Laminar capillary flow of compressible viscous fluids

Laminar flow of compressible Newtonian fluids in capillaries is analysed. A perturbation solution is obtained to the vorticity-stream function form of the hydrodynamics equations for weakly compressible flow, having a relatively simple form. In contrast with previous analyses of this flow, we find both a non-zero radial velocity and non-zero radial pressure gradient. Expressions for pressure drop and friction factor are also found that show significant deviations from the incompressible case (Hagen-Poiseuille equation) that arise from both fluid inertia and bulk viscosity.