Continuity Equation (in Continuum Mechanics)

The continuity equation in continuum mechanics expresses the principle that mass is conserved within a fluid system. It states that the rate at which mass enters or leaves a region, plus the change of mass inside that region, must sum to zero. Essentially, if fluid flows into an area faster than it flows out, the fluid must be accumulating there; if it flows out faster than it flows in, the volume decreases. This principle ensures that, without adding or removing mass, the total amount of fluid in a closed system remains constant over time.