Terminal Shape of a Shallow Liquid Front

A shallow liquid front attains a terminal shape and velocity a short time after the liquid is introduced into an open channel. The equations for the shape of such a front are derived for l aminar flow from Navier-Stokes equations. A simplified differential equation for a turbulent front is then presented with numberical solutions obtained by a high speed computer for various values of the relative roughness parameter. It is then shown that these profiles are the same as for a laminar front when a modification is made in the length parameter to account for channel roughness. Concomitant experimental investigations with oil verify the equation for the shape of a laminar front approximately 1-in. deep, and similar experiments with water verify the equation for turbulent fronts reasonably well over a several-fold variation in slope, discharge, and roughness. Both the theory and the tests are for an impervious bed with zero infiltration.