# Difference between revisions of "Navier-Stokes equations"

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(Created page with 'The Navier-Stokes equation is an equation in fluid mechanics that states: <math>\rho \frac{D \mathbf{V}}{D t} = -\nabla p + \mu \nabla^2 \mathbf{V} + \rho \m…') |
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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> |

== References == | == References == | ||

<references></references> | <references></references> |

## Revision as of 15:36, 15 August 2010

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]}

## References

- ↑ A.J. Smits, "A Physical Introduction to Fluid Mechanics," John Wiley & Sons, ISBN 0-471-25349-9