Estimating the liquid jet breakdown height using dimensional analysis with experimental evidence

Abstract

When opening a sink or pouring water from a bottle an interesting and unintuitive physical phenomenon occurs: the regular cylindrical jet breaks into droplets at a certain height, which changes once the initial conditions of the falling jet change , thus two distinct regions are observable: a steady stream of water at high flow and separate droplets at low flow . In this paper, we found and experimentally tested a model that correlates the parameters of the phenomenon mentioned above. We analyzed how the breakdown height of the jet changes with three initial parameters: jet radius, liquid density, and surface tension. We propose a mathematical model for the relationship between the diameter of the liquid stream and the height at which it breaks into droplets , consisting of a quadratic dependency . There was a good fit between experimental data and the model with a correlation coefficient exceeding 0.95. Finding and exploring this way to analyze fluid mechanics might help understand the fundamental correlation between the parameters involved and design more lucrative industrial techniques in fields such as oil extraction or printing.