On the question of the shape of a free jet when a perfect liquid flows out of a vessel with flat walls

Abstract

The question of the form of a free jet when a perfect liquid flows out of a vessel, when the movement occurs in a plane, was first solved by Helmholtz for the case of liquid flow through a channel protruding into this vessel. Helmholtz’s method was then generalized by Kirchhoff, who gave a solution to several problems related to plane the movement of a fluid, and, by the way, the problem of the flow of fluid through a slot in a flat wall.Both of these problems are considered by Lamb in his treatise on hydrodynamics, and he uses the method of conformal transformations of Schwartz and Christoffel to derive the equation of a free jet. The purpose of my present note is to apply the same method to the derivation of the equation of a free jet when a liquid flows through a hole in a vessel with flat walls, and the walls converge to the hole at an angle of 2a.