Differential Form of Conservation Equations

Abstract

The detailed structure of a flow field and its evolution over time are described by a system of partial differential equations that stem from the conservation of scalar quantities such as mass and energy, or vector quantities such as momentum. Let $\Gamma$ be some field variable, generally defined as a function of space and time, that can be associated to the fluid and V be a control volume that encloses some finite region in space occupied by the fluid at a given instant of time.