Pathlines and streaklines provide ways to visualize flows. Another technique would be to instantly inject a line of dye across streamlines and observe how this line moves as time increases. For example, consider the initially straight dye line injected in front of the circular cylinder shown in Fig. P4.21. Discuss how this dye line would appear at later times. How would you calculate the location of this line as a function of time? This type of line is called a timeline.

Figure P4.21

V Dye at = 0