Fig. 4.

Comparison of the theoretical predictions to experimental data. (A) Surface area $S$ of nasal cavities as a function of body mass $M$. Shown are experimentally measured respiratory turbinal surface areas in canid and arctoid carnivorans (18) (blue dots) and in humans (orange cross; bars indicate standard deviation; parameters in Table 2). Our predictions (green lines) follow from the optimal gap width of parallel plates given in Eq. 7 (dark green) and a numerical solution based on a rectangular geometry (light green; dashed part indicates square geometry). Here, we assumed $\mathcal{E}=1$ and used the scalings given in Table 1. (Inset) The associated volumes $V$ of the nasal cavities as a function of $M$ together with the scaling given in Table 1. (B) Local gap width, given by the shape diameter function (24), for the standardized nasal cavity (23). (C) Hydraulic radius $R_{\text{h}}$ along the main axis $z$ of the standardized cavity (23) (blue line) compared with the predicted $\mathrm{\ell }$ given by Eq. 7 (green line), which was calculated for $\mathcal{E}=1$ and the parameters given in Table 2. (Inset) The cross-sectional area $A$ of the standardized cavity as a function of $z$.