Many times flux and flux density are used interchangeably.
The hydraulic conductivity of a soil is a measure of the ease at which water moves through the soil. If the potential is defined in terms of a unit weight of water, then the gradient in total head has no dimensions and the conductivity has units of length per unit time just as the flux density does. The equivalent conductivity of a non-homogeneous soil is equal to the flux through that soil divided by the driving force or gradient in total potential across that soil. It could be considered the equivalent or average conductivity for the non-uniform soil. The total potential of water in a soil is the amount of work required per unit quantity of water to move a very small amount of water reversibly and isothermally from a pool of pure water at atmospheric pressure and at a reference level to the point of interest in the soil .