In addition to visualization, there are other useful applications of streamlines. Consider, for instance, a bundle of streamlines that pass through a reference volume of arbitrary shape and size. The outermost set of streamlines form the walls of a stream tube and define the surface. Figure 2.6 shows a length of a typical stream tube. If the cross-sectional area of a stream tube is small, it is often referred to as a stream filament. The “streamlines” in an experiment using smoke for flow visualization in reality are stream filaments because the smoke must be injected from orifices of small but finite size. Obviously, all the streamlines passing through neighboring points must be nearly parallel, although they may diverge or become even more closely packed farther downstream.
Because there is no flow across any streamline, a stream filament behaves as a miniature pipe. We show in the next chapter that the average velocity at any point along a stream tube or stream filament is related to its cross-sectional area. It is almost obvious that if the flow is incompressible, the speed must increase when the area decreases and vice versa.