Airway resistance and its measurement

Principle
Airflow between the nose/mouth and the alveoli is driven by a pressure difference. The airways in between form a resistance

R=ΔP/Q 

where R is resistance, ΔP is the pressure gradient and Q is airflow

Resistance itself is described by the Poiseuille law

R = 8ηl/(πr4) - use to explain why during exhalation there is more resistance, because we take all the alveoli all together, compare with their radius and the tracheal radius

Where η is the viscosity of the inspired gas, l and r are the length and radius of the airway

Evidently, contraction of bronchi results in decreased airflow.

Measurement
Airway resistance is measured via pneumotachography (pneumo=lung, tacho=fast, graph=write), which compares pressure differences at two ends of a tube through which the subject breathes. Since the airflow Q is the same everywhere, one can derive an equation to find airway resistance:

Increased airway resistance indicates obstruction of the airways.