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