Equation of continuity

From Glossary of Meteorology

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:
where ρ is the fluid density and u the velocity vector. Under the quasi-static approximation with pressure as vertical coordinate, the equation takes the form
where 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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.