Question

An industrial wind turbine has blades that are 35 m long. On a 20?C day, wind at atmospheric pressure blows with a velocity of 12 m/s , and wind in the turbine wake only has a velocity of 11 m/s .

(a) Will the turbine’s wake have a smaller, larger, or the same cross-sectional area compared to the area the blades sweep out. Why? Calculate this area. Hint: At velocities much lower than the speed of sound, with small pressure gradients, gases can be treated as incompressible.

(b) Draw a control surface for the wind that passes through the area the turbine blades sweep out. Use momentum transport to find the force exerted on the windmill by the air flowing past it.

Answer 1