Stabiele, laminaire stroming in cirkelvormige buizen

Consider steady, incompressible flow through a straight cylindrical tube of constant radius R, known as Hagen–Poiseuille flow.

The cylindrical geometry allows the use of coordinates r, θ, and z for radial, angular, and axial measurements.

The fluid flowing parallel to the tube's axis has a purely axial velocity component and varies only with the radial distance.

These conditions simplify the Navier–Stokes equations, revealing a parabolic velocity profile showing that the velocity is highest at the center and decreases towards the walls, reaching zero at the boundary.

This demonstrates the laminar flow, where fluid particles move smoothly in organized layers.

Integrating this profile over the tube's cross-section gives Poiseuille's law, which expresses the flow rate Q as dependent on the fourth power of the tube's radius, fluid viscosity, and pressure gradient.

The mean velocity V, calculated from Q, is half the maximum velocity observed at the tube's center.

This velocity distribution confirms that flow is highest at the center and decreases parabolically to zero at the wall.