The continuity equation is a fundamental principle in fluid dynamics that expresses the conservation of mass in a fluid flow system. It states that the mass flow rate of a fluid must remain constant from one cross-section of a pipe to another, assuming steady flow and incompressibility of the fluid.
A stream function is a special tool that helps us understand how water or air moves around. It shows us where the flow goes without having to worry about how fast it moves or changes direction.
Incompressible flow refers to a fluid flow in which the fluid density remains constant throughout. This assumption simplifies the analysis of fluid dynamics, particularly for liquids, and is often applied when the flow speed is much lower than the speed of sound in the fluid.
Vector calculus is a branch of mathematics that deals with vector fields and differentiates and integrates vector functions, primarily in two or three dimensions. It is essential for understanding physical phenomena in engineering and physics, such as fluid dynamics and electromagnetism, where quantities have both magnitude and direction.