Consider a planar disk of infinite radius rotating at a constant angular velocity  in fluid which is initially at rest everywhere. Near to the surface, the fluid is being turned by the disk, due to friction, which then causes centrifugal forces which move the fluid outwards. This outward radial motion of the fluid near the disk must be accompanied by an inward axial motion of the fluid towards the disk to conserve mass. Theodore von Kármán noticed that the governing equations and the boundary conditions allow a solution such that  and  are functions of  only, where  are the velocity components in cylindrical  coordinate with  being the axis of rotation and  represents the plane disk. Due to symmetry, pressure of the fluid can depend only on radial and axial coordinate .
Then the continuity equation and the incompressible Navier–Stokes equations reduce to
where  is the kinematic viscosity.