Steady, Laminar Flow Between Parallel Plates

Steady, laminar flow between two parallel plates describes fluid movement in a narrow, confined channel, often used to model simple fluid systems.

For flow between two fixed plates, the Navier-Stokes equations simplify as the velocity varies only perpendicular to the plates, with no acceleration along the flow direction.

This leads to a parabolic velocity profile, where the fluid moves fastest at the center and slows to zero at the plates due to friction, known as the no-slip condition.

The flow rate between the plates depends on the pressure gradient, fluid viscosity, and plate separation; widening the gap or increasing the pressure gradient enhances the flow.

The mean flow velocity is also related to the pressure drop, with the peak velocity at the center of the channel being 1.5 times the mean velocity.

This analysis remains valid only for low Reynolds numbers, indicating laminar conditions, and fails for turbulent, high-Reynolds-number flows.

Applications of this analysis include irrigation channels, groundwater flow and sedimentation basins in water treatment plants, where laminar conditions exist.