# Resistance, flow profile and dimensions of airways

Airway resistance caused by the **forces of friction** is inversely proportional to air flow. It is defined as the ratio of driving pressure to the rate of air flow. Resistance to flow in the airways depends on whether the flow is laminar or turbulent, on the dimensions of the airway, and on the viscosity of the gas.

For laminar flow, resistance is quite low. Therefore a relatively small driving pressure is needed to produce a certain flow rate. Resistance **during laminar flow** can be calculated according to the Poiseuille's Law:

R = 8 * l * η / π * r^{4} (l = length of the tube, η = gas viscosity, r = radius of the tube)
The most important variable here is the **radius**, which, due to its elevation to the fourth power, has an enormous impact on resistance. Thus, if the diameter of a tube is doubled, resistance will drop by a factor of sixteen.

For **turbulent flow** resistance is relatively large. Consequently, compared with laminar flow, a much larger driving pressure is required to produce the same flow rate. Because the pressure-flow relationship ceases to be linear during turbulent flow, no precise equation exists to calculate its resistance.

While a single **small airway** provides more resistance than a single **large airway**, resistance to air flow depends on the number of parallel pathways present. For this reason, the large and particularly the medium-sized airways actually provide greater resistance to flow than do the more numerous small airways. In general airway resistance decreases during inspiration because the airways distend and wider airways have lower resistance.

Literature:

Klinke R, Silbernagel S. Lehrbuch der Physiologie. 2001. Thieme: Stuttgart

Shier D, Butler J, Lewis R. Hole's human anatomy and physiology. 2004. McGraw Hill: New York