Differential Form of Conservation Equations

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.