1- When falling water strikes the blades of a turbine, the shaft of a generator
ID: 586378 • Letter: 1
Question
1- When falling water strikes the blades of a turbine, the shaft of a generator is rotated and electrical energy is produced – hydroelectric energy. For example, there is a hydroelectric power plant at the Hoover Dam. Let’s estimate the maximum conceivable hydroelectric energy that could be generated in one year in the United States based on the following assumptions. The land area of the U.S. is about 8 x 106 km2 with an average elevation of about 500m above sea level. Average yearly rainfall is 75cm, one-third of which eventually flows into the ocean. The gravitational potential energy lost by this water flowing into the ocean represents the maximum possible resulting amount of hydroelectric energy that could be produced in a year. (Note that the mass of 1m3 of water is 1000 kg.)
a) Based on these assumptions calculate the maximum conceivable amount of hydroelectric energy that could be produced in the U.S. in one year.
b) In 2013 the actual amount of hydroelectric energy generated in the U.S. was 9.7 x 1017 J and the total amount of electrical energy generated was 1.46 x 1019 J. What percentage of the total electric energy produced was hydroelectric energy?
Explanation / Answer
(a)
mass of rain water received m = 1000 x 8 x 106 x 106 x 0.75 = 6 x 1015 kg
gravitaional potential energy of this mass = m gh = 6 x 1015 x 9.8 x 500 = 2.94 x 1019 J
one-third of this can be converted to hydroelectric energy,
maximum possible hydroelectric energy that can be generated = 9.8 x1019 J
(b)
percentage of hudro-electric energy in total electrical energy = (9.7 x 1017 ) x 100 / ( 1.46 x 1019 ) = 6.644 %
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