The Amazon wall socket

Classical Mechanics Level 3

Hydrovolts has invented a water powered cell phone charger - the HydroBee. Put the charger in a flow of water, like a stream or faucet, and a little turbine spins, generates electricity, and charges up your phone. Hence if you are out camping you can now charge a phone without carrying along a bunch of batteries. If the HydroBee has a circular opening aperture of radius \(5~\mbox{cm}\) and is placed in a stream with flow rate \(1~\mbox{m/s}\), how long in hours will it take to completely charge an empty cell phone battery rated at \(5~\mbox{W-h}\) (Watt-hours)?

Details and assumptions

  • The density of water is \(\rho=1~\mbox{g/cm}^3\).
  • The energy conversion efficiency of the kinetic energy of the water to electric energy is 50%.
  • The water flows through the entire opening aperture.

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