Bronchial Airflow Model

Generate a bronchial tree model from the trachea $($generation $0)$ to the $10$th generation bronchiole based on Murray's law. Trachea diameter is given by $DO=20mm.$ List the diameter of bronchi for generation $1-10.$

a$)$ Tidal volume $(V_T)$ and breathing frequency $($ f $)$ are given by $V_T=500mL$ and $f=\frac{14}{m}in.$ Find the mean flow velocity of bronchial air flow for each generation $(1-10)$ and evaluate the Reynolds and Womersley numbers for each generation $(1-10).$

b$)$ Trachea length is $L_0=140mm,$ and the length of bronchi at each generation is given by $L_z=3\mathrm{.}5D_z.$ Using the $1-$element LEM $($shown right$)$ and Poiseuille flow resistance model, calculate the total pressure drop through the airway $(z$:$0-10).$