Answer :
a. To determine the rotor diameter size needed to generate 100 kWh of energy with a 25% turbine efficiency, we need to first calculate the total energy produced by the wind turbine. Since the turbine is rated at 1 kW, it can produce 1 kWh of energy per hour. Given that we have a 30-day month, the turbine needs to generate 100 kWh over that period.
To find the number of hours needed to generate 100 kWh, we divide the total energy (100 kWh) by the energy produced per hour (1 kWh). So, 100 kWh / 1 kWh = 100 hours.
Now, we can calculate the rotor diameter size using the formula: Diameter (m) = 2 * (Power (kW) / (π * Wind Speed (m/s) * Turbine Efficiency)). Plugging in the values, we get: Diameter = 2 * (1 kW / (π * 6 m/s * 0.25)) = 2 * (1 kW / (3.14 * 6 m/s * 0.25)) ≈ 2.68 meters.
b. If the efficiency is 30% at the rated power of 1 kW, we can calculate the wind speed needed for the turbine to reach its full power. Using the formula: Wind Speed (m/s) = Power (kW) / (Turbine Efficiency * π * (Rotor Diameter (m)/2)^2), we can plug in the values: Wind Speed = 1 kW / (0.3 * π * (Rotor Diameter/2)^2). Since the rotor diameter is not given, we cannot provide a specific wind speed.
c. To determine the number of hours the turbine would run at its rated power, we can divide the total energy produced (100 kWh) by the energy produced per hour (1 kWh/hour). So, the turbine would run for 100 hours at its rated power during the 30-day month.
Overall, the rotor diameter size needed would be approximately 2.68 meters to generate 100 kWh with a 25% turbine efficiency. The wind speed required to reach the full 1 kW power cannot be determined without knowing the rotor diameter size. The turbine would run at its rated power for 100 hours during the 30-day month.
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