V. On the theory of free stream lines

Abstract

The attention of mathematicians was first called to the subject of the present paper by a memoir of Helmholtz’s in 1868, on “Discontinuous Fluid Motion.” In discussing the steady motion of liquids past salient edges of fixed obstacles, it is found that the assumptio of continuity of the motion leads to negative pressures in the liquid. Helmholtz showed, in the paper above-mentioned, that some cases of this kind could be solved by assuming a surface of discontinuity, on one side of which the liquid is at rest, and he gave a mathematical solution of one case where the motion is in two dimensions.