Question

At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 80-m-diameter (D) blades at that location. Take the air density to be 1.25 kg/m3. The mechanical energy of air per unit mass is kJ/kg. The power generation potential of the wind turbine is kW.

Answer 1

Answer:

$0.05\ \text{kJ/kg}$

$3141.6\ \text{kW}$

Explanation:

v = Velocity of wind = 10 m/s

A = Swept area of blade = $\dfrac{\pi}{4}d^2$

d = Diameter of turbine = 80 m

$\rho$ = Density of air = $1.25\ \text{kg/m}^3$

Wind energy per unit mass of air is given by

$E=\dfrac{v^2}{2}\\\Rightarrow E=\dfrac{10^2}{2}\\\Rightarrow E=50\ \text{J/kg}$

The mechanical energy of air per unit mass is $0.05\ \text{kJ/kg}$

Power is given by

$P=\rho AvE\\\Rightarrow P=1.25\times \dfrac{\pi}{4}\times 80^2\times 10\times 50\\\Rightarrow P=3141592.65=3141.6\ \text{kW}$

The power generation potential of the wind turbine is $3141.6\ \text{kW}$.