Difference between Streak Line and Path Line

Fig 7.4    Description of a Streak line

            Above diagram can be described by the following points:

           Describing a Path Line:

           a)  Assume P be a fixed point in space through which particles of different identities pass at different times.

           b) In an unsteady flow, the velocity vector at P will change with time and hence the particles arriving at P at different times will traverse

               different paths like PAQ,  PBR and PCS which represent the path lines of the particle.

           Describing a Streak Line:

           a) Let at any instant these particles arrive at points Q, R and S.

           b) Q, R and S represent the end points of the trajectories of these three particles at the instant.

           c) The curve joining the points S, R, Q and the fixed point P will define the streak line at that instant.

           d) The fixed point P will also lie on the line, since at any instant, there will be always a particle of some identity at that point.

           Above points show the differences.

           Similarities:

           a) For a steady flow, the velocity vector at any point is invariant with time

           b) The path lines of the particles with different identities passing through P at different times will not differ

           c) The path line would coincide with one another in a single curve which will indicate the streak line too.

           Conclusion: Therefore, in a steady flow, the path lines, streak lines and streamlines are identical.