kontinuitetsekvation

The continuity equation is a fundamental principle in physics that expresses the conservation of a physical quantity. It states that the rate of change of this quantity within a given volume is equal to the net flux of the quantity into that volume. Essentially, it means that the quantity cannot be created or destroyed, only moved around.

In its most common form, the continuity equation describes the conservation of mass. For an incompressible fluid, this means that the product of the fluid's cross-sectional area and its velocity is constant along a flow path. If the area decreases, the velocity must increase to maintain the same mass flow rate.

The equation can also be applied to other conserved quantities, such as electric charge or probability. For example, in electromagnetism, the continuity equation for electric charge relates the change in charge density within a volume to the electric current flowing out of that volume.

Mathematically, the continuity equation can be expressed in differential or integral form. The differential form typically involves a time derivative of a density and a divergence of a flux. The integral form relates the time rate of change of the total quantity in a volume to the flux across its boundary. Its applications span across fluid dynamics, electromagnetism, quantum mechanics, and beyond, underscoring its broad applicability in describing physical phenomena.