Plane Slit Channel Laminar Flow (Poiseuille Flow)

Laminar flow of air in a narrow flat slit channel of height H = 2 mm, width W = 50 mm, and length L = 200 mm at Reynolds number Re_H = 137, verified against the analytical plane Poiseuille pressure drop Delta p = 12*mu*L*U / H^2.

Tolerance:

5%

Problem statement

Geometry

Narrow rectangular slit channel of height H = 2 mm, width W = 50 mm (aspect ratio W/H = 25), and length L = 200 mm.

Material

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

Boundary conditions

Inlet uniform velocity U = 1.0 m/s (Re_H = 137 based on channel height), outlet static gauge pressure 0 Pa, slip symmetry on side lateral walls (surface numbers 3, 4), no-slip viscous wall on top and bottom plates (surface numbers 5, 6).

Measured quantity

Hydraulic pressure drop Delta p between inlet and outlet, verified against analytical plane Poiseuille benchmark Delta p = 10.50 Pa; secondary checks on centerline parabolic acceleration u_max / U_in > 1.15 and mass conservation.

WebCAE Terminal

units mm
import path="cfd_couette_poiseuille_channel.step" format=step
mesh tet size=2.2
cfd fluid air
cfd set mode=steady speed=1 turbulence=laminar iterations=650 tol=1e-5 threads=8 cfl=6 multigrid=0
cfd inlet surface number 1 speed=1 intensity=0.01
cfd outlet surface number 2 pressure=0
cfd symmetry surface number 3
cfd symmetry surface number 4
cfd wall surface number 5 monitor=on
cfd wall surface number 6 monitor=on
solve cfd

Results comparison

Updated: 2026-10-19 · WebCAE solver