I have come across the terms streakline, pathline in fluid mechanics in my UG course but have never been able to get their real applications. If someone may kindly shed some light on this.
Also, how do these become different from streamline if the flow doesn't remain steady and incompressible?
Check out this famous NSF movie by John Lumley of Lagrangian vs Eulerian descriptions in fluid mechanics: http://www.youtube.com/watch?v=mdN8OOkx2ko
There is also a NSF flow visualization movie that describes the difference between streak, path and stream lines: http://www.youtube.com/watch?v=nuQyKGuXJOs
Streak line: Let suppose as some point X_0 in the flow you introduce microscopic bubbles continuously ( assume that the bubbles do not distort the flow and have a negligible buoyant force). Then the streak line is the curve formed by the instantaneous position of all the bubbles at say a given time that passed through X_0.
Path Line: The path line for a bubble released at X_0 at time t_0 is a curve in space that the bubble (release at time t_0) follows for t>t_0.
Stream line: A stream line at some time t is a cuve in space in which the velocity is every where tangent to it. However, each material point ( i.e. bubble) along that curve may have originated at a different X_0 and at a different t_0.
In steady flow a path line=streak line=stream line.
path line, stream line and streak line are kinematic quantities and therefore their definition does not depend on whether the flow is compressible or not. Stream function is another matter.
I was mainly looking for the application of streak-line and path-line. Like in streamline we knoe they are used to analyze flow pattern or flow rate etc. But where are these streak-lines and path-lines used.
Essentially used to visualize transient flows. See the following http://www.met.sjsu.edu/wind/streaklines.shtml
java applet that shows wind patterns over San Francisco Bay area
Well if I had to use streamline in analyzing transient flows, the velocity vector will change every moment and so will the lines,wouldn't it serve the purpose.
In fluid mechanics, you have the standard classic Eulerian approach, but to deal with particles trajectories, another better way is the "Lagrangian approach", for which it is easier to follow trajectories.Navier Stokes equations are somehow different and slightly more complex in the Lagrangian approach. See for example ref: http://hal.archives-ouvertes.fr/docs/00/66/43/43/PDF/lagrangian-NSC.pdf
@Hubert. Kindly correct if I am wrong in interpreting your answer.
If we are to analyze streamlines or rather Eulerian approach, streamlines serve the purpose else for particles we call for Lagrangian approach which is easier to describe using streak-line or path lines.
Check out this famous NSF movie by John Lumley of Lagrangian vs Eulerian descriptions in fluid mechanics: http://www.youtube.com/watch?v=mdN8OOkx2ko
There is also a NSF flow visualization movie that describes the difference between streak, path and stream lines: http://www.youtube.com/watch?v=nuQyKGuXJOs
In a fluid flow streamline is used to represent the position and direction of a particles at a given instant of time and a fixed point in space. Therefor, as the particles pass by that position, its position is represented as a function of time and space.
Path-line shows the position traced by a single particle at different time i.e by a line joining its previous and current positions w.r.t time .
However streak-line represents position of different particles with respect to each other at a given instant of time i.e by a line joining positions of the different particles at a given instant of time thus it represent the particle front .
In a steady flow , where position is not a function of time, even if we forget that at what time which particle was present where they have traversed through the same space. i
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