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The Navier-Stokes equation is an equation in [[Fluid mechanics|fluid mechanics]] that states:

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>

<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 ==

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<references></references>

[[Category:Mathematics]]

[[Category:Mathematics]]