How is the resistance to fluid flow R in a cylindrical pipe related to fluid dynamic viscosity eta?

Answer and explanation

Correct answer: C. Directly proportional to dynamic viscosity eta

  1. Step 1: Hydraulic resistance from Poiseuille's law is R = 8 eta L / (pi r^4). Step 2. Resistance is directly proportional to dynamic viscosity eta; elevated blood viscosity (e.g. polycythemia) increases vascular resistance and cardiac workload. Answer: Directly proportional to dynamic viscosity eta. Why not the others: Inversely proportional is false; resistance depends strongly on viscosity; inverse squared is non-physical.

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