Couette flow is frequently used in undergraduate physics and engineering courses to illustrate shear-driven fluid motion. A simple configuration corresponds to two infinite, parallel plates separated by a distance ; one plate translates with a constant relative velocity  in its own plane. Neglecting pressure gradients, the Navier–Stokes equations simplify to
where  is the spatial coordinate normal to the plates and  is the velocity field. This equation reflects the assumption that the flow is unidirectional — that is, only one of the three velocity components  is non-trivial. If the lower plate corresponds to , the boundary conditions are  and . The exact solution
can be found by integrating twice and solving for the constants using the boundary conditions.
A notable aspect of the flow is that shear stress is constant throughout the domain. In particular, the first derivative of the velocity, , is constant. According to Newton's Law of Viscosity (Newtonian fluid), the shear stress is the product of this expression and the (constant) fluid viscosity.