The maximum theoretical power P of a wind turbine is given by the equation P = kpAv" where p is the density of air, A is the area swept by the turbine blades, v is the speed of the air and k is a constant with no units. What is the value of n? A 1 в 2 с з D 4

Choice C is correct because: To find the value of n based on dimensional analysis, set up the units on both sides of the equation and solve for n. Power (P) has units of watts (W), which is equivalent to joules per second (J/s), or kilograms meters squared per second cubed (kgm^2/s^3) in SI base units. Density (ρ) has units of kilograms per cubic meter (kg/m^3). Area (A) has units of square meters (m^2). Velocity (v) has units of meters per second (m/s). The constant k is dimensionless, meaning it has no units. Given the equation P = kpAv^n, we replace the variables with their corresponding units: kgm^2/s^3 = (kg/m^3) × m^2 × (m/s)^n. Solving for n, we want the units on both sides of the equation to match. The only way for this to happen is if n equals 3. So kgm^2/s^3 = kgm^2/s^3 when n = 3. Choices A, B, and D are incorrect because they state the wrong value of n.

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SI Units and Significant Figures | 2014 - M/J - 9702/12 | Q1