Which factor explains most of the change in flow when the vessel radius changes?

Which factor explains most of the change in flow when the vessel radius changes?

• A. Radius to the fourth power dominates flow changes.
• B. Length is the dominant factor.
• C. Temperature dominates.
• D. Pressure is the only factor.

Answer: (A)

In laminar flow through a cylindrical vessel, the flow rate depends on the radius to the fourth power (from Poiseuille’s law: Q ∝ r^4 ΔP / (η L)). This means even small changes in radius cause huge changes in flow, because the radius is raised to the fourth power. For example, doubling the radius makes flow increase by 2^4 = 16, assuming driving pressure, viscosity, and vessel length stay the same. The other factors—length, temperature, and pressure—do not produce as large a change when only the radius is altered, so the radius to the fourth power is the dominant determinant of flow change. This is why radius changes have such a powerful effect on flow compared with modifying length, temperature (which affects viscosity but not the radius itself), or the pressure gradient.

In laminar flow through a cylindrical vessel, the flow rate depends on the radius to the fourth power (from Poiseuille’s law: Q ∝ r^4 ΔP / (η L)). This means even small changes in radius cause huge changes in flow, because the radius is raised to the fourth power. For example, doubling the radius makes flow increase by 2^4 = 16, assuming driving pressure, viscosity, and vessel length stay the same. The other factors—length, temperature, and pressure—do not produce as large a change when only the radius is altered, so the radius to the fourth power is the dominant determinant of flow change. This is why radius changes have such a powerful effect on flow compared with modifying length, temperature (which affects viscosity but not the radius itself), or the pressure gradient.