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

Abstract

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.

A Dynamical Study of Saline Plumes in Desalination Outfalls

“…A small initially circular 'bubble' grows for small time and then increases up to some height before it levels off and starts to flow outwards horizontally. We discuss these results for different values of Reynolds number, flow rate and density differential, and relate this full detailed model to the S. M. Shraida [2] idealised flows computed in the first section. Finally, the spectral method is extended to solve the viscous Boussinesq equations and to consider the unsteady flow from a source that is located off the bottom.…”

“…2 S. M. Shraida [2] idealised flows computed in the first section. Finally, the spectral method is extended to solve the viscous Boussinesq equations and to consider the unsteady flow from a source that is located off the bottom.…”