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

electric energy = 980 J

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\ =\ (1)/(2).m.v^2`

`=\ (1)/(2)* 125* 7^2`

= 3062.5 J

Efficiency of turbine = 32%

Hence,

total electric energy = 32% of mechanical energy

`=(32)/(100)* 3062.5\ J`

= 980 J

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