If an actual fluid behaved anything like the ideal fluid of theory, the necessity for the ichthyoid form would not exist; any shape, however abrupt, short of producing cavitation, would give rise to stream-line motion and be destitute of resistance. The actual phenomenon of fluid resistance, discussed in the two previous chapters, is characterised by features which at present are not capable of complete elucidation by analytical means.
The principal characteristic in which the actual flow and the Eulerian form differ is as to the existence or otherwise of resistance to motion. In all cases discussed in Chap. I., with the exception of the “stream-line form,” the surface or “stratum” of discontinuity is an ever present feature which is closely related to the resistance encountered by the body in motion. It has been shown that the proneness to develop discontinuity increases the less the viscosity, and it is difficult to understand in what manner the tendency, which grows greater as the value of viscosity approaches to zero, should suddenly cease when zero is reached. This argument may be otherwise stated in the form: It is difficult to understand how a fluid that offers by hypothesis no resistance to shear can assume a rigidity in shear not possessed by a viscous substance.
§ 99. Deficiencies of Theory (continued). Stokes, Helmholtz.—In the year 1847 Stokes, discussing a particular hypothetical case of flow, was the first to suggest the possibility of a discontinuity or “rift” as a phenomenon connected with the motion of the perfect fluid. Helmholtz, writing in 1868 on the “Discontinuous Movements of Fluids” (Phil. Mag., XLIII.), pointed out the familiar instance of smoke-laden air escaping from an orifice as an example in which the motion is not at all in accordance with the hydrodynamic equation, the air moving in a compact stream instead of spreading out, as the theory of the perfect fluid requires. He remarks that such known facts cause physicists to regard the hydrodynamic equation as a very imperfect approximation to the truth, and that “divers and saltatory irregularities, which
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