If the internal diameter of an intravenous catheter were doubled, by what factor would the flow through the catheter change (assuming laminar flow and other conditions constant)?

If the internal diameter of an intravenous catheter were doubled, by what factor would the flow through the catheter change (assuming laminar flow and other conditions constant)?

• A. Decreased by a factor of 2
• B. Decreased by a factor of 4
• C. Increased by a factor of 8
• D. Increased by a factor of 16

Answer: (D)

Poiseuille’s law for laminar flow shows that the flow rate Q through a cylindrical tube is proportional to the fourth power of the radius (Q ∝ r^4) when the pressure gradient, fluid viscosity, and tube length are constant. Doubling the internal diameter means the radius doubles (r → 2r). Substituting gives Q ∝ (2r)^4 = 16r^4, so the flow increases by a factor of 16. In other words, flow becomes sixteen times greater. This strong sensitivity comes from the r^4 relationship, which is why a simple change in diameter dramatically alters flow.

Poiseuille’s law for laminar flow shows that the flow rate Q through a cylindrical tube is proportional to the fourth power of the radius (Q ∝ r^4) when the pressure gradient, fluid viscosity, and tube length are constant. Doubling the internal diameter means the radius doubles (r → 2r). Substituting gives Q ∝ (2r)^4 = 16r^4, so the flow increases by a factor of 16. In other words, flow becomes sixteen times greater. This strong sensitivity comes from the r^4 relationship, which is why a simple change in diameter dramatically alters flow.