Pathline

A railway line (English pathline ) records ( the trajectory) of a single particle in a flow field by the path in the fluid dynamics. Intuitively, a railway line, when the trajectory of a spark is taken over an open fire with a long exposure time.

Railway lines, together with streamlines, streaklines and timelines components of the visualization concept of " characteristic lines ".

Calculation

Rail lines are defined by

Wherein we follow the motion of a particle in the flow.

Note at the point the curve is parallel to the speed vector of the flow of that, the velocity vector is evaluated at the position of the particle at a time.

• Fluid Mechanics