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Calculate the approximate surface area that would be required

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Calculate the approximate surface area that would be required of a lake of an average depth of 20 m at an elevation of 300 m (mean water level between full and empty reservoir) above an array of Francis turbines, operating at an efficiency of 85%, if we were to store enough energy to meet the entire power requirements of the National Grid (say 50 GW) for 24 hours.

Calculate the approximate surface area that would be required of a lake of an average depth of 20 m at an elevation of 300 m (mean water level between full and empty reservoir) above an array of Francis turbines, operating at an efficiency of 85%, if we were to store enough energy to meet the entire power requirements of the National Grid (say 50 GW) for 24 hours.

Let surface area = A m^2

Volume of the stored water = 20 A m^3

Mass of the stored water = 20A*1000 kg as water density = 1000kg/m^3

Potential energy of the stored water = 20A*1000*9.8*300 = 58.8*10^6A Joules

Energy required for 24 requirements = 50*10^9*24*3600/0.85 Joules.

Equating both energies, we get 58.8*10^6A = 50*10^9*24*3600/0.85

Or, A =[ 50*10^9*24*3600]/[0.85*58.8*10^6] = 86.4345*10^6 m^2 = 86.4345 km^2 Ans.

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