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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.

User Dmajkic
by
7.3k points

1 Answer

3 votes

Answer:

The power will be 1.88KW and 52.821KW

Step-by-step 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

User Nanpakal
by
9.0k points
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