Continuity equation

The continuity equation expresses conservation of mass in a flow: changes in mass within a region balance the mass crossing its boundary.

Mass conservation: A physical principle stating that mass remains constant in an isolated system. The equation translates this broad conservation principle into a balance for flowing matter.
Fluid density: Mass per unit volume of a fluid. Density determines how much mass occupies each part of the flow.
Bernoulli's principle: A relation among pressure, speed, and elevation along an ideal steady streamline. For steady incompressible flow, continuity helps connect changing speed to changing area.
Incompressible Navier–Stokes equations: The fluid momentum equations coupled to a zero-divergence velocity condition. They use a specialized continuity constraint rather than evolving density.
Divergence theorem: A theorem equating the flux of a vector field through a closed surface with the integral of its divergence inside. It converts the integral mass balance into the local differential equation.
Velocity field: A vector field assigning a velocity to each point in space and time. It describes the motion that transports mass through a region.
Venturi effect: The pressure decrease that occurs as a fluid accelerates through a narrowed passage. Continuity predicts acceleration through the constriction that produces the pressure change.
Reynolds transport theorem: A theorem relating the rate of change of an extensive property in a moving system to its control-volume balance. It provides the general moving-control-volume framework from which mass continuity follows.
Material derivative: A derivative measuring how a quantity changes while following a moving fluid parcel. It expresses density change along a fluid parcel in the Lagrangian form of continuity.
Divergence: A measure of the net outward flow of a vector field from an infinitesimal volume. Velocity divergence represents local expansion or contraction in the flow.

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