411 REFERENCE · Wikibooks
Introduction to Mathematical Physics/Continuous approximation/Momentum conservation
Reference material by Wikibooks contributors. This retains its source identity and is not 411 news reporting.
We assume here that external forces are described by
and that internal
strains are described by tensor
.
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.
center | frame |Momentum conservation law corresponds to the application of Newton's law of motion to an elementary fluid volume.} figconsp
Partial differential equation associated to this integral equation is:
Using continuity equation yields to:
Momentum conservation equation can be proved taking the first moment of
Vlasov equation. Fluid momentum is then related to repartition
function by the following equality:
Later on, fluid momentum is simply designated by .