Lagrangian approach

Two common techniques are used for describing fluid flow: Lagrangian and Eulerian. The Lagrangian approach requires that the properties of a particular element of the fluid particles be tracked as it traverses the flow. This approach is similar to what we used in particle and rigid-body dynamics. The location of this fluid element is described by its coordinates (x,y,z), which are functions of time. The fluid element can be identified by tracking it from its initial location (x0,y0,z0) at time t = 0, and the velocity of this element at an arbitrary time t is expressed as ${\mathbf{V}} = {\mathbf{V}}({x_0},{y_0},{z_0},t)$. In order to describe a fluid flow using the Lagrangian approach, the sensors that monitor fluid properties would have to move at the same velocity as the fluid element; this is an impractical and often impossible requirement to meet, especially for such complex cases as three-dimensional transient flow. Therefore, the Lagrangian approach is rarely used in description of fluid flow.