Pathlines and streaklines provide ways to visualize flows An

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.

Solution

A strekline is analyzing the flow of the pattern in laboratory.It is done by injecting the dye at some point and then observing the color pattern appearance in the flow.A path line is a line to analyze the flow of the particle from one point to other point.Consider a line of dye is injected across streamlines in front of the cylinder.Show the line of dye is injected across streamlines in front of the cylinder.

The injected dye will have various intensities of flow with increase in depth of the pipe.The different colored line in the flow is the locus of the all dye particles establishing from the same point in the flow region.The flow of dye inside the pipeline is blurring gradually with increasing the time.

Consider one such point A in the flow region of an unsteady flow.The particle at some time t=0 passing through this point will have its pathline AB.The next particle will have a different velocity due to the unsteady flow.This means it moves along some other path AC then locate the point such as B,C,D at any time which represents the position of all the particles that are coming .