In Poiseuille's law, which factors directly influence the volume flow rate?

• A. Pressure difference and radius
• B. Pressure difference and viscosity
• C. Length and radius
• D. Pressure difference and length

Answer: (A)

Volume flow rate is driven by the pressure difference across the ends of the tube and is highly sensitive to the tube radius. According to Poiseuille’s law, Q = (π ΔP r^4) / (8 μ L). This shows that the flow rate increases in direct proportion to the pressure difference and to the fourth power of the radius. The radius matters enormously because even a small change in radius produces a large change in flow due to the r^4 relationship. Viscosity and length also influence flow (flow decreases with higher viscosity and with longer length), but the pair that directly reflects the primary driving factors in the equation is the pressure difference and the radius.