The Lagrangian approach

The Lagrangian Description is one in which individual fluid particles are tracked, much like the tracking of billiard balls in a high school physics experiment.

• 

In the Lagrangian description of fluid flow, individual fluid particles are "marked," and their positions, velocities, etc. are described as a function of time. In the example shown, particles A and B have been identified. Position vectors and velocity vectors are shown at one instant of time for each of these marked particles. As the particles move in the flow field, their potions and velocities change with time, as seen in the animated diagram. The physical laws, such as Newton's laws and conservation of mass and energy, apply directly to each particle. If there were only a few particles to consider, as in a high school physics experiment with billiard balls, the Lagrangian description would be desirable. However, fluid flow is a continuum phenomenon, at least down to the molecular level. It is not possible to track each "particle" in a complex flow field. Thus, the Lagrangian description is rarely used in fluid mechanics.