diff --git a/caimira/docs/full_diameter_dependence.rst b/caimira/docs/full_diameter_dependence.rst index d4a3b628..7551a991 100644 --- a/caimira/docs/full_diameter_dependence.rst +++ b/caimira/docs/full_diameter_dependence.rst @@ -142,10 +142,11 @@ In addition, for each individual interaction, the expiration type may be differe To calculate the short-range component, we first need to calculate what is the **dilution factor**, that depends on the distance :math:`x` as a random variable, from a log normal distribution in :meth:`caimira.monte_carlo.data.short_range_distances`. This factor is calculated in a two-stage expiratory jet model, with its transition point defined as follows: -:math:`\mathrm{xstar}=𝛽_{\mathrm{x1}} (Q_{0} \cdot u_{0})^\frac{1}{4} \cdot (\mathrm{tstar} + t_{0})^\frac{1}{2} - x_{0}`, +: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 the :math:`Q_{0}` is the expired flow rate during the expiration period, in :math:`m^{3} s^{-1}`, :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}D^3}{8𝛽_{\mathrm{r1}}^2𝛽_{\mathrm{x1}}^2Q_{0}}` (in s). +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. +: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). 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}}`.