Exit of Ground Waters on Drainage Boundaries

A known analytical solution provides the location of the exit point of the free surface of ground waters as a function of the slope angle and the reduced discharge in a form of a finite integral. This integral was evaluated numerically and a substitute polynomial equation provided to determine the function. Based on the exact position of the exit point, a new discharge formula free from any preliminary assumptions is derived. It covers the range of slope angles from near 0° to 180° for infinitely long aquifers. It was found that the same formula is applicable to certain finite lengths. Applicability of the function for the location of the exit point and the discharge formula for earth dams is considered. It is explained that a hydraulically equivalent rectangle, which substitutes the upstream prism, must have the width of the base substantially smaller than that used in older theories.