This equation can be integrated to obtain the equation of streamlines.

When bundles of streamlines are considered in a flow field, it constitutes a ‘stream tube' (Fig. 3.1.1-e). Since streamlines are everywhere parallel to the local velocity, fluid cannot cross a streamline, so fluids within a stream tube remain there and cannot cross the boundary at stream tube .

 

 

Fig. 3.1.1: Basic line patterns in fluid flow: (a) Timelines; (b) Pathline; (c) Streakline; (d) Streamline; (e) Streamtube.

The following observations can be made about the fundamental line patterns;

1. 1. Mathematically, it is convenient to calculate a streamline while other three are easier to generate experimentally.

2. The streamlines and timelines are instantaneous lines while pathlines and streakline are generated by passage of time.

3.In a steady flow, all the four basic line patterns are identical. Since, the velocity at each point in the flow field remains constant with time, consequently streamline shapes do not vary. It implies that the particle located on a given streamline will always move along the same streamline. Further, the consecutive particles passing through a fixed point in space will be on the same streamline. Hence, all the lines are identical in a steady flow. They do not coincide for unsteady flows.