The echo attenuation function EΔ (q) and the displacement probability P(Z,Δ) for water flowing through a bed of 0.3 mm glass beads has been measured by means of Pulsed Gradient Spin Echo (PGSE NMR). The encoding time Δ and the flow rates usedin the experiments were chosen such that the average displacement was at least one beaddiameter. The EΔ (q) shows, as expected, a diffraction peak at about the inverse ofthe bead diameter. For longer times EΔ (q) shows another peak at about the inverse oftwice the bead diameter. In analogy with PGSE NMR in presence of diffusion in a closedsystem, these data suggest that the pore space correlation function or featuresclosely related to it, can be accessed through the PGSE experiment with flow. Theconditions, which lead to this possibility, are discussed and supported with theresults of network modelling of fluid flow in a periodic structure. The true porespace correlation function has been determined using the Patterson function approachapplied to a NMR image data set. This has been compared with the one obtained by PGSENMR with flow. The displacement distributions P(Z,Δ) for fluid flow/diffusion in thissystem also show structural information and, it is suggested, can be regarded as aproduct of the pore space correlation function with an evolving smooth distributionwhich starts as an exponential and tends to a Gaussian in the longer time limit.