##  [Continuity Equation](/index.php/continuity-equation) 

  ##  [Continuity Equation](https://natural.quantumdictionary.io/continuity-equation-0) 

  

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**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A local balance relation expressing how the time rate of change of a field's density equals the negative divergence of its flux plus any local sources or sinks.

 

 

 

 

 





 

 



 ##  [Continuity Equation](https://engineering.quantumdictionary.io/continuity-equation-1) 

  

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**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The Continuity Equation is the local mathematical statement of mass conservation for a continuum fluid: ∂ρ/∂t + ∇·(ρ v) = 0, where ρ is density and v the velocity field. Under the incompressible, constant‑density assumption it reduces to ∇·v = 0; for steady one‑dimensional flow it implies ρ A V = constant (mass flow rate conserved).