iMechanica - hydro-electricity
https://imechanica.org/taxonomy/term/1298
enThe efficiency of turbines
https://imechanica.org/node/1900
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Hello students (and also others) at iMechanica,
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Last weekend, while channel browsing on TV, I happened to notice a documentary on the Hoover dam (in the US). It showed a number of jets of water, huge ones, forcefully springing forth out of the rock faces just downstream of the dam. These were the water jets coming off the electricity generation plant of the dam, *after* their job of generating electricity was already over.
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Watching these fascinating water streams reminded me of a brain teaser. Might as well share it here. (It might look like high-school physics, but you can use it to understand higher courses in engineering as well.)
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You know that the hydro-electric power stations convert the energy of the water held in the dam to electricity. If the design of the power station (including the dam, pipes, hydro-turbine, etc.) is really efficient, as much of the energy of the water jet should be extracted and converted into electricity as is possible. Therefore, there should not be much kinetic energy left in the water outgoing the turbine.
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Yet, the force of the water exiting the actual turbines is huge. In case of the Hoover dam, the water seems to fly horizontally in the open gorg perhaps for hundreds of meters. (See if you can find a photo and convince yourself.) Obviously, one can think of installing a second line of generators, so as to extract a little bit more of this energy...
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If you agree with this idea, then, continuing the same logic forward, the water coming off the most efficient power station should have no kinetic energy whatsoever left in it. That is to say, the water should come to a stand still, having given off all its energy to the turbine.
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But in such a case, no water movement would be left to turn the turbine blades at all, and so, there can't be any electricity generated at all.
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How do you resolve this riddle?
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Fun: Once you finish your reasoning, take the case of the sand particles falling vertically down on a sand-turbine. Assume that it is connected to an electricity generator.
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Now, once again see if your reasoning continues to holds or not.
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Fun continued: You can also take the example of a windmill power generator, though the case of the windmill is slightly more complicated. The wind is not physically restricted to a definite region of space--the entire mill sits exposed to a virtually unlimited domain. However, the basic riddle still remains the same. One way to pose it is: If a wind-mill extracts all possible energy, how come there is another one sitting some distance downstream? Where does the energy it extracts come from?
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</div></div></div>Mon, 10 Sep 2007 13:56:23 +0000Ajit R. Jadhav1900 at https://imechanica.orghttps://imechanica.org/node/1900#commentshttps://imechanica.org/crss/node/1900Error | iMechanica