User talk:Dikaiopolis
Hi Dikaiopolis,
It looks like you have yet to be spotted by the welcoming committee. I spotted your comment on another talk page about not knowing the four tilde trick for signatures. Its one of the things mentioned in many of the introduction messages, so allow me the offer you a belated welcome....
Welcome!
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Thanks for noticing that error. ‡ Jarlaxle 00:19, July 18, 2005 (UTC)
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Hi Dikaiopolis,
I am interested in an addition you made to the 'Hydropower' article on the 11th November 2004. In it you added the 'Physics' sebsection.
I would like to know where you got your source material for this from since I am interested in quantifying the kinetic power of water where there is no significant change in elevation. I am therefore interested in the final equation added to this section in particular. Also, what does the greek symbol 'varphi' stand for?
Thanks,
Chris M Parker 09:51, 11 September 2007 (UTC)
Hi Chris. My source is roughly my brain, since I have a B.S. in Physics and an interest in watermills. I haven't found a fluid mechanics book that I would really recommend yet unfortunately, but even introductory physics textbooks might have some information on this water flow problem (it is kind of a classic). varphi is not my edition, but I gather that the author's intent is that it's volume of water per time or volumetric flux. I've 'corrected' the article so that we use the same phi everywhere.
Generally, what you want to do is quantify the energy that the water loses by going through your device, and this is the available energy. Ordinarily (with water wheels), energy is either potential energy or kinetic energy (I could imagine a hydro power system where one could use thermal energy, but that's clearly not what you're interested in here). If you have a water wheel in a flat stream, potential energy is the same everywhere, but the water wheel slows down the downstream flow somewhat (or in the case of the over-shot wheels I mentioned, reduce the speed to a negligible value). If you know the speed of water before and after the wheel, you can calculate the energy that the wheel could have absorbed. However, this is not necessarily the power available to the water wheel, because energy could also have been dissipated through eddies, viscous dissipation in the fluid, et c. For over-shot wheels that don't leak, this is pretty simple, since you know the incoming water stream velocity, and the outgoing velocity is just that of the waterwheel cups. There aren't any other dissipations because there's no river with eddies, et c. For wheels that dip into a river, the situation is more difficult because it's hard to measure the velocity change (the water flows around and isn't confined to little cups), and dissipation through water currents is a bigger issue. For this situation, you could also try an entirely different approach, by calculating the force on the wheel blades using Stoke's Law. Energy is force times distance, so power is force times speed. Of course, force in this case is a function of speed, so there will be some optimal speed between a stopped wheel and a wheel that moves at the water velocity.
dikaiopolis 03:17, 22 October 2007 (UTC)