Annular Water Jets

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Abstract
An analysis is provided of a slender stream of water whose cross-section is the region lying between concentric circular free streamlines. In the absence of gravity, explicit integral expressions are derived for the radii as a function of distance along the jet. In particular, for intially-contracting jets, the collapse distance, at which the inner radius vanishes, is determined. In the presence of gravity, the problem for both vertically upward and vertically downward annular jets can be reduced to that of solving a non-linear ordinary differential equation, and numerical solutions are obtained. An outline is given of the procedures required to match these free jets to exit flows from slender nozzles.

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