Conservation Laws

This section will apply the laws of conservation of mass, momentum, and energy to the fluid instantaneously inside any closed control volume which is fixed in space, shown in Figure 1.2.

All flow-field quantities in general are functions of the spatial position vector r and of time t. Although the subsequent development uses general vector forms and operations, special cases will typically assume Cartesian axes, in which case the position and velocity vectors have the following Cartesian components.

r = x x + y y + z z (1.15)

= u x + v y + w z (1.16)