##  [Navier–Stokes Equations](/navier-stokes-equations-1) 

  ##  [Navier–Stokes Equations](https://engineering.quantumdictionary.io/navier-stokes-equations-2) 

  

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**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A system of coupled nonlinear partial differential equations expressing conservation of mass (continuity) and linear momentum for a viscous, Newtonian continuum: ρ(∂u/∂t + u·∇u) = −∇p + μ∇²u + ρf together with ∇·u = 0 for incompressible flow, where u is velocity, ρ density, p pressure, μ dynamic viscosity and f body force per unit mass.