§ 15. Displacement of the Fluid.—An unfamiliar effect of the passage of a body through a fluid is a permanent displacement of the fluid particles. This displacement may be readily demonstrated. If a mass of fluid be moved from any one part of an enclosure to any other part, the enclosure being supposed filled with fluid, there is a circulation of fluid from one side to the other during transit; and if Ye suppose it to be moved from one side to the other of an imaginary barrier surface, then an equal volume of fluid must cross the same barrier surface in the opposite direction. Now it is of no importance whether the thing we move be a volume of fluid or a solid body, so that when a streamline body passes from one side to the other of a surface composed of adjacent particles of fluid, that surface will undergo displacement in the reverse direction to that in which the body is moving, and the volume included between the positions occupied before and after transit will be equal to the volume of the body itself. Moreover, since the actual transference of the fluid is due to a circulation from the advancing to the receding side of the body, it will take place principally in the immediate vicinity of the body and less in regions more remote; it is, therefore, immaterial whether the fluid be contained within an enclosure or whether one or more of its confines be free surfaces, provided that continuity is maintained, and that the body is not in the vicinity of a free surface.
§ 16. Orbital Motion of the Fluid Particles.—Since the motion of the fluid results in a permanent displacement, the motion of a particle does not, strictly speaking, constitute an orbit. It is, however, convenient in cases such as the present to speak of the motion as orbital.
If we could follow the path of a particle along any streamline, and note its change of position relatively to an imaginary particle moving in the path and with the velocity of the undisturbed stream, we should have data for plotting the orbital
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