# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 3 Results
### Volume Flow  
Figure 6 shows the volume flow relative to the vertical glottal duct length (Figure 6a) and transglottal pressure (Figure 6b), with parameters of minimal diameter and glottal angle for 500 Pa transglottal pressure. The volume flow increased with minimal diameter increase and transglottal pressure increase, but was not sensitive to the glottal duct length, and only weakly to the convergent glottal angle (being higher for a larger convergent angle). The volume flow increased from 23.29 cm\({}^{3}\)/s to 525.78 cm\({}^{3}\)/s (an increase of 21.57 times) when the minimal diameter increased from 0.01 cm to 0.16 cm for the \(-5^{\circ}\) glottal angle, the 0.308 cm minimal diameter, and the 500 Pa transglottal pressure. This flow difference reached 866.09 cm\({}^{3}\)/s (an increase of 18.91 times) when the transglottal pressure increased to 1500 Pa (45.81 cm\({}^{3}\)/s and 911.89 cm\({}^{3}\)/s for 0.01 cm and 0.16 cm, respectively). The larger the minimal diameter, the larger the effect of transglottal pressure. These results suggest that the glottal minimal diameter and transglottal pressure are the primary controllers of volume flow (and therefore also glottal airflow resistance), and the vertical glottal duct length for convergent glottal shapes has relatively little effect on the volume flow.  
Figure 5: Exit coefficients \(k_{\alpha}\) as a function of Reynolds number, with parameters of 0.01 cm, 0.04 cm, and 0.16 cm glottal minimal diameter, 0.108 cm, 0.308 cm, 0.608 cm, and 0.908 cm vertical glottal duct length, and 500 Pa, 1000 Pa, and 1500 Pa transglottal pressure.  
Figure 6: \(Cont.\)  
The ratio of the minimal glottal diameter to the vertical glottal duct length (approximately 0.01 to 0.53 in this study) is an important aspect ratio in the sense that there should be an increase in airflow resistance for either a reduction in glottal diameter or an increase in duct length due to added viscous effects within the duct [46] or an increase in transglottal pressure. Figure 7 shows the volume flow values in relation to this ratio for all of the 0.108 minimal diameter cases and \(-5^{\circ}\) glottal angle cases (Figure 7a) and for all of the 0.308 cm minimal diameter cases (Figure 7b). The airflow has an essentially linear relationship with the ratio for each transglottal pressure, with increasing slope for increasing transglottal pressure and for increasing vertical glottal duct length. However, the change of the convergent glottal angle has negligible effect on the volume flow values relative to this ratio (Figure 7b). These results are consistent with the results shown in Figure 6 and are consistent with our previous results for the uniform glottis.  
Figure 6: (Color online) Glottal flow distributions for \(-5^{\circ}\), \(-10^{\circ}\), and \(-20^{\circ}\) convergent glottal angles and 0.01 cm, 0.04 cm, and 0.16 cm glottal minimal diameters (**a**) for 500 Pa transglottal pressure only; (**b**) for 500 Pa, 1000 Pa, and 1500 Pa transglottal pressures, for 0.108 cm and 0.308 cm vertical glottal duct length.  
Figure 7: (Color online) Glottal volume flow as a function of the ratio of minimal glottal diameter to the vertical glottal duct length (**a**) for 0.108 cm, 0.308 cm, 0.608 cm, and 0.908 cm vertical glottal duct length, 500 Pa, 1000 Pa, and 1500 Pa transglottal pressure for \(-5^{\circ}\)convergent glottal angle; (**b**) for \(-5^{\circ}\), \(-10^{\circ}\), and \(-20^{\circ}\) convergent glottal angles for 500 Pa, 1000 Pa, and 1500 Pa transglottal pressures only for 0.308 glottal duct length cases.