Fluid permeability of solid foams is a crucial parameter to control transport phenomena in numerous engineering applications, such as heat exchangers or filters for example. Open-cell foams with monodisperse pore diameter ranging from 200 to 1000 µm and solid volume fraction ranging from 0.1 to 0.38 are produced and Darcy permeability is measured. The permeability divided by the square of the pore size shows an exponential decay as a function of solid volume fraction. Surprisingly, existing models do not capture this exponential decay and actually they predict permeability values significantly larger than the measured values. The observed exponential decay is then successfully described by using models based on the viscous dissipation occurring through the apertures that connect the foam pores and by accounting for both the mean size of the apertures and the mean number of apertures per pore.