191 4-15. J Resistance to Motion of a Body in a Fluid. 
95 
IX. — On the Resistance experienced by a Body moving in a 
Fluid. By H. Levy, M.A., B.Sc., 1851 Exhibition Research Scholar 
of the University of Edinburgh. Communicated by The General 
Secretary. 
(MS. received January 11, 1915. Read March 1, 1915.) 
A NECESSARY condition in any hydrodynamical problem is that the pressure 
exerted by the fluid at any point must always be positive, and be given by 
p = c-pvy2 ( 1 ) 
C being a constant determined by the boundary conditions of the problem, 
V the velocity, and p the density of the fluid, provided there are no external 
forces involved. Should the velocity at any point, however, be so great 
that the expression C — pf^/2 becomes negative, the problem in this respect 
at least loses its validity as an approximation to actual fact. Now it can 
easily be shown that, in any form of potential streaming about a body with 
sharp edges, the velocity at the sharp edges becomes infinite, and the 
pressure therefore negative. The equations of motion of the fluid having 
been obtained on the assumption of continuity of motion, this suggests at 
once that some form of discontinuity of the fluid probably exists near the 
sharp edges.'* 
The assumption adopted f has therefore been to suppose that from each 
of the sharp edges of the moving body AB (fig. 1), a surface AC and BD 
divides the fluid into two separate and distinct regions, the shaded portion 
representing a region of constant pressure, known as the “ dead water.” 
The pressures being constant along the stream lines AC and BD, it follows 
from equation (1) that the velocity must also be constant there. It is 
assumed that the motion is steady. How it arose does not concern us for 
the moment. 
In the case where the rigid boundaries are straight, all the circumstances 
of the motion may be derived with comparative ease by methods of 
conformal representation.^ 
For the mere construction of such problems, however, we can reverse 
* Enunciated by Stokes, “ On the Critical Values of the Sums of Periodic Series,” 
Trans. Carnb. Phil. Soc., vol. viii. 
t Helmholtz, “Uber diskontinuierliche Eliissigkeitsbewegungen,” Berlin. Monatsherichte, 
1868. 
i E.g. Lamb’s Hydrodynamics, p. 86. 
