Airway resistance: Poiseuille’s law
Basic, Basic Sciences
Resistance in an airway is equal to change in pressure divided by flow rate [Resistance = (Peak Pressure – Plateau Pressure) / Flow L/sec]. Integrating this equation with Poiseuille’s law, which assumes Laminar flow, it can be shown that resistance is directly proportional to viscosity and length and indirectly proportional to radius.
Poiseuille’s Law: Q = π P r4 / 8 n l
Resistance = P / Q
(Where: Q=flow; P = Pressure; r = radius; n = viscosity; l = length)
Resistance = (8 x viscosity x length) / π r4 …
Removing constants from the equation leaves the following…
Resistance = viscosity x length / r4
Airway radius is the variable that has the most impact on airway resistance because resistance is inversely proportional to the radius of the airway to the 4th power, so by halving the diameter of the airway you will increase the airway resistance 16-fold.
The airway resistance is also directly proportional to viscosity of the gas when flow is Laminar. Viscosity of a gas increases with temperature of the gas, as there are an increasing number of intermolecular collisions at higher temperatures. Of note, when flow becomes turbulent, it is the density of the gas, rather than the viscosity, that has the most impact on airway resistance. Less dense gases are more likely to flow in a laminar pattern and produce less resistance when their flow is turbulent.