Difference between revisions of "Navier-Stokes equations"
Jump to navigation
Jump to search
(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…') |
|||
| Line 3: | Line 3: | ||
<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 20:36, August 15, 2010
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 \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. [1]
References
- ↑ A.J. Smits, "A Physical Introduction to Fluid Mechanics," John Wiley & Sons, ISBN 0-471-25349-9