filter $F_{\mathrm{m}} = u_{\mathrm{m}}S_{\mathrm{m}}$, average flow velocity $u_{\mathrm{m}}$ through the surface $S_{\mathrm{m}}$ of the masks filter-piece.

![Simplified geometry for airflow through a generic face mask, which has a gap with height $H_{\mathrm{g}}$ and length $L_{\mathrm{g}}$ over a width $B_{\mathrm{g}}$ along its perimeter and is otherwise tightly fitted to the face; average velocities $u_{\mathrm{t}}$, $u_{\mathrm{m}}$ and $u_{\mathrm{g}}$ denote airflow through nose cross-sectional area $S_{\mathrm{t}}$, mask filter surface $S_{\mathrm{m}}$ and gap cross-sectional area $S_{\mathrm{g}}$; $p_{\mathrm{m}}$ and $p_{\mathrm{a}}$ denote the pressure inside and outside of the mask[]{data-label="FIG2DtheoryGeom"}](images/2Dsketch3.png){width="0.9\linewidth"}

Within the gap, the flow is assumed to be fully-developed laminar Pouseuille flow, which is justified because the average gap velocities $u_{\mathrm{g}}$ within the framework of this analysis were below the critical velocity $$u_{\mathrm{crit}} \approx \frac{\nu \mathrm{Re_{crit}}}{D_{\mathrm{h}}}  \quad ,
\label{EQRecrit}$$

with hydraulic diameter $D_{\mathrm{h}}=2H_{\mathrm{g}}$, gap heights $H_{\mathrm{g}} \in [0.1\, \mathrm{mm},1\, \mathrm{mm}]$, kinematic viscosity $\nu \approx 1.5 \cdot 10^{-5} \, \mathrm{m^{2}/s} $ for air at $20\, \mathrm{C^{\circ}}$ room temperature and critical Reynolds number for plane channel flow $\mathrm{Re_{crit}} \approx 3000$ (cf. Schlichting and Gersten, 2017, p. 104). Gap Reynolds numbers in this work were within $\mathrm{Re} \in [5, 1800]$.

Pressure losses occur in the flow at the gap inlet, within the gap, at the gap outlet, and 