A wind farm is constructed from turbines with a rotor diamet

A wind farm is constructed from turbines with a rotor diameter of 50 m and 40% efficiency that are spaced at a distance of 500 m apart in the prevailing downwind direction and 150 m apart in the crosswind direction. In a wind of 10 m/s. what is the output of the wind farm per Km^2? Select one: 10.14 MW 13.44 MW 6.31 MW 2.58 MW

Solution

Area of wind farm is 1 Km² = 1000*1000 m²

Area occupied by one wind turbine is 500*150 = 75000 m²

No.of Wind turbines in the farm is N = 10⁶ / 75000 = 13

We know power from one wind turbine is given by

P_out = 0.5 * (Swept Area) * (Air Density) * (Velocity)³ * eff

where

Swept Area = pi*D² / 4 = pi * (50*50)/4 = 1963.495 m²

Air Density Da = 1.225 Kg/m³ at sea level

Velocity = 10 m/s

eff = 0.4

Total Power output from wind farm is P_T = N * P_out

P_out = 0.5 * 1000 * 0.4 * 1.225 * 1963.495 = 0.481 MW

P_T = 13 * P_out = 13 * 0.481 = 6.25 MW

option : - C