Excerpt: ...vessel on a whirling-table, and rotating it about the vertical axis coinciding with its axis of figure; but the phenomenon can be quite well seen without this machinery. In this case the velocity of each particle of the water is proportional to its distance from the axis, and the whole mass, when relative equilibrium is set up, turns, as if it were rigid, about the axis of the vessel. Each element of the fluid in this "forced vortex," as it is called, is in rotation, and, like the moon, makes one turn in one ...
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Excerpt: ...vessel on a whirling-table, and rotating it about the vertical axis coinciding with its axis of figure; but the phenomenon can be quite well seen without this machinery. In this case the velocity of each particle of the water is proportional to its distance from the axis, and the whole mass, when relative equilibrium is set up, turns, as if it were rigid, about the axis of the vessel. Each element of the fluid in this "forced vortex," as it is called, is in rotation, and, like the moon, makes one turn in one revolution about the centre of its path. This is, therefore, a true, though very simple, case of vortex-motion. On the other hand, what may be called a "free vortex" may exist, and is approximated to sometimes when water in a vessel is allowed to run off through an escape pipe at the bottom. The velocity of an element in this "vortex" is inversely proportional to its distance from the centre, and the form of the free surface is quite different from that in the other case. The name "free vortex" is often given to this case of motion, but there is no vortex-motion about it whatever. Thomson's great paper on vortex-motion was read before the Royal Society of Edinburgh in 1867, and 163 was recast and augmented in the following year. It will be possible to give here only a sketch of its scope and main results. The fluid is supposed contained in a closed fixed vessel which is either simply or multiply continuous (see p. 156 ), and may contain immersed in it simply or multiply continuous solids. When these solids exist their surfaces are part of the boundary of the liquid; they are surrounded by the liquid unless they are anywhere in contact with the containing vessel, and their density is supposed to be the same as that of the liquid. They may be acted on by forces from without, and they act on the liquid with pressure-forces, and either directly or through the liquid on one another. The first result obtained is fairly obvious. The centre of mass of...
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