Let A be a fixed point in space, at time t1. P1, P2 and P3 (all passing through A) are the three path lines traversed by three particles in an unsteady fluid flow. Let B, C and Dare the end points at time t2 of P1, P2, P3 respectively. If we join ABC D, we will get a line which is called the streak line. Thus a streak line at any instant of time is the locus of the temporary locations of all particles that have passed through a fixed point in the flow field.
In Lagrangian method, if a fluid particle (S) passes through a fixed point (S) in time t
The equation of streak line at a time t is given by
Equation (4.10) is the equation for a streak line referrent to a fixed point (5;).