Question

In the far west states of the country, one can find wind farms with wind turbines that turn in response to a force of high-speed air resistance, R = ½DrhoAv2. The power available is P = Rv = ½Drhoπr2v3, where v is the wind speed and we have assumed a circular face for the wind turbine of radius r. Take the drag coefficient D = 1.00 and the density of air as 1.20 kg/m3.(a) For a wind turbine having r = 1.30 m, calculate the power available (in kW) for a velocity of v = 8.40 m/s.(b) For a wind turbine having r = 1.30 m, calculate the power available (in kW) for a velocity of v = 25.5 m/s.

Answer 1

Answer:

The power will be 1.88KW and 52.821KW

Explanation:

Since

$R = 1/2 * D * /rho * A * v^2$

$P = Rv = 1/2 * D * /rho * /pi * r^2 * v^3$

given

D= 1.0

ρ = 1.2

r = 1.30

v = 8.4

Put all values in the above equation to get

$P = 0.5 * 1 * 1.2 * 3.14 * 1.3^2 * 8.4^3$

$P = 1888.10 Watt = 1.88 KW$

For v = 25.5, putting all the values in above equation gives

$P = 0.5 * 1 * 1.2 * 3.14 * 1.3^2 * 25.5^3$

$P = 52821.2W = 52.821 KW$