4. Movement of a fluid volume element

In the course of its motion, a solid generally undergoes a change of position and orientation. A fluid volume element also undergoes a change in shape.

At time t, let be an element of any volume surrounding the point M (x _i ) – Euler variables – and the point $M^{\prime }\left(x_i^{\text{'}}\right)$ adjacent to M (figure 12 ). In the case of an undeformable system, the velocity at M′ is given, as a function of the velocity at M and the instantaneous rotation vector $$