# Equation of continuity

From AMS Glossary

## equation of continuity

(

*Or*continuity equation.) A hydrodynamical equation that expresses the principle of the conservation of mass in a fluid.It equates the increase in mass in a hypothetical fluid volume to the net flow of mass into the volume. The equation of continuity is usually written in either of two forms: or where ρ is the fluid density and where

**u**the velocity vector. Under the quasi-static approximation with pressure as vertical coordinate, the equation takes the form*p*is the pressure,**v**is the horizontal velocity, ω =*Dp*/*Dt*the vertical*p*velocity, and**∇**_{p}the del operator in the isobaric surface.