If you mean that mathematics is more fun than hanging ductwork I couldn't agree more!
I'd like to hear more about how you use Mathematica for this. You're not doing a full CFD simutation, are you? fwiw, I normalize the flow to a convenient value and then use the square of that as a variable. The fan curve then straightens and of course the system curve becomes a straight line. The solution is then just a linear equation and some arithmetic. With the right normalization value it's easy to do a quick mental calculation for a sanity check.