Question

If a 100 m. diameter wind turbine is exposed to 7 m/s wind with an air density of 1.25 kg/m what is the electricity produced by the turbine? Assume a 32% efficiency of the turbine.

Answer 1

Answer:

electric energy = 980 J

Step-by-step explanation:

Given,

Diameter of wind turbine = 100 m

Speed of wind,v = 7 m/s

Density of air = 1.25 kg/m

Hence, the total mass of air enters into turbine =Speed of wind x Diameter of wind turbine

                                                                             = 1.25 x 100

                                                                              = 125 kg

Hence, total mechanical energy of turbine can be given by,

$E\ =\ \dfrac{1}{2}.m.v^2$

    $=\ \dfrac{1}{2}\times 125\times 7^2$

    = 3062.5 J

Efficiency of turbine = 32%

Hence,

total electric energy = 32% of mechanical energy

                                  $=\dfrac{32}{100}\times 3062.5\ J$

                                  = 980 J

So, the total electric energy produced by the turbine will be 980 J.