Laminar viscous flow through regular arrays of parallel solid cylinders

Solutions are found for the Stokes equations of motion for a viscous fluid flowing either parallel or perpendicular to the axes of cylinders in square, rectangular, triangular and hexagonal arrays. This is done by matching a solution outside one cylinder to a sum of solutions with equal singularities inside every cylinder of an infinite array. Some of the terms in the solution are indeterminate but these indeterminacies are resolved. The resulting solutions are several terms of a power series in the density.High density approximations are found for the longitudinal case when the cylinders overlap.For low densities the mean velocity for transverse flow found to be independent of orientation of the array and is half the mean velocity for parallel flow in the same pressure field to several orders of magnitude of the volume concentration of cylinders.