Double-Sided Couette Flow

The permanent laminar flow of an incompressible viscous fluid in the space between two parallel plates can be described by a linear ODE for : , where is the dynamic viscosity of the fluid and is the pressure gradient.

The boundary conditions are:

(lower plate velocity),

(upper plate velocity).

This problem has an analytic solution:

that varies as a function of the pressure gradient and the upper and lower plate velocity.