the fluid as incompressible, we suppose the enclosure to possess some degree of elasticity so as to exert on the fluid a pressure sufficient to prevent cavitation, then the peripheral pressure will undergo no change in consequence of the vortices, for a change of pressure on the walls of an elastic enclosure must be accompanied by a compression or dilatation of the fluid contents. Under these conditions the greater the energy of the vortex system set up in the fluid the lower will become the pressure in the internal part of the region, so that the plus and minus momentum of the equal and opposite flow taking place across any imaginary barrier plane is accounted for by the ordinary static pressure on the confines of the region, and does not give rise to any added pressure.[1]
If we suppose the enclosure rigid and the fluid elastic, the change of pressure due to the vortices on the boundary walls depends upon the law of elasticity, and is not a function of the magnitude or energy of the vortex system alone. The result of the above reasoning is not at all in harmony with accepted views as to the behaviour of vortices as expounded in the Vortex Atom theory.[2][3] According to the highest authorities the individual vortices carry momentum just as if they were bodies of greater density than the fluid that contains
- ↑ The author has heard it argued that every stream of fluid passing any imaginary barrier plane carries momentum across that plane, and therefore must result in added pressure between the fluid and the enclosure. Such an argument is evidently unsound; on the fluid tension hypothesis (§ 82) we may regard these internal motions of the fluid as giving rise to tension across the barrier plane, and this tension is equal and opposite to the momentum per unit time transmitted by every current and counter current set up in the fluid, and on the principles discussed in §§ 81, 82, and 83; this applies not only for the whole region, but individually for every small element of the fluid cut by the imaginary plane. Interpreting in the usual way, we see that it is the ordinary hydrostatic pressure on the walls of the enclosure that supplies the necessary force to balance the momentum transferred per second, and that a diminution of pressure in the vicinity of the barrier arises automatically, precisely equivalent to the momentum transference taking place.
- ↑ Nature, xxiv., p. 47, also "Motion of Vortex Rings," J. J. Thomson.
- ↑ See: Joseph Larmor, On the Average Pressure Due to Impulse of Vortex-Rings On a Solid, Nature, Vol. xxiv. 1881, p. 47 (Wikisource contributor note)
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