Grand Coulee
The Biggest Dam?!?!? help?
The Grand Coulee dam in Washington State is the largest concrete structure and the largest hydroelectric power station in the US, third largest in the world. The hydraulic height is 116 m and the average release is 3100 m3/s. The average power generation is 21 billion kilowatt hours per year (21000 GWh/yr) according to the official web page.
What’s the efficiency of converting gravitational potential energy of water into electricity? Remember that 1 L of water has a mass of 1 kg.
Assuming that the height of the water doesn't change.
Potential energy E=mgh = mass x acceleration from gravity x height/head.
Power is dE/dt, energy/time. 3100m^3 of water means 3100000kg of water is released every second. So power transferred from potential energy is 3100000 x 9.81 x 116
Multiply this to go from seconds to years: so multiply by 3600 x 24 x 365.25.
This should give you about 1.1E17J. Convert to kWh by dividing by 3600000 and potential is 30.9 billion kWh/year.
21/30.9 ~ 68%.
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