CH ENGR 101A Lecture Notes - Lecture 11: Lagrangian And Eulerian Specification Of The Flow Field, Material Derivative, Total Derivative
Document Summary
Eulerian coordinate - the independent variables are x, y, z and t or xi, t (i=13). The basic conservation equations are in the eulerian frame, r = r (xi,t). In the lagrangian frame attention is fixed on a particular mass of fluid as it flows, r = r (xo i,t), where the coordinate xi: specifies which fluid element is being considered. Consider a variable " such that then the total differential of " can be expressed as division by a time differential *t leads to the following expression. After taking the limit *t 6 0 is obtained for the material derivative (1. 2) (1. 3) (1. 4) (1. 5) in which vi is the fluid velocity in direction i. The material derivative (lagrangian time derivative) represents the total change in " as seen by an observer who is moving with a particular fluid element. In the lagrangian frame we observe the particle for a time *t as it flows.
