# Energy of a falling rain drop

1. Jul 12, 2009

### Kalagaraz

I was bored, my internet was out (from the rain), and so was TV. So all I could was sit there and think...

So I started asking myself, how much energy does a single rain drop have and how much electricity could THEORETICALLY (100% efficiency) be produced from falling rain? So when my internet came back up, I thought I would try and calculate it.

From searching the internet this is the variables I was able to come up with

Typical Rain drop is 2mm in diameter, has a terminal velocity of 6.25856m/2, and has a mass of 4mg.

Using the kinetic energy forumla then I get (0.5) * (4x10-6kg) * (6.25856)^2 = 7.833914655x10-5 joules of energy per rain drop.

Looking up historical weather data for my city, I find that rain fall average is about 4.25 inches per month or 10.79500cm

Density of water is 1g/cm^3. So 1000mg / 4mg is 250 rain drops per cubic cm.

250 * 10.79500 is = 2698.75 rain drops per cm of area

2698.75 * 7.833914655x10-5 = .2114177718 joules per cm per month, multiply by 12 and we get 2.537013261 joules per cm per year.

1 joule = 1 watt second

From a quick google search I came up with the average household power usage being 8900 kilowatt-hours or 32040000000 watt seconds. So to power a house for a year of rain you would need a energy converter that covered as area 1.262902346x1010cm^2 or 78473.11366 square miles.

So if my math was correct, powering our homes from rain probably isn't the best of ideas. If anyone sees any errors in my math/calculations (and there most likely is, been a couple years since i've taken any physics classes) please let me know.

2. Jul 13, 2009

### Andy Resnick

I like this! (except for your poor use of significant digits <grin>) It also shows how much water is involved for hydroelectric dams to be economical.

3. Jul 13, 2009

### Kalagaraz

hehe sorry about the significant digits. You should see how mad my math teachers get any time I have to use pi :)

4. Jul 13, 2009

### Nick Bruno

you know what would be REALLY interesting... if you had a piezoelectric plate which deformed due to rain drops. minimal deflection (depending on thickness) .. but neat concept.

5. Jul 13, 2009

### Kalagaraz

That's what I was thinking, but after calculating how much energy would be produced. I didn't really think it was worth building a prototype or anything. My other idea was capturing electricity from lighting during the storm :), but from google I've found that it's very difficult to intentially attract lightning.

Last edited: Jul 13, 2009
6. Jul 24, 2009

### Nick Bruno

I think this idea is still worth developing a prototype. Think of all the campers who get stormed out. It would be a great way for them to harvest energy for small LED lights or something around their campsite for some night lights. I know in some areas, especially where people camp, it can rain like crazy.