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

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Sophie Drummond

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Sophie Drummond asked the Naked Scientists:
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

What do you think?
« Last Edit: 07/02/2011 02:30:03 by _system »


Offline graham.d

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This is a good question, Sophie. It would depend on the size of the drops from the shower head as well as other matters like the temperature and humidity of the air. Raindrops fall from much higher than 2000 feet and reach the ground so if the shower made drops this big they would reach the ground. If the drops were much finer they could evaporate before reaching the ground but I think that, in practice, they would be blown around a lot. Some drops may hit other drops and merge to make bigger ones; these big ones would then get all the way down.

The reason small drops evaporate faster than big ones is because the ratio of their surface area to volume is larger. The evaporation rate is proportional to the surface area and the amount of liquid in a small drop is smaller, so it takes less time to turn all the drop into vapour.


Offline thedoc

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We discussed this question on our  show
 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've 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. Sophie, 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.
Click to visit the show page for the podcast in which this question is answered. Alternatively, [chapter podcast=3003 track=11.02.13/Naked_Scientists_Show_11.02.13_7910.mp3] listen to the answer now[/chapter] or [download as MP3]
« Last Edit: 01/01/1970 01:00:00 by _system »