# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 3 Results
### Intraglottal Velocity Distributions  
Figure 9 shows the schematic of the glottal configurations as well as the velocity vector streamtraces and the red-to-blue contour levels of intraglottal pressures (the upper portion of each small figure), the corresponding velocity magnitude distributions on the centerline of the glottis (Figure 9a,b), and the corresponding wall shear stress distributions (Figure 9c,d) for the 0.01 cm minimal glottal diameter for 0.308 cm and 0.908 cm vertical glottal duct lengths. The figure shows results for 500 Pa and 1500 Pa transglottal pressures for \(-5^{\circ}\) and \(-20^{\circ}\) convergent glottal angles (the lower portions of each small figures). It can be seen from Figure 9a,b that when the convergent glottal angle increases, the larger glottal cross-sectional area at the glottal entrance location results in a slower increase of the flow velocity. This flow velocity, however, will accelerate rapidly and reach peak values close to the location of the smallest diameter. The peak velocity is slightly higher for the larger convergent angle than for the smaller glottal angle cases. Similar results are shown for the longer vertical glottal duct length. It is noted that the peak velocity in Figure 9a,b of approximately 55 m/s is a Mach number of approximately 0.16, suggesting effectively incompressible flow.  
In Figure 9a,b, the increase of the transglottal pressure also results in a relatively fast increase of the flow velocity and causes a higher peak value. For example, the velocity peak increases from 27.21 to 51.52 m/s (an increase of 89.34%) when the transglottal pressure increased from 500 Pa to 1500 Pa for the \(-5^{\circ}\) glottal angle, 0.01 cm minimal diameter, and 0.308 cm vertical glottal duct length. The peak velocities were quite similar between the cases for 0.308 and 0.908 cm duct lengths, suggesting that the peak velocity was dependent on the minimal glottal diameter and the transglottal pressure rather than vertical glottal duct length and glottal angle.  
The faster increase of flow velocity in the convergent glottis caused a more rapid increase of wall shear stress; the larger the convergent glottal angle or the higher the transglottal pressure, the faster the wall shear stress increased, as shown in Figure 9c,d. The shear stress is similar for both vertical duct lengths (0.308 cm and 0.908 cm) and thus is dependent more on the constriction size and location than on the vertical glottal duct length. It is noted, however, that the largest shear stress value of this study, approximately 85 Pa, is only 6% of the 1500 Pa that created it, so the shearing effect may be relatively small.  
Figure 9: (Color online) Schematic of glottal configurations, the corresponding velocity magnitude distributions on the centerline of the glottis, and the corresponding wall shear stress distributions for 0.01 cm minimal glottal diameter, 0.308 cm and 0.908 cm vertical glottal duct lengths, 500 Pa and 1500 Pa transglottal pressures, and \(-5^{\circ}\) and \(-20^{\circ}\) convergent glottal angles. The upper portion of each figure shows the outlines of the glottal configurations as well as the velocity vector streamlines and the contour levels of intraglottal pressures (via the red-to-blue coloring): (i) \(-5^{\circ}\) glottal angle, 0.01 cm minimal diameter, 0.308 cm glottal duct length, 500 Pa transglottal pressure; (ii) \(-5^{\circ}\) glottal angle, 0.01 cm minimal diameter, 0.908 cm glottal duct length, 500 Pa transglottal pressure; (iii) \(-20^{\circ}\) glottal angle, 0.01 cm minimal diameter, 0.308 cm glottal duct length, 500 Pa transglottal pressure; (iv) \(-20^{\circ}\) glottal angle, 0.01 cm minimal diameter, 0.908 cm glottal duct length, 500 Pa transglottal pressure. The lower portions show the corresponding velocity magnitude distributions (**a,b**) and wall shear stress distributions (**c,d**).