Navier-Stokes equations

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The Navier-Stokes equation is an equation in fluid mechanics that states:

\rho \frac{D \mathbf{V}}{D t} = -\nabla p + \mu \nabla^2 \mathbf{V} + \rho \mathbf{g}

where \nabla p is the pressure difference (expressed as the partial derivative of pressure in each dimension), \frac{D \mathbf{V}}{D t} is the total derivative of velocity, \mu \, is the kinematic viscosity of the fluid, \rho \, is the density of the fluid, and \mathbf{g} is the gravitational acceleration. [1]


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