Conservation of Momentum

Abstract

Conservation of momentum represents the fundamental principle of dynamics (the second Newton law); it is the law governing fluid motion, under the constraint of mass conservation. This law is first formulated in integral terms, for a generic fluid volume, which allows to include the effect of momentum on the forces acting on the surrounding boundaries. It is then written in the form dedicated to one-dimensional streams, which regulate the fluid dynamics in vessels presenting the mainly unidirectional motion. The general differential formulation evidences the need to define a constitutive law that specifies the behavior of the material, how internal stresses develop in reaction to fluid motion. The Navier–Stokes equation governing the fluid dynamics of Newtonian fluid is then derived and discussed.