What does the fluids continuity equation express?

The fluids continuity equation expresses the principle of mass flow rate conservation in fluids, which is a fundamental concept in fluid dynamics. This principle states that for an incompressible fluid flowing through a closed system, the mass flow rate must remain constant from one cross-section of the system to another. Essentially, it indicates that the amount of mass entering a particular volume must equal the amount of mass exiting that volume if the fluid density remains unchanged.

Mathematically, the continuity equation can be expressed as A1V1 = A2V2, where A represents the cross-sectional area and V represents the fluid velocity. This relationship shows how changes in area affect fluid velocity to maintain mass conservation.

Understanding this principle is essential for analyzing fluid systems in engineering applications, as it helps in the design and optimization of various fluid transport systems, such as pipelines and ducts.