An exact solution for the fluid velocity distribution was obtained analytically in the bipolar coordinates system for the fully developed laminar fluid flow in an eccentric annulus with an axially moving core. The effects of the relative velocity of the core, the eccentricity of the annulus and the radius ratio on the fluid velocity and wall shear stress distributions as well as the friction factor have been investigated. It is shown that the peripheral non-uniformities of fluid velocity and wall shear stress distributions are significantly increased with increasing eccentricity and that the resulting friction factors decrease with increasing values of the eccentricity and the relative velocity
