Hagen-Poiseuille Circular Pipe Laminar Flow (Re = 100)

Steady laminar incompressible flow of air through a straight circular pipe of diameter D = 10 mm and length L = 200 mm at Reynolds number Re = 100, verified against the analytical Hagen-Poiseuille parabolic velocity profile u_max / U_mean = 2.0.

Tolerance:

5%

Problem statement

Geometry

Straight circular pipe of inner diameter D = 10 mm (radius R = 5 mm) and length L = 200 mm (L/D = 20).

Material

Air at 20 °C (density rho = 1.204 kg/m³, dynamic viscosity mu = 1.825e-5 Pa·s, kinematic viscosity nu = 1.516e-5 m²/s), incompressible steady laminar Navier-Stokes model.

Boundary conditions

Inlet uniform velocity U_in = 0.1516 m/s (Re_D = 100 based on diameter), outlet static gauge pressure 0 Pa, no-slip viscous wall on cylinder surface (surface number 1).

Measured quantity

Centerline maximum velocity ratio to mean cross-sectional velocity u_max / U_mean, verified against analytical Hagen-Poiseuille value 2.000; secondary checks on positive pressure drop Delta p and mass conservation |Delta m| <= 2%.

WebCAE Terminal

units mm
import path="cfd_hagen_poiseuille_pipe.step" format=step
mesh tet size=1.7
cfd fluid air
cfd set mode=steady speed=0.151578 turbulence=laminar iterations=800 tol=1e-5 threads=8 cfl=25 multigrid=1
cfd inlet surface number 3 speed=0.151578 intensity=0.01
cfd outlet surface number 2 pressure=0
cfd wall surface number 1 monitor=on
solve cfd

Results comparison

Updated: 2026-10-19 · WebCAE solver