A water turbine at a dam has an efficiency of 80%. What is the energy generated from a reservoir that is in the shape of a cuboid with height 200 m and area 500 m^2
Water stored in a reservoir is used to produce electricity. The electric turbine has an efficiency of 80%. It can convert 80% of the potential energy stored in the water that fills the reservoir to electrical energy.
An object with mass m at a height h has a gravitational potential energy of m*g*h.
The density of water is 1000 kg/m^3. The volume of water stored in the reservoir is 200*500 = 100000 m^3. The mass of the water is 10^8 kg. As the reservoir is a cuboid the center of mass of the water is halfway to the top or 100 m.
This gives the potential energy stored in the water as 100*10^8*9.8 = 9.8*10^10 J
As the turbine has an efficiency of 80%, the electrical energy generated is 7.84*10^10 J