Airway resistance greatest in tertiary bronchi As the title reads, why is airway resistance greatest in tertiary bronchi? Primary and secondary bronchi have a lower surface area than tertiary bronchi so what makes resistance greatest at this branching point of the lungs?
 A: If you pump gas along a pipe then pressure drop per unit length of the pipe depends on the diameter of the pipe. The smaller the pipe the harder it is to pump the gas through it. The pressure drop is given by the Darcy-Weisbach equation:
$$ \Delta P = f_D \frac{\rho v^2}{2} \frac{\ell}{d} $$
though with the complication that the density of the gas depends on the pressure. In the lungs I'd guess the density changes are small and we can take the density as roughly constant.
Anyhow, the pressure drop is inversely proportional to the diameter, $d$. The tertiary bronchi have a smaller diameter than the primary and secondary bronchi so the pressure drop will be greater. That means it's harder to pump gas through them.
A: I believe the question can be rephrased as asking

why is a single big pipe better than two smaller pipes with the same area

Since that's really what you are asking. The bronchial tree splits into smaller branches, but tries to carry the same amount of air.
Now the answer should be obvious: for the same area A = $2\pi r^2$, where $r$ is the radius of the larger tube, you need two smaller pipes with radius $\frac{r}{\sqrt{2}}$. Which means that the total area of the wall increased by $\sqrt{2}$. And the closer molecules are to the wall, the more often they will be slowed down (if you look at the velocity profile of any viscous fluid, you see it go to zero as you approach the wall). This is ignoring boundary layer effects and other subtle things that the body does to limit the air resistance, but that's the basic idea: when all the air molecules are close to the wall, they all "feel" the wall.
You can express that mathematically - John showed the first part of that, all you would have to do is sum over all the branches, keeping area constant. But not before my first coffee...
A: Decreasing diameter indeed leads to increasing flow resistance, and that is the dominant factor in lung airway resistance. But branching itself also contributes to airway resistance. When flow is forced to change direction there are energy losses which also cause pressure drop and this adds to the resistance. The trachea is more or less a straight pipe with the first pair of branching into the left and right bronchi - which are  are more or less straight pipes of smaller diameter. But below this level the degree of branching increases geometrically.
