On which fundamental principle is the continuity of flow based?

The continuity of flow is fundamentally based on the principle of conservation of mass. This principle states that mass cannot be created or destroyed in a closed system, meaning that the mass flow rate must remain constant from one cross-section of a flow to another, assuming incompressible flow conditions.

In practical terms, this implies that if fluid is flowing through a pipe or any conduit, the amount of fluid entering one section must equal the amount of fluid leaving that section, assuming there are no leaks or additions to the system. This ensures that under steady-state conditions, the mass flow rate at any two points along the flow must be the same, which mathematically is often expressed in the form of the continuity equation.

Understanding this principle is crucial for analyzing fluid systems in hydraulics, as it governs the behavior of fluids in piping systems, channels, and various applications in both engineering and environmental contexts.