Large wind turbines with a power capacity of 8 MW and blade span diameters of over 160 m are available for electric power generation. Consider a wind turbine with a blade span diameter of 100 m installed at a site subjected to steady winds at 8 m/s. Taking the overall efficiency of the wind turbine to be 44 percent and the air density to be 1.25 kg/m3, determine the electric power generated by this wind turbine. Also, assuming steady winds of 8 m/s during a 24 hour period, determine the amount of electric energy and the revenue generated per day for a unit price of $0.09/kWh for electricity.

The density of air is given to be rho-1.25 kg/m3

The electric power generated by the wind turbine is kWh.

The amount of electric energy generated is `` kWh

The revenue generated per day is $ .

The electric power generated by the wind turbine is 1105.84 kWh

The amount of electric energy generated is 26540.17 kWh

The revenue generated per day is $2388.62

Explanation:

Consider a wind turbine with a blade

Span diameter of 100 m installed at a site

subjected to steady winds at 8 m/s

l.e wind speed v = 8 m/s

Span diameter d = 100 m

A, sweap area = πd² / 4

                        = π x 100² / 4

                        = 7853.98 m²

Lets solve for wind speed v = 8 m/s

Density of Area ρ = 1.25 kg/m³

η = 44%

P = 1/2 ρAv³η

  = 1/2 x 1.25 x 785.98 x 8³ x 44/100

  = 1/2 x 1.25 x 7853.98 x 512 x 0.44

  = 1105840.38

  = 1.10584038 mw

  = 1105.84038 kWh

  = 1105.84 kWh

Energy generated by wind turbine per day

⇒ P x H

      = 1105.84038 x 24

      = 26540.16912 kwh

      = 26540.17 kwh      

Revenue generated per day = Energy x 0.09 kwh

                                                = 26540.16912 x 0.09

                                                = $2388.615

                                                = $2388.62

answer; equivalent to a one(1) horsepower motor;