According to Poiseuille's principle, how does increasing the vessel radius affect flow if pressure difference and viscosity remain constant?

According to Poiseuille's principle, how does increasing the vessel radius affect flow if pressure difference and viscosity remain constant?

• A. It increases dramatically
• B. It decreases slightly
• C. It remains unchanged
• D. It reduces flow

Answer: (A)

Poiseuille's law shows that flow is highly sensitive to the vessel radius: the flow rate Q is proportional to r^4 when the pressure difference, viscosity, and length are constant. This means small changes in radius produce large changes in flow. For example, doubling the radius makes flow 16 times greater, and a 50% increase yields about five times more flow. So increasing the vessel radius leads to a dramatic increase in flow, not a small change or a decrease. This is why the correct description is that flow increases dramatically.

Poiseuille's law shows that flow is highly sensitive to the vessel radius: the flow rate Q is proportional to r^4 when the pressure difference, viscosity, and length are constant. This means small changes in radius produce large changes in flow. For example, doubling the radius makes flow 16 times greater, and a 50% increase yields about five times more flow. So increasing the vessel radius leads to a dramatic increase in flow, not a small change or a decrease. This is why the correct description is that flow increases dramatically.