When a wind turbine is in action, all the wind coming in to the front must obviously exit out the back. The air can't just pile up at the blades. However, extracting kinetic energy from the wind slows it down, which means the air isn't getting out of the way fast enough for new air to come in$.$ To compensate, the moving air changes its geometry. If you imagine a long cylinder of air being fed into the front of a windmill, the cylinder of air coming out the back will have a larger radius in order to move more air, which compensates for the slower speed that moves less air. This sudden increase in the radius at the blades causes turbulence. How much bigger is the new radius? Well I am glad you asked $...$

$$

Suppose you have a wind turbine with $27$ m long blades spinning in $11$ m$/$s wind. Let's say the turbine extracts $31\%$ of the kinetic energy from the wind. Assuming the volume of the air doesn't change, how much bigger is the radius of the cylinder of exiting air compared to the entering air?