Magnetic resonance imaging (MRI) volume- and velocity-measurement techniques are used to probe structure-how correlations within the interparticle space of a packed bed of ballotini. Visualisation of the z-component of the flow velocity within six slices perpendicular to the symmetry axis of the bed permit the flow to be monitored throughout the bed. Significant heterogeneity in the flow is observed; in one slice it is found that approximately 8% of the pores carry 40% of the volume flow. High volume flow through any given pore is seen to be influenced most strongly by the local geometry of the pore space; i.e. the radial position of the pore within the bed, the radius of the pore and the relative amount of interfacial surface area adjoining neighbouring pores. In contrast, the topology of the bed plays a crucial role in determining the mean flow velocity through a given pore. Correlations are found between the flow velocity within a pore and both the local Reynolds number and coordination number associated with that pore. These results are discussed with reference to a simple pore network model.