Magnetic resonance imaging (MRI) volume- and velocity-measurement techniques are used to probe structure-flow correlations within the interparticle space of a packed bed of ballotini. Images of the three mutually orthogonal components of the velocity field are obtained in two perpendicular slices within a bed of 5 mm diameter ballotini packed within a glass column of internal diameter 4.6 cm. Comparison of flow images obtained for two beds of identical column-to-particle diameter ratio but of differing length show that velocity enhancements at the walls of the bed are greater in the shorter, more ordered, bed. A three-dimensional volume image of each bed is also obtained and analysed to partition the interparticle space into individual pores and determine the location of pore necks. Correlations between volume flow rate and the surface area of the constrictions (pore necks) within the interparticle space lie between two limiting behaviours. For pores associated with low local Reynolds number, the volume flow rate through the constrictions scales as the square of the cross-sectional area of the constriction, whereas at the extreme of high local Reynolds number pores show volume flow rates scaling with cross-sectional area.