{title2=$K=k\rho g/\mu$}
{wiki}

<Hydraulic conductivity> is the coefficient in $\mathbf q=-K\nabla h$, with units $\mathrm{m\,s^{-1}}$. Because the gradient of <hydraulic head> is dimensionless, <hydraulic conductivity> has the dimensions of <velocity>, but it is not the actual <Darcy velocity> unless the driving gradient has magnitude one. Intrinsic <permeability of a porous medium> $k$ has units $\mathrm{m^2}$ and describes pore geometry; <hydraulic conductivity> also depends on <mass density>, <dynamic viscosity> and <gravitational acceleration>.https://books.gw-project.org/hydrogeologic-properties-of-earth-materials-and-principles-of-groundwater-flow/chapter/hydraulic-conductivity/{ref}

For $k=10^{-12}\,\mathrm{m^2}$, $\rho=1000\,\mathrm{kg\,m^{-3}}$, $g=9.81\,\mathrm{m\,s^{-2}}$ and $\mu=10^{-3}\,\mathrm{Pa\,s}$, <hydraulic conductivity> is $K=9.81\times10^{-6}\,\mathrm{m\,s^{-1}}$. Doubling <dynamic viscosity> while keeping pore geometry, <mass density> and <gravitational acceleration> fixed halves <hydraulic conductivity> without changing intrinsic <permeability of a porous medium>. Thus a value quoted as a material's <hydraulic conductivity> needs its <fluid> conditions.


Hydraulic conductivity ( $K = k ρ g / μ$ )

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