Streamlines, streaklines and pathlines

[R Power]

Hi PFians

I searched net for hours about understanding the concept of streamlines, streaklines and pathlines but I am still under confusion.
1.) See, streamlines are tangent to velocity vector at everypoint. Right? Now velocity is a characteristic of a moving fluid particle. So, shouldn't streamlines equivalent to path lines.
e.g take a particle moving in a circle, path traced by that particle is a circle or we can say circle is the pathline for that particle. Right? Also circle is tangent to velocity vector for the particle at a certain instant. So , circle or pathline is same as fieldline(streamline in case of fluid particle) for the particle because streamline is tangent to velocity vector by definition. Now these two are same in steady flows but not in unsteady flows. Why? These both are same things, then why different in unsteady flows.

2. In case of steady flow streaklines are also same as pathlines. Why and how? Consider particles moving from origin towards infinity in x-y plane at differerent angles in straight lines and with different speeds but the flow is steady. Here velocity vectors of particles will concide with the straight pathlines. So these pathlines should be the streamlines. Now the locus particles that have moved from a fixed certain point over certain time will be a line or curve intersecting all the pathlines and streamlines. This locus will be streakline. So how streamline , streakline and pathline all three concide in steady flow??

 

[arildno]

1.) See, streamlines are tangent to velocity vector at everypoint. Right? Now velocity is a characteristic of a moving fluid particle. So, shouldn't streamlines equivalent to path lines.

The streamlines represent a snapshot of the fluid domain at some particular time t.

These curves will have, at each point, a DIFFERENT particle as defining the local tangent to the curves.

Thus, there is no reason why the streamlines should represent particle PATHS, since they aren't that to begin with.

Only in the case of locally steady flows will this be the case.



In contrast to both particle paths and streamlines, the streak line is an expanding MATERIAL CURVE, in which the particles defining it remain the same over time (with, possibly new particles added to it at some precise locus)

The motion of the streak line is therefore the motion of an AGGREGATE of individual particle paths, and there is no reason why it should mimic any single one of those particle paths.

 

[R Power]

you mean streamlines are a net effect of all particles moving and they represent net orientation of flow.

 

[R Power]

you mean streamlines are a result of motion of all particles not only one and represent overall orientation of flow ??