general velocity of the fluid (the body, as before, being reckoned stationary). We know that at and about the region C. Fig. 3, the fluid has a less area through which to pass than at other points in the field of flow. It is in sum less than the normal area of the stream by the area of cross-section of the body at the point chosen. But the field of flow is made up of a vast number of tubes of flow, so that in general each tube of flow wall be contracted to a greater or less extent, the area of section of the tubes being less at points where the area of the body section is greater. We know that a contraction in a tube of flow denotes an increase of velocity.
Thus on the whole the velocity of the fluid is augmented across any normal plane that intersects the body itself, but the increase of velocity is not in any sense uniform in its distribution. In fact, towards the extremities of the body, and in its immediate neighbourhood, we have already seen that the motion of the fluid is actually slower than the general stream.
The motion of the fluid is examined from a quantitative point of view in a subsequent chapter (Chap. III.), where plottings are given of the hydrodynamic solution in certain cases.
§ 14. A Question of Relative Motion.—The motion of the fluid has so far been considered from the point of view of an observer fixed relatively to the body; it will be found instructive to examine the same motions from the standpoint of the fluid itself, that is to say, to treat the problem literally as a body moving through a fluid, instead of as a fluid motion round a fixed body.
It is evident that the difference is merely one of relative motion. The problems are identical: we require to consider the motions as plotted on co-ordinates belonging to the fluid instead of co-ordinates fixed to the body itself. The relation of the streamlines (which we have so far discussed) to the paths of motion (which we now propose to examine) is analogous to that of the cycloid or trochoid to its generating circle.
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