Built on Facts

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.

Comments

#1 NAME
April 17, 2009

Incidentally, if you extend the reasoning a bit, you immediately have an upper bound for world hydropower potential. Just replace building heights with height above sea level, and extend the area to the earth’s surface:

http://www.google.com/search?hl=en&q=40+in%2Fyr+*+30%25+*+4*pi*radius+of+earth^2+*+1+kg%2FL+*+earth+gravity+*+0.5+kilometer&btnG=Search

http://en.wikipedia.org/wiki/File:Earth_elevation_histogram_2.svg

The upper bound is the same OOM as world energy demand. Throw in real-world limitations (only a fraction of surface can feasibly be dammed over; only a fraction of elevation difference (‘head’) is practically harnessed) and you’re an OOM lower – so hydropower can never meet world demand. This is the reasoning physicist David MacKay uses in ‘Sustainable Energy – Without The Hot Air’:

http://www.inference.phy.cam.ac.uk/withouthotair/c8/page_55.shtml
#2 Chad Orzel
April 18, 2009

There was a news squib in Physics World or one of those magazines some time ago about people who were working on a technology that would convert the kinetic energy of raindrops into electricity. They pitched it as a complement to solar panels, to generate electricity even on rainy days. That would kick the estimate up at least one order of magnitude, so it’s at least not obviously silly…
#3 Chris
April 18, 2009

Pretty pointless if the only purpose of collecting the rainwater is to generate electricity. But suppose you were collecting rainwater anyway — for example to water all the grass on campus, which might be worthwhile even if you don’t generate energy. If you were building that infrastructure anyway, would adding generators of some sort to the main collection pipes to also generate energy be cheap enough to make sense?
#4 Uncle Al
April 18, 2009

460 watt-hrs is 1,656,000 joules! You are a Green saboteur. All we must do to save the world is believe (and voluntarily fill the collection plate – or else). Engineering calculations are apostasy dating back to the Tree of Knowledge in the Garden of Eden. Do not accept fruit from the Serpent!

(More likely a pomegranate and a koala bear, but nevermind.)
#5 Peter
April 18, 2009

But all hydroelectricity IS rainpower! One simply has to increase the collection area, and reservoir height if possible.

Water pumped to altitude is also a potential (pun intended) means of energy storage, though fairly low efficiency, for solar or wind farms. Near my home there was a natural terrain that was considered for a storage hydroelectric project using off-peak power to pump water up into a natural ravine which would be easy to dam up. The project foundered on environmental issues….
#6 alufelgi
April 19, 2009

In my opinion the largest threat for California are cataclysms and ecological catastrophes. Not important is how many money we have because one tragedy can us take all.
#7 Tualha
April 19, 2009

Oh, you can convert rain to plenty of energy. You just have to work out practical fusion technology first. Trivial details…
#8 Laborum
April 20, 2009

Someone mentioned generators. What’s the energy flow through rain gutters on the building mentioned? Pressure from water moving through a smaller focus could produce more energy, no? I’d wager not enough for the need, but still.