The data for a wind turbine is given below:
Wind speed = 14 m/sec
Length of blade = 20 m
Rotor efficiency = 50%
Gear Box efficiency = 75% Generator Efficiency = 85%
i) Calculate the power in the wind.
ii) Calculate the power output of wind turbine
*To find output power of wind turbine we have to use rotor efficienct which is 50% or we have use 0.35 ? please explain for me this point clearly
To calculate the power in the wind, you can use the equation:
Power in the wind = (1/2) * rho * A * v^3
where:
rho is the air density (assumed to be constant)
A is the swept area of the rotor blades
v is the wind speed
Assuming the air density is 1.225 kg/m^3, and the swept area of the rotor blades is given by:
Swept area = pi * (length of blade)^2
= 3.14159 * (20)^2
= 1256.6371 m^2
Plugging in these values and the wind speed of 14 m/sec into the equation, you will get the power in the wind.
ii) To calculate the power output of the wind turbine, you need to consider the efficiencies of various components in the system.
The power output of the wind turbine is given by:
Power output = Power in the wind * Rotor efficiency * Gear Box efficiency * Generator Efficiency
In this case, the rotor efficiency is given as 50%, which means that the rotor is capable of converting 50% of the power in the wind into mechanical power that drives the generator.
The gear box efficiency is given as 75%, which means that the gear box can convert 75% of the mechanical power from the rotor into electrical power.
The generator efficiency is given as 85%, which means that the generator can convert 85% of the mechanical power from the gear box into electrical power.
Therefore, you can calculate the power output of the wind turbine by multiplying all these efficiencies together with the power in the wind.
To calculate the power in the wind, you can use the following formula:
Power = 0.5 * air density * swept area * wind speed^3
Since we don't have the air density or the swept area, we cannot calculate the power in the wind directly.
To calculate the power output of the wind turbine, you need to know the rotor efficiency, gear box efficiency, and generator efficiency. The rotor efficiency of 50% is the correct value to use in this case. It represents the proportion of the power captured by the rotor compared to the power in the wind.
Therefore, to calculate the power output of the wind turbine, you can multiply the power in the wind by the rotor efficiency:
Power output = Power in the wind * Rotor efficiency
Please note that using a rotor efficiency of 50% is the correct approach in this case because it represents the efficiency of the rotor in capturing the power in the wind.