## The Betz limit

There is an interesting discussion to be had about the possible efficiency of wind turbines which presents opportunities for the instructor to look at several different kinds of computations.  The discussion ends up with an optimization problem which could be approached by the classical methods of calculus – if the students have that available to them – or could be approximated simply by drawing a graph of one critical function. Continue reading “The Betz limit”

## Sample question and response

$\frac{\partial^2\chi}{\partial x^2} + \frac{1}{4\sqrt{\pi}}\frac{\partial \chi}{\partial t} \approx 0,$
where $$\chi$$ is the local density of chickens, we may arrive at the answer, “Because it wanted to get to the other side (to a first order approximation).”