carefully thinks through reader questions using his considerable brain power.

Most recently, David Axel Kurtz asked him:

I just moved into a new apartment. It includes hot water but I have to pay the electric bill. So being a person on a budget ... what's the best way to use my free faucet to generate electricity?

Munroe proposes building a hydroelectric dam in the bathtub:

It would generate power, though not very much of it. The formula for power is pressure times flow rate.[1] Since bathtubs are pretty shallow, the pressure at the bottom isn't very high, so this works out to around two watts of power, or about 25 cents per month.

You can get more power if you increase the pressure of the water passing through the generator. To do this, you could increase the depth of the water. If you have two floors in your apartment, you could have the water column stretch from the second to the first floor, generating at least ten times the pressure and ten times the power.[2] In effect, the local authorities would be paying to pump the water up to your apartment, and you're getting some of that energy back when you let it flow back down.

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