Flow Description, Streamline, Pathline, Streakline and Timeline

Streamline, pathline, streakline and timeline form convenient tools to describe a flow and visualise it. They are defined below.  
 
Figure 3.5 : Streamlines

Figure 3.6: Streamline definition

A streamline is one that drawn is tangential to the velocity vector at every point in the flow at a given instant and forms a powerful tool in understanding flows. This definition leads to the equation for streamlines.

$${ {du} \over u} = {{dv} \over v} = {{dw} \over w}$$ (3.7)

where u,v, and w are the velocity components in x, y and z directions respectively as sketched.

Figure 3.7 : Streamtube

Hidden in the definition of streamline is the fact that there cannot be a flow across it; i.e. there is no flow normal to it. Sometimes, as shown in Fig.3.7 we pull out a bundle of streamlines from inside of a general flow for analysis. Such a bundle is called stream tube and is very useful in analysing flows. If one aligns a coordinate along the stream tube then the flow through it is one-dimensional.

Figure 3.8: Pathlines
 
                                
Figure 3.9: Streaklines                                                                 Figure 3.10: Timeline

Pathline is the line traced by a given particle. This is generated by injecting a dye into the fluid and following its path by photography or other means (Fig.3.8). Streakline concentrates on fluid particles that have gone through a fixed station or point. At some instant of time the position of all these particles are marked and a line is drawn through them. Such a line is called a streakline (Fig.3.9). Timeline is generated by drawing a line through adjacent particles in flow at any instant of time. Fig.3.10 shows a typical timeline.

In a steady flow the streamline, pathline and streakline all coincide. In an unsteady flow they can be different. Streamlines are easily generated mathematically while pathline and streaklines are obtained through experiments.

The following animation illustrates the differences between a streakline and a pathline.

Figure 3.11: Animation to illustrate Streaklines and Pathlines.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney