# Effects of Vertical Glottal Duct Length on Intraglottal Pressures in the Convergent Glottis
## 3 Results
### Transglottal Pressure Coefficient  
The transglottal pressure coefficient provides a nondimensional quantitative measure of how the pressure drop from the trachea to downstream of the glottis differs from lossless Bernoulli pressure. Conversely, for a constant flow, a large transglottal pressure coefficient would correspond to a large pressure difference across the glottal region. The transglottal pressure coefficient is also a primary variable in [PERSON]'s PTP expression [6; 7; 46]. The nondimensional transglottal pressure coefficient \(k_{t}\) is given by  
\[k_{t}=\frac{P}{0.5\times\rho\times V^{2}} \tag{4}\]  
where \(P\) is the transglottal pressure (the pressure drop between the trachea and a location downstream of the glottis), \(\rho\) is the density of the air, and \(V\) is the average velocity in the glottis, given by the volume flow \(U_{g}\) divided by the minimal glottal cross-sectional area \(L_{g}D_{m}\), where \(L_{g}\) and \(D_{m}\) are the cross-sectional dimensions (anterior-posterior length and minimal diameter, respectively) of the glottal duct.  
Figure 8 shows the transglottal pressure coefficient values for different vertical glottal duct lengths, glottal diameters, convergent glottal angles, and transglottal pressures. The longest duct (0.908 cm) had the largest transglottal pressure coefficient values when the convergent angle was smallest (\(-5^{\circ}\)).  
The value of \(k_{t}\) was significantly higher for the smallest diameter (0.01 cm) compared to the other diameters, ranging from approximately 1.3 to 2.3 across the convergent angles, duct lengths, and transglottal pressures, with values decreasing within that range as the convergent angle increased or the transglottal pressure increased. For that diameter, the longest duct (0.908 cm) also had the lowest values, which were for the largest convergent angle of \(-20^{\circ}\).  
Figure 8: Transglottal pressure coefficient \(k_{t}\) as a function of Reynolds number, with parameters of 0.108 cm, 0.308 cm, 0.608 cm, and 0.908 cm vertical glottal duct length, \(-5^{\circ}\), \(-10^{\circ}\), and \(-20^{\circ}\) convergent glottal angle, and 0.01 cm, 0.04 cm, and 0.16 cm glottal minimal diameter.  
The minimal glottal diameter is a major factor for the transglottal pressure coefficient. For any glottal convergent angle, vertical glottal duct length, and transglottal pressure, decreasing the minimal glottal diameter increased the transglottal pressure coefficient value. For example, \(k_{t}\) increased from 1.15 to 1.37 and then to 2.28 for minimal diameters of 0.16 cm, 0.04 cm, and then 0.01 cm, respectively, for the \(-5^{\circ}\) glottal angle, 0.908 cm duct length, and 500 Pa transglottal pressure condition. The transglottal pressure coefficient \(k_{t}\) also tended to slightly increase as the duct length increased. For example, \(k_{t}\) increased from 1.09 to 1.15 (an increase of 5.5%) when the duct length increased from 0.308 to 0.908 cm for the \(-5^{\circ}\) glottal angle, 0.16 cm minimal diameter, and 500 Pa transglottal pressure. If the 0.01 cm minimal diameter is chosen for those conditions, the \(k_{t}\) value increased from 2.17 to 2.28, or 5.1%.