Question

Which of the following estimates the potential wind energy sites by power density of the site?

• A. \( P = \frac{1}{2} mv^2 \)
• B. \( P = \frac{1}{2} \rho v^3 \)
• C. \( P = \frac{1}{2} \rho A v^2 \)
• D. \( P = \frac{1}{2} \rho A v^3 \)

Hint:

Wind power is proportional to the cube of wind velocity. Small increases in wind speed significantly increase power generation.

Answer 1

The Correct Option is D

Step 1: Understanding Wind Power Formula
The power available from wind energy is given by: \[ P = \frac{1}{2} \rho A v^3 \] where: - \( P \) = Power (W) - \( \rho \) = Air density (kg/m³) - \( A \) = Swept area of turbine blades (m²) - \( v \) = Wind velocity (m/s)
Step 2: Eliminating Incorrect Options
- \( P = \frac{1}{2} mv^2 \) is the kinetic energy formula, not for wind power. - \( P = \frac{1}{2} \rho v^3 \) does not account for blade area \( A \), making it incomplete. - \( P = \frac{1}{2} \rho A v^2 \) is incorrect because wind power is proportional to the cube of velocity.
Step 3: Conclusion
The correct expression for wind power density includes air density, swept area, and wind velocity cubed.