How to Determine the Steady State Velocity Profile in a Channel with Moving Plates?

Steady State Velocity Profile in a Channel

The steady state velocity profile in a channel with moving plates will have a parabolic shape, with the velocity increasing from the plates towards the center. The velocity will be zero at the plates and maximum at the center of the channel. This profile is a result of the shear forces exerted by the moving plates on the incompressible Newtonian fluid.

Determining Steady State Velocity Profile

To determine the steady state velocity profile in a channel with moving plates, we can use the principle of fluid dynamics. In an incompressible Newtonian fluid, the velocity profile can be described by the Hagen-Poiseuille equation. This equation states that the velocity is directly proportional to the pressure drop and the fourth power of the distance from the center of the channel. Since no external pressure gradients are applied, the pressure drop is constant throughout the channel. Therefore, the velocity profile will vary parabolically from zero at the plates to a maximum value at the center of the channel.