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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.
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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.

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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