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. Partial differential equation associated to this integral equation is:

Using continuity equation yields to:

Later on, fluid momentum is simply designated by $$p$$.