In this article, we present fundamental transport property relations incorporating direct descriptors of the pore structure. The pore structure descriptors are defined from streamline decomposition of the numerical solutions of the transport equations. These descriptors have been introduced earlier, while the calculations are extended to voxel-based microstructures in this article. The pore structure descriptors for the respective transport equations are used in turn to obtain rigorous cross-property relations for porous media. We derive such cross-property relations exemplarily for computed tomography (CT) data and digital rock models of Fontainebleau sandstone, and CT data of two reservoir sandstone facies. Pore structure parameterizations of these porous media are given for electrical conductance and fluid permeability in the microstructure, yielding correlations for the transport property-dependent descriptors of effective porosity, tortuosity and constriction. These relations are shown to be well-correlated functions over the range of sample porosities for the Fontainebleau sandstone. Differences between the outcrop Fontainebleau sandstone and the reservoir samples are observed mainly in the derived hydraulic length descriptor. A quantitative treatment of the obtained cross-property functions is provided that could be applied for porous medium characterization. It is suggested that such cross-property investigation honoring the detailed microstructure will lead to more fundamental relations between porous medium properties, which could be exploited for example in rock typing or wire-line log interpretation.