A wind turbine works by slowing the air that passes its...

A wind turbine works by slowing the air that passes its blades and converting much of the extracted kinetic energy to electric energy. A large wind turbine has $45-\mathrm{m}$ -radius blades. In typical conditions, $92,000 \mathrm{kg}$ of air moves past the blades every second. If the air is moving at $12 \mathrm{m} / \mathrm{s}$ before it passes the blades and the wind turbine extracts $40 \%$ of this kinetic energy, how much energy is extracted every second?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Power Calculation

Power is the rate at which energy is transferred or converted, measured in watts (joules per second). In the context of wind turbines, calculating the power output involves determining the kinetic energy from the moving air per unit time and then applying the conversion efficiency to obtain the electrical power produced.

Energy Conversion Efficiency

Energy conversion efficiency represents the percentage of the available energy that is actually converted to another form, such as electrical energy. Turbines rarely capture all the kinetic energy from the wind, so this efficiency factor is crucial in determining the actual output power from the wind turbine.

Kinetic Energy

Kinetic energy is the energy of motion and is given by the formula ½mv², where m is mass and v is velocity. This concept is fundamental in understanding how moving air contains energy that can be harnessed by devices such as wind turbines.

Mass Flow Rate

Mass flow rate refers to the amount of mass passing through a given area per unit time. In wind energy applications, it determines how much air (and thus kinetic energy) flows through the turbine, making it a key factor in calculating the potential energy available for conversion.

Transcript

Please give Ace some feedback