For example, the continuity equation for electric charge states that the amount of electric charge in any volume of space can only change by the amount of electric current flowing into or out of that volume through its boundaries.Ĭontinuity equations more generally can include 'source' and 'sink' terms, which allow them to describe quantities that are often but not always conserved, such as the density of a molecular species which can be created or destroyed by chemical reactions. A continuity equation is the mathematical way to express this kind of statement. A stronger statement is that energy is locally conserved: energy can neither be created nor destroyed, nor can it ' teleport' from one place to another-it can only move by a continuous flow. This statement does not rule out the possibility that a quantity of energy could disappear from one point while simultaneously appearing at another point. For example, a weak version of the law of conservation of energy states that energy can neither be created nor destroyed-i.e., the total amount of energy in the universe is fixed. Since mass, energy, momentum, electric charge and other natural quantities are conserved under their respective appropriate conditions, a variety of physical phenomena may be described using continuity equations.Ĭontinuity equations are a stronger, local form of conservation laws. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. A continuity equation or transport equation is an equation that describes the transport of some quantity.

Flux integral through a pipe