Correct Answer - Option 4 : cube of the wind velocity
Wind Generation
- The wind is a by-product of solar energy. Approximately 2% of the sun's energy reaching the earth is converted into wind energy.
- The wind-mill contains three blades about a horizontal axis installed on a tower
- A turbine connected to a generator is fixed about the horizontal axis
- Like the weather in general, the wind can be unpredictable. It varies from place to place, and from moment to moment.
- Because it is invisible, it is not easily measured without special instruments.
- Wind velocity is affected by the trees, buildings, hills and valleys around us.
- Wind is a diffuse energy source that cannot be contained or stored for use elsewhere or at another time.
Mathematical Expression Governing Wind Power
The wind power is generated due to the movement of wind.
The energy associated with such movement is the kinetic energy and is given by the following expression:
Energy= KE=1/2 x m x v2
where,
- m = Air mass in Kg = Volume (m3) x Density (Kg/m3) = Q x ρ
- Q = Discharge
- v = Velocity of air mass in m/s
Hence, the expression for power can be derived as follows:
Power= dE/dT
= 1/2 x d/dT { m x v2} ......(Since, Energy= 1/2 x m x v2)
= 1/2 x d/dT { ρ x Q x v2}
= 1/2 x ρ x dQ/dT x v2
Here dQ/Dt = = Rate of discharge (m3/s) = A (m2) • v (m/s)
Where, A = Area of cross section of blade movement.
Power = 1/2 x ρ x A x v3
We know that for given length of blades, A is constant and so is the air mass density ρ.
Hence we can say that wind power is directly proportional to (wind velocity)3.
Therefore, Wind energy is very sensitive to the wind velocity because wind power is directly proportional to the cube of the wind velocity.
