Considering the wind power equation P = 1/2ρAv³, if the wind speed doubles, how does the available power change?

Question

Question

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BHEL Supervisor Trainee Mechanical 21 Jan 2024 Official Paper

Answer 1

Concept:

The power available in the wind is given by the equation:

\( P = \frac{1}{2} ρ A V^3 \)

Where:

Calculation:

If the wind speed doubles, i.e., V' = 2V, then substituting in the equation:

\( P' = \frac{1}{2} ρ A (2V)^3 \)

\( P' = \frac{1}{2} ρ A \cdot 8V^3 \)

\( P' = 8 \times \left( \frac{1}{2} ρ A V^3 \right) \)

\( P' = 8P \)