When we cough, the trachea (windpipe) contracts to increase the velocity of the air going out. This raises the questio
Posted: Wed Jul 06, 2022 1:19 pm
When we cough, the trachea (windpipe) contracts to increasethe velocity of the air going out. This raises the question of howmuch it should contract to maximize the velocity and whether itreally contracts that much when we cough.
Under reasonable assumptions about the elasticity of thetracheal wall and about how the air near the wall is slowed byfriction, the average flow velocity v can be modeled by theequation below, where ro is the resting radius ofthe trachea in centimeters, r is the radius of the trachea and c isa positive constant whose value depends in part on the length ofthe trachea. Given the function below, complete parts a and bbelow.
v(r)= c(r0 - r)r2 cm/s, wherer0 /2 < r < r0.
Under reasonable assumptions about the elasticity of thetracheal wall and about how the air near the wall is slowed byfriction, the average flow velocity v can be modeled by theequation below, where ro is the resting radius ofthe trachea in centimeters, r is the radius of the trachea and c isa positive constant whose value depends in part on the length ofthe trachea. Given the function below, complete parts a and bbelow.
v(r)= c(r0 - r)r2 cm/s, wherer0 /2 < r < r0.