An investigation was carried out into external-Coanda Effect flares designed by British Petroleum International plc. The phenomenon of interest was breakaway of an under expanded axisymmetric curved wall jet from the guiding surface due to high blowing pressure. A survey of investigations of similar flows suggested very complex jet fluid dynamics. Strong cell structure including shock waves was present giving bulk and discrete compression and bulk dilatation. More expansion was imposed by the radial velocity components. Wall curvature and a rear-facing step added further significant influences. The combination of these factors is known to produce highly non-linear turbulence, and this constitutes a major difficulty for the application of computational methods to the flare. In view of the amount of resources required to eliminate the problems of using a Navier-Stokes code, an economical approach was adopted, matching the Method of Characteristics to various simplified models and an integral boundary layer. In the experimental work, a planar model of the flare was contructed and studied using a wide range of methods in order to achieve accuracy and provide comparability with other work. An axisymmetric model was designed and investigated in a similar manner, so that the influence of this geometry could be clearly distinguished. A full-scale flare was subjected to a restricted range of tests to compare the laboratory results with the industrial application. The results from all the experiments demonstrated good correspondence. The main conclusion was that amalgamation of separation bubbles is crucial for breakaway. These are present long before breakaway, and are strongly reduced by decreasing the cell scale, adding a rear-facing step and axisymmetry, which leads to improved breakaway performance. Although the computational methods did not prove robust enough for all design purposes, they did permit significant insights into the mechanism of breakaway.