Question

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

a) Airflow will be unchanged
b) Airflow will be halved
c) Airflow will be quadrupled
d) Airflow will be sixteen times greater

Answer 1

When the radius of an airway is halved, the resistance to airflow increases by a factor of sixteen (since R is proportional to 1/radius^4), which means the airflow will be one-sixteenth of its original value. The correct option is d).

Step-by-step explanation:

If R = 1/(radius^4), then a change in the radius of an airway affects the airflow significantly. If the radius is halved, we replace the original radius r with r/2 in the formula. Plugging in this new value, we get:

R' = 1/((r/2)^4) = 1/(r^4/16) = 16/(r^4).

Comparing this with the original resistance, R, we can see that:

R' = 16 * R.

So, the resistance increases by a factor of sixteen when the radius is halved. Since air resistance and airflow are inversely related, the airflow would be one-sixteenth of its original value, which means that the correct answer to the student's question is:

d) Airflow will be sixteen times greater.