Question

1. Explain the Betz’s theorem and various terms in the equation

Answer 1

Let us assume that the wind speed at the inlet area of the turbine is V₁

_{The wind speed at an otutlet area of the turbine is V2}

The mass of air flowing through the rotor is ................eq.1

where, m= is mass flowing per second,

   = density of air

F = Swept area of the rotor

The power extracted from wind by rotor is equal to,

according to the Newton law , power P = (1/2) m * (V²₁ - V²₂ )..................eq.2

put m value of eq.1 into eq.2

P = ( /4) (V²₁ - V²₂  ) (V_{1 +} V₂ ) F

Let us assume P₀ is the power generated in the rotor at same F value without blocking air by the rotor,

P₀ = ( /2) V₁³ F

The ratio of power developed by actual turbine and an undisturbed or ideal turbine is

(P/P ₀ ) = (1/2) (1 - (v ₂  / v ₁ ) ² ) (1 + (v ₂  / v ₁ ))

as per the literatre the graph between P/P ₀ and v₂  / v₁

We can see in the graph that, the function reaches a maximum of 16/27 or 0.59 of total power.