Navier-Stokes Equations

The Navier-Stokes equations are the fundamental partial differentials equations used to describe incompressible fluid flows. These equations describe incompressible fluid flow and are essential in computational fluid dynamics.

Navier-Stokes Equations

The Navier-Stokes equations are the fundamental partial differential equations used to describe incompressible fluid flows.

Overview

A theoretical introduction to The Navier-Stokes Equations. The Navier-Stokes Equations are the fundamental partial differentials equations describing incompressible fluid flow.

References

Wolfram MathWorld - Navier-Stokes Equations

Calculator

Inputs

Velocity (X-component) (m/s)

Velocity (Y-component) (m/s)

Pressure (Pa)

Dynamic Viscosity (Pa·s)

Fluid Density (kg/m³)

Results

Kinematic Viscosity-- m²/s

Reynolds Number (characteristic)--

Parameter	Symbol	Unit	Description
Velocity	u, v, w	m/s	Flow velocity components in x, y, z directions
Pressure	p	Pa	Fluid pressure
Density	ρ	kg/m³	Fluid mass density
Dynamic Viscosity	μ	Pa·s	Measure of fluid resistance to shear stress
Kinematic Viscosity	ν	m²/s	Ratio of dynamic viscosity to density
External Force	f	N/m³	Body forces per unit volume