Combining a capillary bundle model and the functional form of a j-function has deduced the relative hydraulic conductivity of a mesh-wick as a function only of the reduced saturation. The empirical expression of the relative hydraulic conductivity has also provided steady-state saturation profiles observed in a wick with infiltrating liquid percolating to a liquid table. The final average residual saturation can be reasonably estimated from a calculation of a newly defined capillary number, which takes into account the final equilibrium saturation profile as well as the j-function.