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Hagen-Poiseuille Equation — FRCA Primary MCQ

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ModeratePhysiology - CardiovascularHagen-Poiseuille EquationFRCA Primary

A Newtonian fluid undergoes steady laminar flow through a rigid, straight, cylindrical tube. According to the Hagen–Poiseuille equation, with all other variables unchanged, the volumetric flow rate is proportional to:

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Correct answer: D — The fourth power of the radius

The correct answer is D. For steady laminar flow of a Newtonian fluid through a rigid cylindrical tube, the Hagen–Poiseuille equation is Q = πΔPr⁴/(8ηL). Flow is therefore directly proportional to the fourth power of the internal radius. Doubling the radius theoretically increases flow 16-fold. Flow is inversely, not directly, proportional to tube length and fluid viscosity, excluding B and D. Radius squared determines cross-sectional area, but flow depends on radius to the fourth power, excluding C. Flow is directly proportional to the pressure difference; a square-root relationship is associated with idealised orifice flow derived from Bernoulli's principle, excluding E. The equation is an idealised model and becomes less accurate with turbulence, non-Newtonian fluids or non-rigid tubes.

Reference: Jayanthi NVG, Dabke HV. The effect of IV cannula length on the rate of infusion. Injury. 2006;37(1):41–45. https://pubmed.ncbi.nlm.nih.gov/16356500/