SOLUTION: The power produced by a windmill varies directly with the square of its diameter and the cube of the wind speed. A fan with a diameter of 2.5 meters produces 560 watts of power if

Question 980442: The power produced by a windmill varies directly with the square of its diameter and the cube of the wind speed. A fan with a diameter of 2.5 meters produces 560 watts of power if the wind speed is 4 m/s. How much power would a similar fan produce if it had a diameter of 6 meters and the wind speed was 5 m/s?
Answer by ikleyn(52841) (Show Source): You can put this solution on YOUR website!

The condition of this problem means exactly the following:

The power produced by a windmill is proportional to the product of the square of its diameter and the cube of the wind speed.

In other words,

= ..,

where is the power produced by a windmill, is a windmill diameter, is the wind speed, and is the proportionality coefficient which is the constant value for the selected unit system.

Therefore, the proportion is valid
= . = . = . = 2.56*1.953 = 5.

where the index "1" relates to the "smaller windmill", and the index "2" relates to the "larger windmill".

Finally, its gives = . = 5*560 watts = 2800 watts.

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