The electricity is produced using the potential energy of dammed water. The water forces a turbine to rotate. The turbine is linked to an electric generator, where the electricity is generated.
Depending on how much potential energy the water has, the generated power is higher or minor, and the potential energy is proportional to the height/head.
There is a simple formula that let us calculate an approximate value of the generated power by a dam in a river:
‘P=h.r.g.k’.
‘P’ is the power (Kilowatts); ‘h’ is the height (meters); ‘r’ is the flow rate of the water (cubic meters per second); ‘g’ is the gravity acceleration (9.8m/s2); ‘k’ is the coefficient of efficiency which varies between 0 and 1. Usually that coefficient is higher when the turbines are bigger and modern.
As I already said in other post, exploring this energy has 2 main types of costs: money and the change of nearby habitats.
Sources:
http://en.wikipedia.org/wiki/Hydroelectricity
http://www.youtube.com/watch?v=htT_8sFJx1w
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