Continuity Equation

The continuity equation derives from the principle of mass conservation, stating that the mass of fluid entering and leaving a system remains constant.

For incompressible fluids, the product of flow area and velocity remains consistent throughout the flow path, adjusting to changes in cross-sections.

As the cross-sectional area decreases, the fluid velocity increases to maintain a constant flow rate.

This relationship is crucial for analyzing systems such as water pipelines, stormwater management, and open channels, ensuring stability and efficiency in various fluid flow applications.

In water supply systems, the continuity equation helps maintain steady distribution by predicting velocity changes when pipes narrow, which is essential for avoiding pressure drops.

It helps design detention basins for stormwater management. When runoff enters the basin during a storm, the outflow rate must match the inflow rate, adjusted to prevent flooding downstream.

For open channels like rivers or canals, the continuity equation helps understand how variations in width or depth affect water levels and flow speeds. This understanding is vital for designing effective flood control and navigation systems.