Which relationship best describes how vessel radius affects peripheral resistance?

• A. Resistance is inversely proportional to the fourth power of the radius
• B. Resistance is proportional to the radius
• C. Resistance is independent of radius
• D. Resistance is proportional to radius squared

Answer: (A)

The main concept is how vessel radius controls vascular resistance. Poiseuille’s law shows that resistance to laminar flow in a cylindrical vessel is inversely proportional to the fourth power of the radius (R ∝ 1/r^4). This means even small changes in radius cause large changes in resistance: doubling the radius reduces resistance to one-sixteenth, while halving the radius increases it sixteen-fold. This strong sensitivity arises because flow depends on how easily fluid layers slide past each other, which is greatly affected by the narrowness of the vessel.

So the description that best fits this relationship is that resistance is inversely proportional to the fourth power of the radius. The other ideas—resistance increasing with radius, resistance being independent of radius, or resistance scaling with radius squared—do not align with the physics of laminar flow in tubes.