What does the continuity equation express in the context of fluid flow?

The continuity equation is fundamentally based on the principle of conservation of mass in fluid mechanics. It states that, for an incompressible fluid, the mass flowing into a system must equal the mass flowing out of the system, assuming no mass is added or lost within the system over time. This concept can be expressed mathematically as the product of the fluid's velocity and cross-sectional area being constant along a streamline, which reinforces the idea that if the area decreases, the velocity must increase to maintain mass continuity.

In practical terms, this means that in any finite volume of fluid within a flow system, the rate at which mass enters must equal the rate at which it exits. This is crucial in the design and analysis of drainage systems and stormwater management, as designers must ensure that these systems can handle the expected flow rates without causing backups or overflow. Understanding this equation allows professionals to predict how changes in pipe size or flow conditions can affect overall drainage performance.