Introduction to Mathematical Physics/Continuous approximation/Momentum conservation

We assume here that external forces are described by $f$ and that internal strains are described by tensor ${\tau }_{ij}$.

This integral equation corresponds to the applying of Newton's law of motion\index{momentum} over the elementary fluid volume as shown by figure figconsp.

Momentum conservation law corresponds to the application of Newton's law of motion to an elementary fluid volume.} Template:IMP/label

Partial differential equation associated to this integral equation is:

Using continuity equation yields to:

Template:IMP/rem Later on, fluid momentum is simply designated by $p$.