Via Lattice Boltzmann simulations we show there is a great deal of universality in the reduced mobility of spheres moving along the centre line of capillaries or rectangular microchannels. The reduced mobility follows a generalization of the Haberman-Sayre correlation, which is a function of the degree of confinement, e. This quantity e = d(p)/D-e, is defined as the ratio of the particle diameter and the length scale D-e, which is a weighted mean of the square root of the cross section area D-A, and the hydraulic diameter D-h. The force experienced by spheres in pressure driven flow can be described by a generalized Faxen theorem, combined with effective medium theory. This force can be decomposed in a drag force and a pressure gradient force, both inversely proportional to the reduced mobility. (C) 2010 Elsevier Inc. All rights reserved.