What effect do constrained airways have upon velocity, when the volume remains the same?

When dealing with the principle of fluid dynamics as related to airways, particularly in a situation where the volume of airflow remains constant, the relationship between the cross-sectional area of the airway and the velocity of the airflow becomes crucial.

In a scenario where the airways are constricted, the cross-sectional area decreases. According to the principle of continuity, which states that for an incompressible fluid (like air at low speeds), the product of the cross-sectional area (A) and the velocity (V) must remain constant. This is expressed mathematically as A1V1 = A2V2, where the subscripts represent the conditions before and after constriction.

As the cross-sectional area is reduced when the airways are constrained, to maintain the same volume flow rate, the velocity of the airflow must increase. The increase in velocity is inversely proportional to the area; as the area decreases, the velocity must correspondingly increase to maintain that constant flow rate. This is why the correct answer specifies that the velocity is increased in inverse proportion to the area.

In summary, when the volume of airflow remains constant, the constriction (or decrease) of the airway area results in an increase in the velocity of the airflow, based on