We’ll assume a one acre [1] area, and 3 inches of rain per day [2].

[1] Yes, I’m an American and we still use these crazy units. But, quite a few housing lots here are still sized in acres or a fraction there of (e.g., 1/2 acre, 1/4 acre, etc.). And, I know that a typical house won’t occupy the entire lot. A house is typically only a small fraction of the lot, but we’ll still use 1 acre, since it provides a reasonable upper bound.[/1]

[2] I’m definitely over-estimating the amount of rain, probably by well over an order of magnitude, even for the Vancouver/Seattle area, but we’ll use this as a reasonable upper bound, too.[/2]

Ok, let’s find out how much water is actually involved. One acre is defined as an area of 66 feet wide by 660 feet long [3], which gives an area of 43,560 square feet. With three inches of rain falling on this area, we come up with a volume of water of 10,890 cubic feet. Translating this into metric, we arrive at a volume of 308.4E6 cubic centimeters (about 308.4 cubic meters). Since the density of water is approximately 1 gram per cubic centimeter, this gives a mass of water of 308.4E6 grams, or 308,400 kg (about 678,480 pounds [5]). That’s a lot of water!

[3] An acre was based on how much a farmer could reasonably plow in a day with a good ox.[/3]

[5] This passes the sanity test, since I remember that water weighs about 64 pounds per cubic foot, so 10,000 cubic feet of water should be about 640,000 pounds.[/5]

Now, we’ll assume the gutters on the house are about 10 feet off of the ground [4], which is a little over 3 meters.

[4] This should be a reasonable value, although two story (and higher) houses will have a greater height.

Now, since energy is force times distance (well, the integral of it, if you want to be technical), and since force is mass times acceleration (of gravity), this means that energy is mass times distance times the acceleration of gravity (We’ll assume that gravity is constant over such a relatively small vertical distance, although if the distance was much greater, we’d have to take in the fact that gravity varies inversely as the square of the distance). So, plugging into E=msa, we find that the energy is:

(308,000 kg)(3 meters)(9.8 m/s**2)=
9E6 J

Now, 9 million Joules sounds like a lot of energy.
And, in most cases it would be. But, to get a better feel for it, let’s convert it into power.
Since power equals energy divided by time:

P=E/t=(9.E6 J)/(1 day)(24 hours/day)(3600 seconds/hour)=
104 Joules/second=104 Watts

So, all of that 3 inches of rain per day, falling on that huge house roof, with an area of one acre, and dropping a distance of 10 feet will produce an average power of 104 Watts (ignoring losses, which are sure to be rather significant!).

Hmm, you know, we could save more power than that just by turning off two lights that we don’t really need.

Dave