which can be computed from the flow rate $F_{\mathrm{m}}$ through the mask.

It is expected that the assumption, that the pressure loss depends linearly on the velocity, can be made with good approximation for these flow rates. Unfortunately, only qualitative curves were available to the authors to validate this statement. However, Jung et al. (2014) present experimental data for pressure drop $\Delta p$ for flow rate $F_{\mathrm{t}}=30\, \mathrm{L/min}$ and $F_{\mathrm{t}}=85\, \mathrm{L/min}$ for FFP-type masks, and even when linearly scaling the pressure drop $\Delta p(30\, \mathrm{L/min})$ for $F_{\mathrm{t}}=30\, \mathrm{L/min}$ via $\Delta p(85\, \mathrm{L/min}) \approx \Delta p(30\, \mathrm{L/min}) \frac{85\, \mathrm{L/min}}{30\, \mathrm{L/min}}$ gives only differences to the actually measured value of $15\%$ to $40\%$. This is acceptable for the present purposes, because the results in Sect. \[SECres\] show that changing $\Delta p$ by even $300\%$ changed the ratio $F_{\mathrm{g}}/F_{\mathrm{t}}$, i.e. gap flow rate divided by total flow rate, by ca. $10\%$ or less, i.e. the flow did not change qualitatively.

The pressure drop $\Delta p $ through the gap must be equal to the pressure drop through the mask filter-piece

$$\frac{u_{\mathrm{t}}}{|u_{\mathrm{t}}|}  \zeta  \frac{\rho }{2} u_{\mathrm{g}}^{2} + \frac{12 \mu L_{\mathrm{g}}}{H_{\mathrm{g}}^{2}}  u_{\mathrm{g}} = C_{\mathrm{m}} \rho u_{\mathrm{m}} \quad ,
\label{EQdpsum1}$$

and because the total flow rate 