A more general Couette flow includes a constant pressure gradient  in a direction parallel to the plates. The Navier–Stokes equations are
where  is the dynamic viscosity. Integrating the above equation twice and applying the boundary conditions (same as in the case of Couette flow without pressure gradient) gives
The pressure gradient can be positive (adverse pressure gradient) or negative (favorable pressure gradient). In the limiting case of stationary plates (), the flow is referred to as Plane Poiseuille flow, and has a symmetric (with reference to the horizontal mid-plane) parabolic velocity profile.