Potential flow of fluid from an elevated, two-dimensional source

Abstract

• Hodograph solutions for high flow from an elevated source are computed. • Linear solutions for high flow are computed using Fourier techniques. • Nonlinear solutions for all parameter values are computed using an integral equation formulation. • Each configuration has a minimum flow rate beneath which no solutions exist. • Interesting solutions with mushroom shapes are found to occur just before the solution method fails. When fluid is pumped from an elevated source it flows downward and then outward once it hits the base. In this paper we consider a simple two dimensional model of flow from a single line source elevated above a horizontal base and consider its downward flow into a spreading layer on the bottom. A hodograph solution and linear solutions are obtained for high flow rates and full nonlinear solutions are obtained over a range of parameter space. It is found that there is a minimum flow rate beneath which no steady solutions exist. Overhanging surfaces are found for a range of parameter values. This flow serves as a model for a two-dimensional water fountain, or approximates a similar flow in a density stratified environment.