perfect streamline motion is that the energy account shall balance.
§ 12. Need for Hydrostatic Pressure,—Cavitation.—The motion impressed on the fluid by the pressure region of the head is compulsory, unless (as may happen in the case of a navigable balloon) deformation of the envelope can take place. The motion impressed by the shoulder, on the contrary, depends upon hydrostatic pressure, for otherwise there is no obligation on the part of the fluid to follow the surface of the body; hydrostatic pressure is necessary to prevent the formation of a void. The pressure measured from the real zero must everywhere be positive, otherwise the fluid will become discontinuous and cease to follow the surface. This is a difficulty that has been actually experienced in connection with screw propellers, and termed cavitation.
§ 13. The Motion in the Fluid.— It has been shown that the head of a streamline form is surrounded by a region of increased pressure. Consequently the fluid as it approaches this region will have its velocity reduced, and the streamlines will widen out, as shown in Fig. 3 (see also Figs. 42, 44, 45, etc.). This behaviour of the fluid illustrates a point of considerable importance, which is frequently overlooked. Whenever a body is moving in a fluid, its influence becomes sensible considerably in advance of the position it happens to occupy at any instant. The particles of fluid commence to adjust themselves to the impending change with just as much certainty as if the body acted directly on the distant particles through some independent agency, and when the body itself arrives on the scene the motion of the fluid is already conformable to its surfaces. There is no impact, as is the case with the Newtonian medium, and the pressure distribution is more often than not quite different from what might be predicted on the Newtonian basis. This behaviour of a fluid is due to its continuity. It follows from elementary considerations that the fluid in the "amidships" region possesses a velocity greater than the
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