Final answer:
The power produced by a 50%-efficient wind turbine with a radius of 10 m varies with wind speed: 9.81 kW for 5 m/s, 78.54 kW for 10 m/s, 266.59 kW for 15 m/s, and 628.32 kW for 20 m/s. Determining the number of windmills on the plain is not possible without more context.
Step-by-step explanation:
To calculate the power produced by a windmill or wind turbine, you can use the formula for the power of wind hitting a windmill:
P = 0.5 x ρ x A x Cp x V3 , where:
- ρ is the air density (approximately 1.225 kg/m3 at sea level),
- A is the swept area of the turbine blades (π x radius2 for a circular sweep),
- Cp is the coefficient of performance (which is 0.50 according to the given efficiency),
- V is the wind speed in m/s.
To answer the question "How much power would a moderate-sized 50%-efficient wind turbine produce whose radius is 10 m at wind speeds of 5 m/s, 10 m/s, 15 m/s, and 20 m/s?". The swept area A is π x (10 m)2 = 314.16 m2. Then, we insert this value along with each wind speed into the formula and calculate the power for each scenario in kW:
- For V = 5 m/s, P would be approximately 9.81 kW.
- For V = 10 m/s, P would be approximately 78.54 kW.
- For V = 15 m/s, P would be approximately 266.59 kW.
- For V = 20 m/s, P would be approximately 628.32 kW.
Regarding the question about the number of windmills on the plain, without additional context or a relationship in the given data, there is not enough information to determine the correct answer from the four options presented.