  Analytical expressions for the velocity field and the effective slip length
of pressure-driven Stokes flow through slippery pipes and annuli with
rotationally symmetrical longitudinal slits are derived. Specifically, the
developed models incorporate a finite local slip length or shear stress along
the slits and thus go beyond the assumption of perfect slip commonly employed
for superhydrophobic surfaces. Thereby, they provide the possibility to assess
the influence of both the viscosity of the air or other fluid that is modelled
to fill the slits as well as the influence of the micro-geometry of these
slits. Firstly, expressions for tubes and annular pipes with superhydrophobic
or slippery walls are provided. Secondly, these solutions are combined to a
tube-within-a circular pipe scenario, where one fluid domain provides a slip to
the other. This scenario is interesting as an application to achieve stable
fluid-fluid interfaces. With respect to modelling, it illustrates the
specification of the local slip length depending on a linked flow field. The
comparisons of the analytically calculated solutions with numerical simulations
shows excellent agreement. The results of this article thus represent an
important instrument for the design and optimization of slippage along surfaces
in circular geometries.
