at the mask filter-piece. The combined pressure loss at gap inlet and gap outlet can be expressed as $$\Delta p_{\mathrm{g,io}} = \frac{u_{\mathrm{t}}}{|u_{\mathrm{t}}|} \zeta  \frac{\rho }{2}  u_{\mathrm{g}}^{2}  \quad ,
\label{EQpg1}$$ with loss coefficient $\zeta = \zeta_{\mathrm{in}} + \zeta_{\mathrm{out}}$, density of air $\rho\approx 1.2\, \mathrm{kg/m^{3}}$, average gap velocity $u_{\mathrm{g}}$, average flow velocity $u_{\mathrm{t}}$ through the nose and its absolute value $|u_{\mathrm{t}}|=\sqrt{u_{\mathrm{t}}^{2}}$; the term $u_{\mathrm{t}}/|u_{\mathrm{t}}|$ is included to obtain the correct sign for both inhaling and exhaling.

The loss coefficients $\zeta_{\mathrm{in}}$ and $\zeta_{\mathrm{out}}$ were taken from Idelchik (1986, p. 92 and p. 128) as $\zeta_{\mathrm{in}} = 0.5$ and $\zeta_{\mathrm{out}} = 1.0$.

Assuming a fully-developed laminar flow in a plane-channel, the pressure loss within the gap is $$\Delta p_{\mathrm{g,2}} = \frac{12 \mu L_{\mathrm{g}}}{H_{\mathrm{g}}^{2}}  u_{\mathrm{g}}\quad ,
\label{EQpg2}$$ with dynamic viscosity of air $\mu \approx 1.8 \cdot 10^{-5} \, \mathrm{Pa s}$, gap length $L_{\mathrm{g}}$, gap height $H_{\mathrm{g}}$ and average gap velocity $u_{\mathrm{g}}$.

The pressure loss due to the flow through the mask surface $S_{\mathrm{m}}$ is approximately

$$\Delta p = p_{\mathrm{m}} - p_{a} \approx C_{\mathrm{m}} \rho u_{\mathrm{m}} \quad ,
\label{EQpm}$$

with viscous porous resistance $C_{\mathrm{m}}$, which is a property of the mask filter material, density $\rho$ of air and velocity $u_{\mathrm{m}}$ of the airflow through the mask, 