# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 3 Results  
### Intraglottal Pressures  
Figure 2 shows the intraglottal pressure distributions for the various conditions, where the variables are glottal angle, minimal glottal diameter, and vertical glottal duct length. Table 2 indicates where any specific condition is located in Figure 2. The outlines of the convergent glottal configurations are shown in the upper portion of the figures. The results of the lossless Bernoulli equation for the same cases are also shown for comparison purpose (the lines that return to the original 500, 1000, and 1500 Pa at the glottal exit in each figure). Figure 2 shows that the intraglottal pressures decrease as the glottal cross-sectional area reduces following the glottal convergence shape. The pressure decrease would be due to flow acceleration within the glottis, with the pressure reduction reaching minimum values (and the largest velocities) essentially at the minimum diameter position near the end of the glottal duct. In addition, the larger the transglottal pressure, the greater the minimal pressure dip. The pressures near the pressure dip positions are negative (less than atmospheric). Past this location, the pressure recovers (increases) as the cross-sectional area expands at the rounded glottal exit position. Lengthening the vertical glottal duct acts to produce a primary and important change in the driving pressures on the vocal folds. As shown in Figure 2, as the length of the vertical glottal duct increases, the surface air pressures in the region of the glottal entrance increase, and they increase more so for larger diameters and larger transglottal pressures. The longer the vertical glottal duct length, the closer the glottal entry region pressure comes to the upstream (tracheal) pressure. For example, the pressure at the glottal entrance increases from 125.94 Pa to 663.82 Pa (an increase of 427.09%) between diameters 0.308 cm and 0.908 cm for the following case: 0.16 cm minimal diameter, 1500 Pa, and \(-10^{\circ}\) glottal angle. The effect is less as the minimal diameter is decreased. For example, from Figure 2, the increase is 1324.14 Pa to 1480.51 Pa (an increase of 11.81%) for the 0.01 cm minimal diameter, 1500 Pa transglottal pressure, and \(-10^{\circ}\) glottal angle case. Similarly, the increase in pressure at the glottal entrance for the \(-20^{\circ}\) glottal angle for an increase of the vertical glottal duct length from 0.308 cm to 0.908 cm is 1.55% and 81.89% for the 0.01 cm and 0.16 cm minimal diameters, respectively, for the 1500 Pa transglottal pressure case. Because the minimal pressure at the minimal cross-sectional area near the glottal exit did not change appreciably with glottal duct length, the higher pressures at glottal entry for longer vertical glottal duct lengths created higher pressures within the glottal duct over a longer length of the vertical duct. This finding suggests that the outward force acting upon the medial vocal fold surfaces would be greater for longer vertical glottal ducts, especially over the first half of the duct (from the glottal entrance). The larger pressures would drive the lower portion of the glottal surface outward using more force at