please answer quickly. Calculate energy available in 14 Kg wind, if the power available at the rotor of a wind turbine is 673 kw,diameter of the rotor, D = 88 m, Air density, p = 1.23 kg/m³ and Power Coefficient, C, = 0.59.

Given: Mass of the air=14kg Diameter of the rotor (D)=88m Swept area A=π×8824=6082.123m2 Power…

Answered: Calculate energy available in 14 Kg…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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please answer quickly.

Calculate energy available in 14 Kg wind, if the power available at the rotor of a wind turbine is 673 kw,
diameter of the rotor, D = 88 m, Air density, p = 1.23 kg/m³ and Power Coefficient, C, = 0.59.

Expert Solution

Step 1

Given:

Mass of the air=14kg

Diameter of the rotor (D)=88m

Swept area A= $\frac{π \times 88^{2}}{4} = 6082.123 m^{2}$

Power available at the rotor of the wind turbine P_avail=673kW

The density of the air ( $ρ$ )=1.23kg/m³

Power coefficient C_f=0.59

Solution:

Using the equation of available power we can find wind velocity V

Therefore,

$P_{a v a i l} = \frac{1}{2} ρ A V^{3} C_{f} 673 \times 10^{3} = \frac{1}{2} \times 1.23 \times \frac{π \times 88^{2}}{4} \times V^{3} \times 0.59 V = 6.73 m / s$

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