As noted, this is termed the hydraulic conductivity . The physical meaning of Darcy's constant was not fully explored for 100 years. Note that porosity of packed spheres does not depend on their grain size, just there packing geometry. Formally, viscosity is the ratio of stress to strain rate in a fluid. N and d depend on the rock matrix.
Permeability is a measure of the ability of a material to transmit fluid under a hydraulic gradient.
It is the most important rock parameter pertinent to fluid flow. It is an intrinsic property of rock and relates to the presence of fractures and interconnected voids. Further conversions are endless and tiresome. 5 k cgs. Despite Hubbert's work, which provided a physical basis for the Darcy constant, our best information on K is empirical.