Path Lines

        Definition:  A path line is the trajectory of a fluid particle of fixed identity as defined by Eq. (6.1).

Fig 7.3    Path lines

         A family of path lines represents the trajectories of different particles, say, P₁, P ₂, P₃, etc. (Fig. 7.3).

       Differences between Path Line and Stream Line

Path Line Stream Line This refers to a path followed by a fluid particle over a period of time. This is an imaginary curve in a flow field for a fixed instant of time, tangent to which gives the instantaneous velocity at that point . Two path lines can intersect each other as or a single path line can form a loop as different particles or even same particle can arrive at the same point at different instants of time.   Two stream lines can never intersect each other, as the instantaneous velocity vector at any given point is unique.

Note: In a steady flow path lines are identical to streamlines  as the Eulerian and Lagrangian versions become the same.

Lets Do Some Examples