= Airway resistance
{title2=$R_{\rm aw}=\Delta P/Q$}
\b[Airway resistance] quantifies the <pressure difference> needed to drive a specified <volumetric flow rate> through the conducting <airways>. For a steady linear relation with flow $Q$ positive toward the <alveoli>,
$$
P_{\rm mouth}-P_{\rm alv}=R_{\rm aw}Q.
$$
The units are pressure divided by volume per time, for example $\mathrm{cm\,H_2O\,s\,L^{-1}}$. A stipulated pressure drop of 1 cm water at $Q=0.5\,\mathrm{L\,s^{-1}}$ gives $R_{\rm aw}=2$ in those units. The pressure references matter: mouth-to-alveolar pressure concerns the flow path, whereas <transpulmonary pressure> also describes elastic loading of the <lung>.
An instructive idealization is the <Hagen-Poiseuille equation>. For a rigid cylindrical tube carrying steady laminar flow of a fluid with <dynamic viscosity> $\mu$,
$$
R=\frac{8\mu\ell}{\pi r^4}.
$$
Reducing its radius to 80% while holding length and <dynamic viscosity> fixed multiplies resistance by $1/0.8^4\approx2.44$. Real <airways> form a branching, deformable network and need not carry fully developed laminar flow. The tube equation explains a sensitivity, not a universal law for every lung measurement.
Network structure also matters. For $m$ identical linear branches in parallel, pressure drop is shared and their <volumetric flow rates> add, giving $R_{\rm eq}=R/m$. Many narrow distal branches can therefore have a very different combined resistance from one isolated narrow tube. Radius alone is insufficient without the arrangement and number of pathways.
<Secant versus differential airway resistance> distinguishes two values when the relation is nonlinear. For an original model $\Delta P=aQ+bQ|Q|$, the finite ratio is $\Delta P/Q=a+b|Q|$, while its local slope is $d\Delta P/dQ=a+2b|Q|$ away from zero. Report the operating flow and which definition is used.
A 1959 primary study combined mouth pressure with an intra-esophageal balloon and a differential pressure transducer to investigate resistance and compliance.<Airway Resistance and Lung Compliance by Ole Storstein and others>[Methods: balloon pressure, mouthpiece connection and Sanborn transducer]{ref} The mouth-to-esophageal difference is not a pure airway pressure drop: its elastic component must be separated. Simultaneous pressure, volume and flow information is what makes this mechanical distinction experimentally accessible.
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