Consider steady flow between two infinite parallel moving plates with a uniform pressure field. Consider plates located at y = h. The top plate moves in the x direction with speed UH, and the other plate moves in the x direction with speed UL. A schematic of this flow is shown in the figure below. The governing equations are the NavierStokes equations without body forces:

Couette flow between two parallel, infinite plates.

Make the necessary assumptions and approximations and solve the Navier-Stokes equations to find velocity distribution between the plates. Write down the boundary conditions.