The absolute permeability, k, and Knudsen diffusion coefficient, D-kn, of mesoporous alumina (alpha-Al2O3) supports are measured by fitting transient and steady-state measurements of the flow rate versus the pressure drop across a disk-shaped sample to analytical solutions of the relevant macroscopic equations. The microscopic properties of the pore structure of the alumina disks, such as the pore and throat radius distributions and network accessibility functions, are determined by employing Hg intrusion/retraction data. To this scope, the estimates of an optimization algorithm, based on analytical percolation models of Hg intrusion/retraction, are coupled with results of simulators of the drainage/imbibition in pore-and-throat networks. The permeability and Knudsen diffusion coefficient are computed by solving the viscous flow and Knudsen flow problems separately in cubic networks of constricted unit cells. The numerically predicted values of k and Dkn may differ by +/- 30-40% from the experimentally measured ones. In light of the uncertainties embedded into the experimental measurements and the simplifications adopted in the computational procedure, such a predictability is satisfactory. Therefore, Hg porosimetry data can provide all necessary information for obtaining reliable estimates of the transport properties of alumina supports or any similar mesoporous material.