Collateral vessels have a _____ length and a ______ diameter, both resulting in ______ resistance to flow.

Collateral vessels have a _____ length and a ______ diameter, both resulting in ______ resistance to flow.

• A. Shorter length and larger diameter, Decreased
• B. Longer length and larger diameter, Decreased
• C. Longer length and smaller diameter, Increased
• D. Shorter length and smaller diameter, Increased

Answer: (C)

The main concept tested is how resistance to flow in a vessel depends on its length and radius. Poiseuille’s law shows that resistance increases with longer length and decreases with radius to the fourth power (R ∝ L / r^4). Collateral vessels form as alternative pathways and are typically longer than a single straight artery and have smaller diameters. Because radius has such a powerful effect (r^4), even a modest decrease in diameter greatly raises resistance, and the added length further increases it. So the combination of longer length and smaller diameter leads to increased resistance to flow, which is why that option is the best answer.

The main concept tested is how resistance to flow in a vessel depends on its length and radius. Poiseuille’s law shows that resistance increases with longer length and decreases with radius to the fourth power (R ∝ L / r^4). Collateral vessels form as alternative pathways and are typically longer than a single straight artery and have smaller diameters. Because radius has such a powerful effect (r^4), even a modest decrease in diameter greatly raises resistance, and the added length further increases it. So the combination of longer length and smaller diameter leads to increased resistance to flow, which is why that option is the best answer.