Question

At a certain location, wind is blowing steadily at 7 m/s. Determine the mechanical energy of air per unit mass and the power generation potential of a wind turbine with 80-m-diameter blades at that location. Also determine the actual electric power generation assuming an overall efficiency of 30 percent. Take the air density to be 1.25 kg/m3.

Answer 1

Step-by-step explanation:

From the information given;

The velocity of the wind blow V = 7 m/s

The diameter of the blades (d) = 80 m

Percentage of the overall efficiency
`\eta_(overall) = 30\%`

The density of air
`\rho = 1.25 kg/km^3`

Then, we can use the concept of the kinetic energy of the wind blowing to estimate the mechanic energy of air per unit mass by using the formula:

`e_(mechanic) = (mV^2)/(2)`

here;

m =
`\rho AV`

=
`1.25 * (\pi)/(4)(80)^2 * 7`

= 43982.29 kg/s

∴

`W = e_(mechanic) = (mV^2)/(2)`

`= (43982.29 * 7^2)/(2)`

`= 1077566.105 \ W`

`\mathbf{ =1077.566 \ kW}`

The actual electric power is:

`W_(electric) = \eta_(overall) * W`

`W_(electric) = 0.3 * 1077.566`

`\mathbf{W_(electric) =323.26 \ kW}`