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Calculate the wind speed distribution using the Rayleigh distribution for an average wind speed of 8 m/sec

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Answer:

The Rayleigh distribution is often used to model wind speed distribution. It is characterized by a scale parameter, often denoted as "σ" (sigma), which depends on the average wind speed.

The probability density function (PDF) of the Rayleigh distribution is given by:

f(x; σ) = (x / σ^2) * e^(-x^2 / (2σ^2))

Where:

f(x; σ) is the PDF of the Rayleigh distribution with scale parameter σ.

x is the wind speed.

σ is the scale parameter.

In your case, you have an average wind speed of 8 m/s. To calculate the wind speed distribution using the Rayleigh distribution, you need to determine the appropriate value of σ.

The relationship between σ and the average wind speed (V_avg) is given by:

σ = V_avg / √(π/2)

Substituting the average wind speed of 8 m/s into the formula:

σ = 8 m/s / √(π/2)

σ ≈ 8 m/s / 1.2533 ≈ 6.37 m/s (approximately)

Now that you have the value of σ, you can use it to describe the Rayleigh distribution for your average wind speed of 8 m/s. This distribution will describe the probability of various wind speeds occurring around the average wind speed of 8 m/s.

Step-by-step explanation:

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User Mark Rabey
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