Which statement best describes how changes in vessel radius influence flow rate under typical physiological conditions?

Which statement best describes how changes in vessel radius influence flow rate under typical physiological conditions?

• A. Flow rate does not depend on radius
• B. Flow rate decreases when radius increases
• C. Flow rate is minimally affected by radius
• D. Flow rate increases when radius increases

Answer: (D)

Radius has a dominant effect on flow rate because, under typical laminar flow in a cylindrical vessel, the flow rate scales with the fourth power of the radius: Q ∝ r^4 when the pressure gradient, blood viscosity, and vessel length are held constant. This means even small changes in radius produce large changes in flow. For example, doubling the radius increases flow 16-fold. In physiology, this is why vasodilation greatly increases perfusion to tissues, while vasoconstriction reduces it. The other ideas—flow being independent of radius, decreasing with radius, or being only minimally affected by radius—don’t fit the strong r^4 dependence.

Radius has a dominant effect on flow rate because, under typical laminar flow in a cylindrical vessel, the flow rate scales with the fourth power of the radius: Q ∝ r^4 when the pressure gradient, blood viscosity, and vessel length are held constant. This means even small changes in radius produce large changes in flow. For example, doubling the radius increases flow 16-fold. In physiology, this is why vasodilation greatly increases perfusion to tissues, while vasoconstriction reduces it. The other ideas—flow being independent of radius, decreasing with radius, or being only minimally affected by radius—don’t fit the strong r^4 dependence.