MathLiveNavier–Stokes equations
These equations describe how a viscous fluid moves, balancing acceleration against advection, viscous diffusion and a kinematic pressure term, together with incompressibility. They are used throughout fluid dynamics to model flows in pipes, rivers, aircraft and weather.
\begin{aligned}\frac{\partial \vec u}{\partial t}+\vec u\cdot\nabla\vec u-\nu\nabla^2\vec u&=-\nabla h\\\nabla\cdot\vec u&=0\end{aligned}What the symbols mean
| flow velocity vector (m/s) | |
| time (s) | |
| kinematic viscosity (m^2/s) | |
| kinematic pressure p/rho, pressure divided by density (m^2/s^2) | |
| vector gradient operator | |
| vector Laplacian operator | |
| divergence operator |
About this formula
- FieldPhysics
- TopicFluid dynamics
- LevelAdvanced
- Also calledNavier-Stokes equations, Navier-Stokes equation, incompressible fluid flow equations, viscous fluid motion equations, fluid momentum equation, incompressible Navier-Stokes
- SourceWikidata Q201321
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