Problem Graphic

Power Generated by a
Hydraulic Turbine


A hydroelectric power plant is to be built in a mountain region. Water flows from the elevated reservoir through pipes to a hydraulic turbine, whose shaft is connected to a electric generator. Thus, the mechanical energy of water is converted to electrical energy. A designer orders some 0.5-m-diameter-pipes but he needs the engineer to specify the exact number of intake pipes.

What is known:

  • The water surface in the reservoir is 105 m higher than the turbine.
  • The entrance to the intake pipes is located 5 m below the water surface in the reservoir.
  • Water enters the intake pipe at 1 m/s and exhausts to a river directly after exiting the turbine with almost the same velocity.
  • The ambient pressure is 1 bar.
  • The pipe diameter is 0.5 m.
  • The power output is 1 MW.



A Hydroelectric Power Plant


How many intake pipes are to be installed?


  • Take the system from point 1 to 2 shown on the left as a control volume.
  • Consider the power plant works in reversible and steady flow conditions. Then the power output from the power plant equals the reversible steady-flow work of the turbine.

Schematic of the Power Plant