A wind turbine is subjected to forces caused by the wind pushing against the blades and the tower. These forces can be simplified to two point loads: the force Fg on the blades (acting at point X) and the force Fron the tower (acting at point Y). These forces generate a bending moment at the base of the tower (at point Z). F х H F, N Given FB = 47 KN, H = 40 m, h = H/2 and Ft is determined using the equation: F1 = Cd * Apv2/2 Where the drag co-efficient Cd - 1.2, the frontal surface area of the tower A = 700 m2, the velocity of the wind v is 7.4 m/s and the density of the airp is 1.2 kg/m³. What is the magnitude of the moment acting at Point Z?

Question

11-05-2025
Physics

High School

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A wind turbine is subjected to forces caused by the wind pushing against the blades and the tower. These forces can be simplified to two point loads: the force Fg on the blades (acting at point X) and the force Fron the tower (acting at point Y). These forces generate a bending moment at the base of the tower (at point Z). F х H F, N Given FB = 47 KN, H = 40 m, h = H/2 and Ft is determined using the equation: F1 = Cd * Apv2/2 Where the drag co-efficient Cd - 1.2, the frontal surface area of the tower A = 700 m2, the velocity of the wind v is 7.4 m/s and the density of the airp is 1.2 kg/m³. What is the magnitude of the moment acting at Point Z?

Answer :

Final answer:

To calculate the magnitude of the moment at point Z in a wind turbine, we need to calculate the force Ft acting on the tower and then use the equation M = F * h. Substituting the given values and equations, we can find that the magnitude of the moment at point Z is 47.109.2 Nm.

Explanation:

To determine the magnitude of the moment acting at point Z, we need to calculate the force Ft acting on the tower. Using the given equation Ft = Cd * A * p * v^2/2, we can substitute the values: Cd = 1.2, A = 700 m^2, p = 1.2 kg/m^3, and v = 7.4 m/s. Calculating Ft, we get:

Ft = 1.2 * 700 * 1.2 * 7.4^2 / 2 = 2211.84 N

To find the magnitude of the moment at point Z, we can use the equation M = F * h, where F is the total force acting on the tower (Fg + Ft) and h is the height of the tower (H/2). Substituting the values, we have:

M = (47 + 2211.84) * (40/2) = 47.109.2 Nm

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