Streamlines, streaklines, and pathlines

Streamlines, streaklines and pathlines are field lines in a fluid flow.They differ only when the flow changes with time, that is, when the flow is not steady.Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics, we have that: Streamlines, streaklines and pathlines are field lines in a fluid flow.They differ only when the flow changes with time, that is, when the flow is not steady.Considering a velocity vector field in three-dimensional space in the framework of continuum mechanics, we have that: