Consider a plane wall located at  in the cylindrical coordinates , moving with a constant velocity  towards the left. Consider another plane wall(scraper), at an inclined position, making an angle  from the positive  direction and let the point of intersection be at . This description is equivalent to moving the scraper towards right with velocity . The problem is singular at  because at the origin, the velocities are discontinuous, thus the velocity gradient is infinite there.
Taylor noticed that the inertial terms are negligible as long as the region of interest is within ( or, equivalently Reynolds number ), thus within the region the flow is essentially a Stokes flow. For example, George Batchelor gives a typical value for lubricating oil with velocity  as . Then for two-dimensional planar problem, the equation is
where  is the velocity field and  is the stream function. The boundary conditions are