Electricity Generated using Water Power

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Problem Description

  Hydroelectric power is the largest source of renewable energy produced in the United States. As water flows through turbines, mechanical energy in terms of shaft work is produced, and electricity is generated by converting this mechanical energy through generators. Consider a turbine with the inlet and outlet conditions as shown in the figure. The water flows at a rate of 200 slugs/s. The pressure drop is 50 psi across the 100 ft elevation difference between the inlet and outlet. The inlet and outlet pipe radii are 2 ft and 3 ft, respectively. How much power will the hydraulic turbine produce?


Determine the rate of work done (power) produced by the turbine.


  • Assume the flow is steady.
  • Assume the hydraulic turbine has no power loss (i.e., adiabatic and no change in the internal energy).
  • The density of the water is 1.94 slugs/ft3.
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