**x**

_{0}. Looking at streaklines is a way to visualise a flow. In a steady flow the streaklines will coincide with the streamlines and particle paths, but this is not true in general for non-steady flows.

To compute what the streakline originating from **x**_{0} looks like at time t_{0} in a flow with velocity field **u**(**x**, t) you simply find the location of the fluid particle that was at **x**_{0} at time t' for all t' < t_{0}. This is done by integrating the differential equation d**x**/dt = **u** with initial conditions **x**(t') = **x**_{0}, which can take some effort.

Streaklines are not really the best way to visualise a flow. Rather their usefulness lies in the fact that in an experiment they are very easy to exhibit. All you have to do is to place somethings that emits some sort of dye at **x**_{0} and the streakline will be visible as a dyed streak.