Turbines deflect wind

Stream tube through a turbine         The image on the page for the energy in the wind is a bit simplified. In reality, a wind turbine will deflect the wind, even before the wind reaches the rotor plane. This means that a wind turbine will never be able to capture all of the energy in the wind. This will be further explained in the next page on Betz' Law.
        In the image the wind is coming from the right and a device is used to capture part of the kinetic energy in the wind. In this case a three bladed rotor is used, but some other mechanical device could be used.

The streamtube         
        The wind turbine rotor must obviously slow down the wind as it captures its kinetic energy and converts it into rotational energy. This means that the wind will be moving more slowly to the left of the rotor than to the right of the rotor. Since the amount of air entering through the swept rotor area from the right at every second must be the same as the amount of air leaving the rotor area to the left, the air will have to occupy a larger cross section, diameter, behind the rotor plane.
        In the image above this has been illustrated this by showing an imaginary tube, a so called stream tube around the wind turbine rotor. The stream tube shows how the slow moving wind to the left in the picture will occupy a large volume behind the rotor. The wind will not be slowed down to its final speed immediately behind the rotor plane. The slowdown will happen gradually behind the rotor, until the speed becomes almost constant.

The air pressure distribution behind and in front of the rotor
Air pressure graph         The graph shows the air pressure plotted vertically, while the horizontal axis indicates the distance from the rotor plane. The wind is coming from the right and the rotor is in the middle of the graph. As the wind approaches the rotor from the right, the air pressure increases gradually, since the rotor acts as a barrier to the wind. Note, that the air pressure will drop immediately behind the rotor plane to the left. It then gradually increases to the normal air pressure level in the area.

What happens farther downstream?
        Farther downstream the turbulence in the wind will cause the slow wind behind the rotor to mix with the faster moving wind from the surrounding area. The wind shade behind the rotor will therefore gradually diminish when moving away from the turbine. This will be further discussed on the page Park effect.

Why not a cylindrical streamtube?
Wind turbine inside a cylindrical tube         The turbine rotor could also turn if it were placed in a large glass tube, but consider what happens: the wind to the left of the rotor moves with a lower speed than the wind to the right of the rotor. But at the same time the volume of air entering the tube from the right each second must be the same as the volume of air leaving the tube to the left. Therefore it can be deduced that if there is some obstacle to the wind, in this case the rotor, within the tube, then some of the air coming from the right must be deflected from entering the tube due to the high air pressure in the right end of the tube.
        So, the cylindrical tube is not an accurate picture of what happens to the wind when it meets a wind turbine. This picture at the top of the page is the correct picture.