Difference between revisions of "Navier-Stokes equations"
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| − | The Navier-Stokes equation is an equation in [[ | + | The Navier-Stokes equation is an equation in [[fluid mechanics]] that states: |
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<math>\rho \frac{D \mathbf{V}}{D t} = -\nabla p + \mu \nabla^2 \mathbf{V} + \rho \mathbf{g}</math> | <math>\rho \frac{D \mathbf{V}}{D t} = -\nabla p + \mu \nabla^2 \mathbf{V} + \rho \mathbf{g}</math> | ||
| − | where <math>\nabla p</math> is the pressure difference (expressed as the partial derivative of pressure in each dimension), <math>\frac{D \mathbf{V}}{D t}</math> is the total derivative of velocity, <math>\mu</math> is the kinematic viscosity of the fluid, <math>\rho</math> is the density of the fluid, and <math>\mathbf{g}</math> is the gravitational acceleration. <ref>A.J. Smits, "A Physical Introduction to Fluid Mechanics," John Wiley & Sons, ISBN 0-471-25349-9</ref> | + | where <math>\nabla p</math> is the pressure difference (expressed as the partial derivative of pressure in each dimension), <math>\frac{D \mathbf{V}}{D t}</math> is the total derivative of velocity, <math>\mu \,</math> is the kinematic viscosity of the fluid, <math>\rho \,</math> is the density of the fluid, and <math>\mathbf{g}</math> is the gravitational acceleration.<ref>A.J. Smits, "A Physical Introduction to Fluid Mechanics," John Wiley & Sons, ISBN 0-471-25349-9</ref> |
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| + | == In Incompressible flow == | ||
| + | <math>\boldsymbol \tau = \mu (\nabla\mathbf{u} + ( \nabla\mathbf{u} )^\mathrm{T})</math> | ||
== References == | == References == | ||
<references></references> | <references></references> | ||
| + | [[Category:Mathematics]] | ||
Latest revision as of 16:30, July 13, 2016
The Navier-Stokes equation is an equation in fluid mechanics that states:
where 
is the pressure difference (expressed as the partial derivative of pressure in each dimension), 
is the total derivative of velocity, 
is the kinematic viscosity of the fluid, 
is the density of the fluid, and 
is the gravitational acceleration.[1]
In Incompressible flow
References
- ↑ A.J. Smits, "A Physical Introduction to Fluid Mechanics," John Wiley & Sons, ISBN 0-471-25349-9
