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IX.—On the Resistance experienced by a Body moving in a Fluid
Published online by Cambridge University Press: 15 September 2014
Extract
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
C being a constant determined by the boundary conditions of the problem, ν the velocity, and ρ 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 — ρν2/2 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.
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- Copyright © Royal Society of Edinburgh 1915
References
page 95 note * Enunciated by Stokes, “On the Critical Values of the Sums of Periodic Series,” Trans. Camb. Phil. Soc, vol. viii.
page 95 note † Helmholtz, , “Über diskontinuierliche Flüssigkeitsbewegungen,” Berlin. Monatsberichte, 1868.Google Scholar
page 95 note ‡ E.g. Lamb's, Hydrodynamics, p. 86.Google Scholar
page 97 note * Proc. Roy. Soc, Feb. 3, 1887; Phil. Mag., xxiii, 1887, p. 255; Math, and Phys. Papers, vol. iv, p. 149.
page 97 note † “Flüssigkeits und Luftwiderstand,” Phys. Zeitschrift, xiii, 1912.
page 98 note * For a more rigorous definition of stability, see one given by Prof. Love in Proc. London, Math. Soc, xxxiii, p. 325 (1901).
page 100 note * From equations (66) and (70) in Appendix it is easily found that 
page 106 note * See equation (67) in Appendix.
page 107 note * Phys. Zeitsch., Bd. xiii, 1912.