Continuity Equation for Incompressible Fluid Flow

The continuity equation for incompressible fluid flow is derived from the principle of conservation of mass. The equation asserts that, in a steady-state flow system, the mass flow rate must remain constant from one cross-section to another. Mathematically, this is reflected in the equation V2 = V1 * (A1 / A2), where V1 and V2 are the fluid velocities at two different cross-sections of a pipeline, and A1 and A2 are the respective areas of these cross-sections. This equation is based on the assumption of incompressibility, meaning the density of the fluid is constant and does not change with pressure or temperature.

In practical applications, the continuity equation allows engineers and scientists to calculate flow rates and velocities of fluids in pipes and channels. It's imperative in designing hydraulic systems, determining pump requirements, and analyzing fluid behavior in various engineering scenarios.