Calculating the power of a hydroelectric plant

The energy produced in a hydroelectric plant comes from falling water. This means that the water moves from a higher altitude to a lower altitude. The difference between these different altitudes or heights is called the head .

A hydroelectric plant changes gravitational potential energy (GPE) to kinetic energy and finally to electrical energy. The power, the rate at which energy is being produced, depends on two things:

1. The height of water above the turbine;
   
2. The flow rate of water i.e. the mass of water flowing through the turbine per second.

Now the power generated by the falling water is given by: i.e. Power = flow rate x gravity x height Where: GPE = mass x gravitational acceleration x height = gravitational potential energy KE = 1/2 x mass x velocity squared = kinetic energy t = time Flow rate = mass/time Power is measured in Watts (W) Because power stations produce large amounts of power the unit of measure is usually expressed as megawatts (MW).

Example

Suppose a hydroelectric plant has a head of water (i.e. the height of water above the turbines) of 50 metres. The flow rate of the water through the turbines is 500 kg/s. To calculate the power produced by this plant we use the formula: Power = flow rate x gravity x height = 500 kg/s x 9.8 ms -2 x 50 metres = 245,000 Watts or 0.245 MW