Flow with a free surface in a Hele-Shaw cell: experiments and theory

Abstract

ABSTRACTThe solution of Boussinesq's equation that describes the free surface of water flowing steadily through a dam on an impervious bottom can be generalized to quasi steady propagation of water into an initially dry dam. If the water level in the reservoir rises with constant speed from zero, a closed solution of Boussinesq nonlinear equation can be found since the problem lacks characteristic length. The solution shows that the advance rate of the saturated zone is constant. Experiments in a vertical Hele-Shaw cell, resting on an impervious bottom and connected with a reservoir filled with glycerine have been made. The results show that if the level in the reservoir rises linearly with time from zero, the horizontal advancement of the glycerine increases linearly with time.