Which statement best describes the relationship expressed by Q = A × V?

Which statement best describes the relationship expressed by Q = A × V?

• A. Air flow increases with either a larger area or higher velocity
• B. Air flow decreases with a larger area
• C. Air flow is independent of velocity
• D. Air flow equals velocity divided by area

Answer: (A)

Volumetric flow rate is how much air passes through a cross-section per unit time. The equation Q = A × V expresses that flow rate grows when you either have a larger cross-sectional area or push the air faster (velocity). If you keep velocity the same and widen the passage, more air can pass each second; if you keep the area the same but increase velocity, more air passes each second as well. So the flow rate increases with either a larger area or a higher velocity. The other statements don’t fit this relationship. Increasing area while claiming flow decreases would contradict the product form; saying flow is independent of velocity ignores the velocity component entirely; and saying flow equals velocity divided by area uses a ratio rather than the product, which is not what Q = A × V describes.

Volumetric flow rate is how much air passes through a cross-section per unit time. The equation Q = A × V expresses that flow rate grows when you either have a larger cross-sectional area or push the air faster (velocity). If you keep velocity the same and widen the passage, more air can pass each second; if you keep the area the same but increase velocity, more air passes each second as well. So the flow rate increases with either a larger area or a higher velocity.

The other statements don’t fit this relationship. Increasing area while claiming flow decreases would contradict the product form; saying flow is independent of velocity ignores the velocity component entirely; and saying flow equals velocity divided by area uses a ratio rather than the product, which is not what Q = A × V describes.