What happens to flow rate when radius decreases?

What happens to flow rate when radius decreases?

• A. Increase
• B. Remain Constant
• C. Decrease
• D. Become Unpredictable

Answer: (C)

Flow rate through a vessel is governed by how easily fluid can move under a given pressure difference, and radius has a dramatic effect because of the r^4 dependence in laminar flow. In Poiseuille’s law, the flow rate Q equals the pressure difference times πr^4 divided by 8ηL. That means if the radius shrinks, the r^4 term drops quickly, so the flow rate falls steeply even if the pressure gradient and fluid properties stay the same. Physically, narrowing the vessel increases resistance (R ∝ 1/r^4), and with a fixed driving pressure, the resulting flow decreases. This is why a decrease in radius leads to a decrease in flow rate.

Flow rate through a vessel is governed by how easily fluid can move under a given pressure difference, and radius has a dramatic effect because of the r^4 dependence in laminar flow. In Poiseuille’s law, the flow rate Q equals the pressure difference times πr^4 divided by 8ηL. That means if the radius shrinks, the r^4 term drops quickly, so the flow rate falls steeply even if the pressure gradient and fluid properties stay the same. Physically, narrowing the vessel increases resistance (R ∝ 1/r^4), and with a fixed driving pressure, the resulting flow decreases. This is why a decrease in radius leads to a decrease in flow rate.