§ 91. Difficulty in the Case of the Perfect Fluid.—In any actual fluid there can be no difficulty. If, for example, we suppose a plane of infinite lateral breadth gliding edgewise through the fluid to have a force applied at right angles to the direction of motion, this force is borne immediately by the fluid, and the conditions necessary to the development of the cyclic system are fulfilled. In a perfect fluid, however, a plane can move without resistance in any aspect, and thus it is not possible to generate a difference of pressure between its two sides except for the period whilst the normal component of its velocity is undergoing acceleration. Being limited in this manner, the quantity of energy disposable for the production of cyclic motion would appear to be strictly limited, and consequently we may form the following conclusions:—
(1) In an infinite fluid where a cyclic motion, however weak, possesses infinite energy, it will be impossible to generate cyclic motion.
(2) In a finite region it would appear possible that cyclic motion may be induced by a body whose normal motion is accompanied by kinetic energy and which therefore exerts a pressure on the fluid while it is acquiring lateral motion under the influence of the applied force; a portion of the applied force being eventually borne by the cyclic motion developed.
(3) Assuming (2), the more limited the region the less the body will yield to the applied force in the production of the cyclic motion necessary to give rise to an equal and opposite reaction.[1]
§ 92. Superposed Rotation.—If rotational motion be superposed on a motion of translation, equilibrium cannot be maintained by forces applied to the boundary either internal or external.
- ↑ Conclusions (2) and (3) may be taken as provisional, pending proof or disproof on analytical lines. The inviscid fluid of Eulerian theory is a very peculiar substance on which, to employ non-mathematical reasoning. It is quite likely that in the inviscid fluid the dynamic conditions are satisfied without the production of cyclic motion under any circumstances.
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