Laminar Flow in a Circular Pipe: Verification of Hagen–Poiseuille Law

Abstract

This study presents a computational verification of the Hagen–Poiseuille law for steady, incompressible laminar flow through circular pipes using Computational Fluid Dynamics (CFD). The investigation aims to analyse the relationship between pressure drop, velocity distribution, and pipe diameter under laminar flow conditions. Three pipe models with diameters of 15 mm, 20 mm, and 25 mm, each with a length of 1.2 m, were simulated using ANSYS Fluent. The governing equations of continuity and momentum were solved using the Finite Volume Method (FVM), with water at 25°C as the working fluid. A uniform inlet velocity of 0.03 m/s was applied, while a pressure outlet boundary condition of 0 Pa was set at the exit. Mesh independence testing ensured numerical stability and accuracy. The geometry was discretized using a multizone mesh, and a grid independence test was performed to ensure numerical accuracy. Velocity contours revealed the development of the expected parabolic profile, while pressure results showed a linear decrease along the pipe length for all diameters. The theoretical pressure drops were compared with CFD predictions resulting in errors of 19.46%, 32.87%, and 82.70%. The deviation increased with diameter due to longer entrance length effects, yet the overall flow behaviour remained consistent with laminar theory. The study demonstrates that CFD can reliably reproduce laminar pipe flow characteristics and provides quantitative validation of the Hagen–Poiseuille relationship.