Occasionally, one gets what they perceive as a brilliant idea. An idea that comes up regularly is 'Can I put hydro-turbines in my downspouts and make power'. I answered one of these on the IRC channel recently and thought I should post the math here. In this manor, my math, it it is wrong, will get corrected and Wooferhound can stick this thread in the unseen FAQ section.
We will start win a 1000SF roof and a 12 inch/1 foot rain in an hour. I realize this is absurd but, putting turbines in gutters is in the same league so just bear with this a bit. We will also use a 10' drop or 'head' for our figures.
On to the numbers:
We have 1000SF area getting 1 foot of water so we have 1000 cubic feet of water at 62.4 pounds a cubic foot or 62,400 pounds of water. This will fall 10 feet so we have 624,000 foot pounds of energy in one hour time. As power is in 'foot pounds a minute', we divide this by 60 and get 10,400 foot pounds of energy a minute.
We take the 10,400 foot pounds of energy and divide by 33,000 foot pounds of energy in a horsepower and get .31HP. At this time we have no inefficiencies or loses due to friction or anything else. I think if we got 20% efficiency out of our turbine for such a small one we would be doing very well. We end up producing .062HP for the hour.
This we need to convert to our International Watt or Kilowatt so we can converse with the world. 1HP = 746 Watts and .062 X 746 = 46.25W. Since we got this over an hour this is .046kWh for every foot of rain.
Just to finish the thinking, I'll take an example of a 3500SF roof here in North Central Texas where we get about 30" (2-1/2') of rain per year. In a year, if one had a place to store the 63,000 gallons of water, the electrical production would be ~.4kW. That is $0.07 worth of electricity/year at $0.16 kWh rate (one of the highest in the nation).
Ron
Yeah, woofer should stuff this in the often unread FAQ / WIKI.