On Curved Barriers

Abstract

In two-dimensional discontinuous fluid motion one point of considerable importance has not hitherto been given sufficient attention. I raise it formally in a paper to be published soon (Fluid Motion past Circular Barriers, Scripta Universitatis atque Bibliothecae Heirosolymitanarum, 1923, Vol. I., XI., 1–14) in the following manner. Given the form of the barrier by means of, say, the radius of curvature in terms of the angle of contingence, how does the solution take into account the angular extent of the barrier? Clearly barriers which are defined by the same curve, but differ in the extent of curve used, must necessarily give rise to different solutions. Further, there must be a limiting extent of barrier, so that if it extends beyond this limit the part of the barrier in excess must lie in the “dead” fluid.