Drainage of groundwater resting on a sloping bed with uniform rainfall

The differential equation derived by Childs for groundwater flow over a sloping bed, the streamlines being assumed to be parallel to the slope, is integrated for the case of ditches and uniform rainfall. Expressions are obtained for the maximum vertical water table height, the location of this maximum and of the watershed, and the water table shape. Calculated water table heights are in much better agreement with previously published experimental data than those calculated from an earlier theory based on the assumption that streamlines are horizontal. Thus Childs' revised assumption is confirmed. An approximate solution for the form of the water table under small rainfall rates is also derived.