Dammed up water has a lot of potential energy. Water has a density of eight pounds per gallon, so even a small stream dammed up has a lot of energy, but when you dam up the Colorado River then you have power.
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So you've got a dam with a penstock (funnel) where a controlled amount of water is let through. Then at the bottom of the penstock there's a turbine, very similar to a wind turbine, but powered by moving water. When the turbine turns it spins an electric generator and produces electricity.
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Hydro power is a very good source of power, it produces a lot of electricity worldwide but it is completely dependent on amount of water, so if theres a severe drought lasting months on end there's going to be a problem. Also, it's completely up to the government as to where the dam goes, you can't just buy a dam and put it in your backyard and create electricity it doesn't work that way. But you can live in places where a large portion of the electricity is hydro-electric, New York is probably the city that has the most hydro-electric power, in some places over 20% is hydro-electric.