A pumped-storage facility has an upper reservoir that can hold m³ of water at an…
PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials
Problem
A pumped-storage facility has an upper reservoir that can hold 1.2×106 m³ of water at an average height difference of 300 m relative to the lower reservoir. During off-peak hours, electric pumps raise water to the upper reservoir with an efficiency of 70%. During peak demand, the stored water is released and the combined turbine–generator system converts 85% of the water’s mechanical energy back into electrical energy. Take g=9.8 m s⁻² and the density of water as 1.0×103 kg m⁻³.
(i) Calculate the electrical energy consumed to completely fill the upper reservoir from the lower one.
(ii) Determine the maximum electrical energy that can be generated when the full reservoir is emptied through the turbines.
(iii) Compute the round-trip energy efficiency of the entire cycle.
(iv) If the facility must supply a peak power of 250 MW, estimate the maximum number of hours it can operate at full output before the upper reservoir is emptied.