Drainage Due to Gravity Under Nonlinear Law

A gravity drainage problem for a horizontal soil stratum underlain by a highly pervious material is analyzed. A non-linear relation between velocity and gradient is assumed. Capillary rise is also taken into account. The general differential equation (non-dimensionalized) for the problem is developed and analytically solved. The degree of drainage as a function of time and the real time of complete drainage are calculated and presented for typical values of the non-linear factor. It is shown that the analyzed non-linear drainage occurs faster compared to linear flow.