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And I came up with a larger number some how.
http://www.atsecosolutions.com/saveonshowering.html
This site suggests that the average 10 minute shower in the United States costs $2.10!
National average cost of water is $.0030274 per liter
Cost of electricity: $0.0944 per kWh
30 degrees Centigrade temperature rise
131.125 liters in ten minutes
and assuming one liter =one kilogram.
one KWH=3.6MegaJoules
the specific heat of water is 4184J/kgK
so 4184*30*131.125=1.646*107J
1.646*107/3.6*106=4.572 KWH
4.572*$0.0944+131.125*$.0030274=$.829 for a ten minute shower or 8.3 cents per minute.
Also, you might want to use something with an anti-caking agent if you're going to have it in a very moist environment, i.e. a shower.
The easy way to calibrate it to 5 minutes is to totally fill the top bottle, let it run through for exactly 5 minutes then stop- then you know you have 5 minutes' worth of sand in the bottom bottle. I'd recommend using sand rather than sugar, DeusXMachina is right that in a damp environment sugar may well cake up and become useless.
I'm not sure about showering with a friend- sharing with the sort of person I could imagine sharing a shower with might lead to "distractions" that could end up with you being in the shower for longer than you intended in the first place...
speaking entirely hypothetically of course
??? My toilet uses cold water, and so does the upstairs one in the other apt. When they flush, the cold goes away and we get BURNT.
As do all the best things in life. Ok, I'm going to stop the innuendo now.
Being able to stop the shower in the middle would be nice- I have a power shower which probably counts as on demand, but if you turn it off and straight back on again it oscillates between cold and burningly hot for a minute or so while the temperature control gets itself together.