Question

a 40kW , three-blade wind turbine is designed to deliver the power at a wind speed of 15m/s. The blade depth of 14m, a rated speed of the turbine 48 rpm. The air density of 1,226kg/m³. calculate (a) area swept out by the turbine

Answer 1

The area swept out by the wind turbine with a blade length of 14m is calculated using the formula for the area of a circle, yielding an approximate area of 615.75 square meters.

Step-by-step explanation:

To calculate the area swept out by the wind turbine, you need to use the blade length to determine the radius of the circle the blades make and then apply the formula for the area of a circle (A = πr^2).

In this case, the blade depth, or length, is given as 14m. this is effectively the radius of the circle the blades are sweeping out. So, the area A would be π(14m)^2. Doing the math

• A = π(14m)^2
• A = π(196m^2)
• A ≈ 3.1416 (196m^2)
• A ≈ 615.7516m^2

So, the area swept out by the blades is approximately 615.75 square meters.