Question

Wind turbines convert wind energy into a useful energy like electricity. The formula for wind power is shown below. D stands for density, E for energy efficiency, V for wind velocity, and A for windmill area. Which option shows this formula correctly rearranged to solve for wind velocity, V?

a) V= DE⋅A
​b) V= AD⋅E
​c) V= EA⋅D
​d) V= DA⋅E
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Answer 1

None of the provided options correctly solve for wind velocity because they do not account for the cube relationship between power and velocity or the power generated. The correct rearrangement involves isolating V cubed on one side and then taking the cube root to solve for V.

Step-by-step explanation:

The formula for wind power involving wind turbines is dependent on the density of air (D), energy efficiency (ε), wind velocity (V), and the area of the windmill (A). To solve for wind velocity, V, the formula can be rearranged from the power equation P = 1/2 * D * A * V3 * ε. Noticing that V3 is multiplied by constants and A, we isolate V3 to get V3 = P / (1/2 * D * A * ε). Afterward, we take the cube root of both sides to solve for V, leading us to the correct formula V = ∛(P / (1/2 * D * A * ε)). This simplifies the options provided in the question to an incorrect format since they do not account for the cube relationship or the power involved. Therefore, none of the provided options a, b, c, or d correctly represent how to rearrange the formula to solve for wind velocity, V, as they ignore the power generated and the cube root needed to solve for V.