Chapter 7, Problem 34RQ

Wind energy uses large fans to extract energy from the wind and turn it into electric power. Examine the equations below using fundamental dimensions and indicate for each if the equation is a valid or invalid equation; justify your answer for each case.

a. P= η ρA² v²

b. P= η ρA v²

c. P= η ρA v³

d. P= η ρ²A v

e. $p=\eta \sqrt{\rho A{v}^3}$

Here, the variables are as follows:

A =area [=] m²

P = power [=] W

v =velocity[=] mi/h or mph

η =efficiency[=] unitless

ρ = density [=] kg/m³