Would water from 2000 ft up evaporate befoe it hits the ground?

13 February 2011

Question

Dear Naked Scientists

If you put a showerhead over a 2000 ft high cliff would the water keep going to the ground or would it evaporate?

From Sophie Drummond age 11
In Rochford, Essex

Answer

Dave - Well to start off, I didn't have the answer in my head, so I thought I would do some science properly and actually do an experiment. So in the office last week, I got a lemonade bottle lid and a set of very accurate scales and I rigged up a fan next to it because I figured that we're interested in how fast the water is evaporating. If the drops of water from the shower head evaporate before they hit the ground, then they're never going to hit the ground, but if they get all the way down there, they will. So, I got some water in this lid, I put a fan across it. The fan probably wasn't really powerful enough, but it gives us a general idea what's going on, and I ran it for about 10 minutes. And in that time, about half a gram of water evaporated.

Chris - So that's half a ml.

Dave - Yeah, so half a millilitre of water and that was for a 28-millimetre diameter lid. If you work that all out, it comes out that you lose about 0.1 cubic millimetres of water per minute, per square millimetre of water.

Chris - So extrapolating that to Sophie's showerhead going over the cliff...

Dave - So then I've worked out the area of a raindrop, for different sized raindrops, and worked out how long it takes to evaporate. So probably, a normal to large size of raindrop is about 6 millimetres, so probably what you're getting from the showerhead. If you worked that out, it probably takes about 18 minutes for it to evaporate.

Chris - How long does a raindrop really take to fall 2,000 feet over a cliff?

Dave - Terminal velocity is about 10 metres per second, so it probably takes 70 seconds.

Chris - What fraction will evaporate then?

Dave - A tiny fraction. Maybe about an 18th of it, about 20th of it will evaporate.

Chris - But not zero. I mean, there is some evaporation.

Dave - Not zero.

Chris - Because there was a paper in Nature a couple of years ago where they were using oxygen isotopes to work out how much rainfall evaporates when rain falls from the sky, and something enormous like 40 or 50% of the rain that falls doesn't ever make it to the ground.

Dave - I could quite believe that. So I then thought I'd do some other calculations to work out what would happen if I have a smaller droplet - because, from a showerhead, you get the big droplets coming out but they also tend to break up into small ones. And around about 1-millimetre diameter raindrops falling off a 2,000-foot cliff, they'll probably just about evaporate before they hit the ground if the air was about the same as in our office, which is not necessarily a good assumption.

Chris - I'm not sure that's a good idea at all!

Dave - It would depend whether you do it in a desert or if you do it in Scotland where it's raining already. So, it very much depends, but certainly the small ones could evaporate depending on the weather.

Chris - There you go, Sophie. So if you have a very fine shower then a significant proportion could evaporate, but if you've got a really good quality power shower with big drop sizes, then a very small fraction of the water will evaporate on the way down.

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