Question

If R = 1/(radius^4) then how much will airflow be affected if radius of an airway is halved?

Answer 1

Halving the radius of an airway increases its resistance
`16` times, resulting in a considerable decrease in airflow. The airflow will be reduced to one-sixteenth of the original value, which is
`6.25%` of the original airflow.

Step-by-step explanation:

If
`R = 1/(radius^4)` then how much will airflow be affected if the radius of an airway is halved is a question related to the principles of fluid dynamics, specifically Poiseuille's law. Poiseuille's law states that the resistance to laminar flow of an incompressible fluid in a tube is directly proportional to the length of the tube and the fluid viscosity while inversely proportional to the fourth power of the radius of the tube.

If the radius is halved the new resistance can be calculated as follows:

`R(new) = 1 / (0.5 * radius)^4`

`R(new) = 1 / (radius^4 * 0.5^4)`

`R(new) = 1 / (radius^4 * 1/16)`

Thus, the new resistance is
`16` times the original resistance.

Airflow is inversely related to resistance in a tube; hence if the resistance increases the airflow decreases. Cutting the radius in half leads to a decrease in airflow to one-sixteenth the original flow rate. This means that given all other factors remain constant if the radius of an airway is halved, the airflow will be reduced to
`6.25%` of its original value.