Slender streams with gravity: Outer asymptotic expansions. I

A method is presented to determine the steady, three-dimensional, potential flow (neglecting surface tension) of a slender stream of fluid in the presence of gravity. Three basic flows are considered: jet flow (for which the bounding surface is entirely free); pipe flow (for which the bounding surface is entirely specified) and channel flow (for which the bounding surface is partially free and partially specified). The leading terms in the asymptotic expansions of these flows, which are called outer expansions, are presented. The leading terms in the pressure distribution for each of the three basic flows are also computed and several examples are presented.