From a5b295a1650319dd259005b4e5981a8526102c8e Mon Sep 17 00:00:00 2001 From: "CERN\\Andrejh" Date: Tue, 8 Nov 2022 17:12:07 +0100 Subject: [PATCH] exh_coef additional explanation --- caimira/docs/full_diameter_dependence.rst | 7 +++++-- 1 file changed, 5 insertions(+), 2 deletions(-) diff --git a/caimira/docs/full_diameter_dependence.rst b/caimira/docs/full_diameter_dependence.rst index 7551a991..43dd7128 100644 --- a/caimira/docs/full_diameter_dependence.rst +++ b/caimira/docs/full_diameter_dependence.rst @@ -144,9 +144,12 @@ This factor is calculated in a two-stage expiratory jet model, with its transiti :math:`\mathrm{xstar}=𝛽_{\mathrm{x1}} (Q_{\mathrm{exh}} \cdot u_{0})^\frac{1}{4} \cdot (\mathrm{tstar} + t_{0})^\frac{1}{2} - x_{0}`, -where :math:`Q_{\mathrm{exh}}=\textrm{exh_coef} \cdot \mathrm{BR}` is the expired flow rate during the expiration period, in :math:`m^{3} s^{-1}`, :math:`\textrm{exh_coef}` is the exhalation coefficient defined as `2`, and :math:`\mathrm{BR}` is the given exhalation rate. +where :math:`Q_{\mathrm{exh}}=\textrm{exh_coef} \cdot \mathrm{BR}` is the expired flow rate during the expiration period, in :math:`m^{3} s^{-1}`, :math:`\textrm{exh_coef}` is the exhalation coefficient +(dimensionless) and represents the ratio between the total period of a breathing cycle and the duration of the exhalation alone. +Assuming the duration of the inhalation part is equal to the exhalation and one starts immediately after the other, :math:`\textrm{exh_coef}` will always be equal to `2` no matter what is the breating cycle time. :math:`\mathrm{BR}` is the given exhalation rate. :math:`u_{0}` is the expired jet speed (in :math:`m s^{-1}`) given by :math:`u_{0}=\frac{Q_{0}}{A_{m}}`, :math:`A_{m}` being the area of the mouth assuming a perfect circle (average `mouth_diameter` of `0.02m`). -The time of the transition point :math:`\mathrm{tstar}` is defined as `2s` and corresponds to the end of the exhalation period, i.e. when the jet is interrupted. The distance of the virtual origin of the puff-like stage is defined by :math:`x_{0}=\frac{\textrm{mouth_diameter}}{2𝛽_{\mathrm{r1}}}` (in m), and the corresponding time is given by :math:`t_{0} = \frac{\sqrt{\pi} \cdot \textrm{mouth_diameter}^3}{8𝛽_{\mathrm{r1}}^2𝛽_{\mathrm{x1}}^2Q_{exh}}` (in s). +The time of the transition point :math:`\mathrm{tstar}` is defined as `2s` and corresponds to the end of the exhalation period, i.e. when the jet is interrupted. The distance of the virtual origin of the puff-like stage is defined by +:math:`x_{0}=\frac{\textrm{mouth_diameter}}{2𝛽_{\mathrm{r1}}}` (in m), and the corresponding time is given by :math:`t_{0} = \frac{\sqrt{\pi} \cdot \textrm{mouth_diameter}^3}{8𝛽_{\mathrm{r1}}^2𝛽_{\mathrm{x1}}^2Q_{exh}}` (in s). Having the distance for the transition point, we can calculate the dilution factor at the transition point, defined as follows: :math:`\mathrm{Sxstar}=2𝛽_{\mathrm{r1}}\frac{(xstar + x_{0})}{\textrm{mouth_diameter}}`.