kontinuaalsusvõrrandiga

The continuity equation is a fundamental principle in physics and engineering that expresses the conservation of a conserved quantity. It states that the rate of change of the conserved quantity within a given region is equal to the net flux of that quantity into the region. This principle applies to various physical phenomena, including mass, energy, momentum, electric charge, and probability.

Mathematically, the continuity equation is often expressed in differential form as ∂ρ/∂t + ∇⋅J = 0, where ρ represents the density of the conserved quantity, t is time, and J is the flux of the conserved quantity. The term ∂ρ/∂t describes the rate of change of density over time, while ∇⋅J represents the divergence of the flux, indicating the net flow out of a small volume. In simpler terms, if the density of a quantity within a region is decreasing, it must be flowing out of that region.

In fluid dynamics, the continuity equation for an incompressible fluid simplifies to ∇⋅v = 0, meaning the divergence of the velocity field is zero. This implies that the volume of the fluid is conserved. For compressible fluids, the mass continuity equation is used, which accounts for changes in density. The continuity equation is a cornerstone for analyzing flows, transport phenomena, and many other physical processes.