Correct Answer - Option 2 : Increase in rotor diameter
Power of wind turbine, P = 0.5 × swept area × Air density × (Velocity)3
or we can say that,
The power is available from wind ∝ Area (A)
∴ Available wind power in wind turbines increases with an increase in the area which is proportional to the rotor diameter.
Proof:
Wind power is the conversion of wind energy into a useful form of energy, wind turbines convert this energy into useful electric energy. The wind turbine consists of mainly three blades which are mounted over a tower above the ground. The turbine catches wind energy and the combination of lift and drag force causes the rotor to spin like a propeller.
Since the velocities close to the ground are very low and there must be good clearance between the lower parts of the blade and the ground, the wind turbines are placed on top of tower at significant height above the ground. The towers are between 30 and 100 m high.
The energy of the wind is given as \(E = \frac{1}{2}m{v^2}\)
The power in the wind will be given by the rate of change of energy
\(P = \frac{{dE}}{{dt}}\)
\(P = \frac{1}{2}{v^2}\frac{{dm}}{{dt}}\;\)
and mass flow rate is given by \(\frac{{dm}}{{dt}} = \rho A\frac{{dx}}{{dt}}\)
and the rate of change of distance is given by \(\frac{{dx}}{{dt}} = v\)
Therefore \(\frac{{dm}}{{dt}} = \rho Av\)
∴ \(P = \frac{1}{2}{v^2} \times \;\rho Av = \frac{1}{2} \times \rho A{v^3}\)
