Shape of an Annular Liquid Jet

Abstract

Analytical and experimental studies have been done to determine the shape of a vertical, axisymmetric, annular liquid jet. From a balance of the surface, pressure, gravity, and inertia forces, a nonlinear, second-order, ordinary differential equation is obtained for the shape of the annular jet. This equation is solved numerically by the Runge-Kutta-Nyström method. An annular jet either converges (closes), diverges, or maintains (theoretically) its original radius depending upon the magnitude of the difference between the inside and outside pressure. This corresponds to, in terms of a dimensionless pressure p , whether p is less than, greater than, or equal to 2. An experiment has been performed to verify the analytical solution. The jet velocity, inside pressure and other parameters have been varied to obtain different shapes of the jet, both closing and diverging. Good agreement with the analytical prediction is found.