Calculate the maximum energy (J) that could be obtained from 1 kg of water, assuming that the energy content of the mass, E = Mc², could be completely converted to useful energy in some sort of incredible reactor. Calculate the water consumption rate (kg/s) by such a reactor if it has the same power output as the maximum power output of the hydroelectric power plant of Exercise 1.3, and compare the water mass flow rates of the two systems.

Data From Exercise 1.3

Let V be the water velocity in a river of width w and depth d, flowing along at a height h above a hydraulic power station. Show that the maximum electrical power that could be obtained by converting the potential energy of the river water to electrical energy is ρ · ν · w · d · h · g, where ρ is the water mass density. Calculate the maximum available power (MW) for ω = 20 m, d = 10 m, h = 100 m, ν = 2 m/s, using ρ = 1000 kg/m³.