Open AccessOn the displacements of the particles and their paths in some cases of two-dimensional motion of a frictionless liquid
Author(s) -
W.B. Morton
Publication year - 1913
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1913.0068
Subject(s) - ellipse , cylinder , perpendicular , motion (physics) , curvature , geometry , shell (structure) , particle (ecology) , mechanics , physics , ellipsoid , line (geometry) , classical mechanics , optics , mathematics , materials science , geology , oceanography , astronomy , composite material
The paths described by the individual particles of a liquid have been investigated only in a few cases, excluding those in which the motion is steady, so that the particles follow the stream-lines. Clerk Maxwell, in 1870, published drawings for the paths in an unbounded liquid disturbed by the passage of a circular cylinder. The curves for particles in contact with the cylinder were plotted by calculation; the other paths were drawn by eye from a knowledge of their terminal points and curvature. From these curves were derived others, showing the successive stages in the deformation of a row of particles which, before the approach of the cylinder, lay in a straight line perpendicular to its motion. In 1885, Lord Kelvin investigated the paths of particles of a liquid enclosed in a rotating ellipsoidal shell. He showed that they moved, relatively to the shell, along a set of similar ellipses in parallel planes, the period of this motion being the same for all the particles, so that after this period the configuration comes back to the initial one rotated through an angle.