When area decreases in a fluid, what happens to the velocity according to the continuity equation?

According to the continuity equation in fluid dynamics, the relationship between the area through which a fluid flows and the velocity of that fluid is described by the principle of conservation of mass. This principle states that for an incompressible fluid, the mass flow rate must remain constant throughout a streamline flow.

When the area decreases within a fluid flow system, such as through a pipe narrowing at one end, the fluid must move faster in order to conserve the same volume of fluid passing through any cross-section per unit time. This increase in velocity compensates for the reduction in area, ensuring that the volume flow rate remains constant.

For instance, if you imagine water flowing through a wider section of a pipe and then narrowing in a subsequent section, the same amount of water must pass through that narrower section in the same amount of time. To achieve this, the velocity of the water must increase as the area decreases, demonstrating the direct relationship between area and velocity as expressed in the continuity equation.