In an Eulerian description, we use space-time coordinates.
We will want to find ,
, ...
Example:
2D ideal stagnation point flow
Particle paths: Lines traced by the fluid particles. Particle paths can be found from solving:
Streamlines: Lines that are everywhere in the direction of the velocity field. Streamlines can be found from solving:
Streaklines: Lines of smoke coming out of smoke generators. Streaklines can be found by integrating the path lines for all the smoke coming out the generator.
Steady Flow: .For steady flow, pathlines, streamlines, and streaklines are all the
same.