It was a dark and stormy night. Well, it was day. And it wasn’t all that dark either, but it was very stormy. Yes, in College Station today it was pretty miserably wet and so was everyone on campus. Even if you had an umbrella.

Well, I thought, I wonder if you could *do* something with all this rain? Maybe generate electricity?

Unlikely, because it’s a pretty obvious idea and were it practical surely someone would have tried it. But it can’t hurt to run the numbers for ourselves.

The physics building at Texas A&M is five stories high, and at a very rough estimate I’d guess the cross-sectional area is around 30,000 square feet. Not all of that is ours, much of it belongs to various of the engineering disciplines. Now, how much hydroelectric power can we get from what hits the roof?

Well, we know that the potential energy due to gravity is E = mgh, where m is the mass, g is the acceleration due to gravity (9.8 m/s^2) and h is the height above the ground. Power is energy per time, and so we can convert the equation to one describing power by replacing mass with the rate at which the mass of rain appears on the roof. By my calculation, we end up with

Where for clarity A is the roof area, r is the rate of rainfall in terms of depth/time, and rho is the density of water. Plugging in my rough estimates and a figure of 4mm/hr for a typical somewhat heavy rain, I get about 460 watts. Not a tiny figure (it’s about the average power I use in my apartment), but it is pretty tiny with respect to the energy budget of a large building, especially since it could only work in the rain. Averaged over the entire year we can just plug in the overall 40 inches/year or so that College Station gets, for an average of 13 watts. Not worth the effort, certainly. Some of the rainier regions of the country could probably push this into the low 20s, but still it’s pretty pointless.

It’s not easy being green.