Question 11In GWA 3 find the mean power density W/m^2 and mean wind speed at 100m for the 10% of the windiest areas of Denmark.

To find the mean power density and mean wind speed for the 10% of the windiest areas of Denmark based on the Global Wind Atlas (GWA) data, we can follow these steps:

1. Break Down the Problem

1. Define what is meant by "mean power density" and how it relates to wind speed.
2. Identify data sources that give wind speed data for Denmark.
3. Calculate the mean values for the highest 10% of wind speed areas.

2. Relevant Concepts

1. Mean Power Density Formula: The mean power density $P$ can be calculated using the wind speed $V$ with the formula: $P = \frac{1}{2} \cdot \rho \cdot V^3$ where $\rho$ is the air density (approximately $1.225 \, \text{kg/m}^3$ at sea level).

2. Finding the 10% Windiest Areas: Filter the wind speed data to identify the top 10% windiest areas.

3. Analysis and Detail

1. Gather Wind Speed Data: Collect wind speed data for various locations in Denmark, specifically the average wind speed at 100m height.

2. Calculate Mean Values:

   • Sort the data to find the wind speeds for the top 10% windiest locations.
   • Calculate the mean wind speed $V_{mean}$ for these locations.

3. Calculate Mean Power Density:

   • Use the mean wind speed calculated above in the power density formula.

4. Verify and Summarize

1. Ensure the validity of the wind speed data, confirming it's for the 10% windiest regions.
2. Verify calculations for power density and wind speed.

Final Answer

If you provide the actual wind speed measurements or a dataset, I can assist with the computations to present the final values. Otherwise, the following is a general structure of what the findings would look like:

• Mean Wind Speed at 100m: $V_{mean} = X \, \text{m/s}$
• Mean Power Density: $P = \frac{1}{2} \cdot 1.225 \cdot (X)^3 \, \text{W/m}^2$

Make sure to replace $X$ with the actual mean wind speed value in your calculations.