Description can be an Imagination, but Action must be Real …… P M V Subbarao Professor Mechanical Engineering Department I I T Delhi Material Derivative using Eulerian Description

Eulerian Description of Flow : The Concept Adopt the point of view that we will observe fluid properties at few selected points x i as a function of time. The association with a given fluid particle must be broken. Realize that as time flows different fluid particles will occupy the position x i. Once properties are expressed as functions of (x; t), it is said to be the Eulerian description of a fluid.

The Lagrangian Displacement of Particle in Eulerian Description It is of very high importance to compare these two descriptions of a fluid and validate Euler description. The most basic definition is the meaning of velocity: the definition is That is to say, following the particle one need to calculate the rate of change of position with respect to time. Given the Eulerian velocity field, the calculation of Lagrangian displacement is therefore mathematically equivalent to solving the initial value problem. A set of ordinary differential equations for the function x(t), with the initial condition x(0) = . This is of very high importance to compare these two descriptions of a fluid and validate Euler description.

Material Derivative with Imaginary Description Consider Eulerian quantity during any infinitesimal time  t The time rate of change of attached to this fluid parcel is expressed as: Attribute this quantity to lgrangians’parcel, p.