According to Poiseuille's law, which statement about radius and flow is true?

• A. Flow is inversely proportional to the radius.
• B. Flow is proportional to the radius to the fourth power.
• C. Flow is independent of radius.
• D. Flow decreases as radius increases.

Answer: (B)

The key idea is that, for laminar flow through a long straight tube with a Newtonian fluid, the volume flow rate depends on the radius to the fourth power. Poiseuille’s law gives Q = (π ΔP r^4) / (8 μ L), so with pressure difference, viscosity, and tube length held constant, flow rises dramatically as the radius increases. For example, doubling the radius makes the flow increase 16-fold. That strong r^4 relationship means flow is not simply proportional to radius, not independent of radius, and certainly not decreasing as radius grows. This explains why even small changes in vessel radius can cause large changes in blood flow.