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  2. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_equations

    The NavierStokes equations, even when written explicitly for specific fluids, are rather generic in nature and their proper application to specific problems can be very diverse. This is partly because there is an enormous variety of problems that may be modeled, ranging from as simple as the distribution of static pressure to as complicated ...

  3. Navier–Stokes existence and smoothness - Wikipedia

    en.wikipedia.org/wiki/NavierStokes_existence...

    In mathematics, the NavierStokes equations are a system of nonlinear partial differential equations for abstract vector fields of any size. In physics and engineering, they are a system of equations that model the motion of liquids or non-rarefied gases (in which the mean free path is short enough so that it can be thought of as a continuum mean instead of a collection of particles) using ...

  4. Derivation of the Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Derivation_of_the_Navier...

    The derivation of the NavierStokes equations as well as their application and formulation for different families of fluids, is an important exercise in fluid dynamics with applications in mechanical engineering, physics, chemistry, heat transfer, and electrical engineering.

  5. Computational fluid dynamics - Wikipedia

    en.wikipedia.org/wiki/Computational_fluid_dynamics

    Compressible Navier-Stokes equations (C-NS): Start with the CCL. Assume a Newtonian viscous stress tensor (see Newtonian fluid) and a Fourier heat flux (see heat flux). [44] [45] The C-NS need to be augmented with an EOS and a caloric EOS to have a closed system of equations. Incompressible Navier-Stokes equations (I-NS): Start with the C-NS.

  6. Stokes flow - Wikipedia

    en.wikipedia.org/wiki/Stokes_flow

    The equation of motion for Stokes flow can be obtained by linearizing the steady state NavierStokes equations.The inertial forces are assumed to be negligible in comparison to the viscous forces, and eliminating the inertial terms of the momentum balance in the NavierStokes equations reduces it to the momentum balance in the Stokes equations: [1]

  7. Stokes' law - Wikipedia

    en.wikipedia.org/wiki/Stokes'_law

    In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. [1] It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the NavierStokes equations. [2]

  8. Millennium Prize Problems - Wikipedia

    en.wikipedia.org/wiki/Millennium_Prize_Problems

    However, theoretical understanding of their solutions is incomplete, despite its importance in science and engineering. For the three-dimensional system of equations, and given some initial conditions, mathematicians have not yet proven that smooth solutions always exist. This is called the NavierStokes existence and smoothness problem.

  9. Reynolds-averaged Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Reynolds-averaged_Navier...

    The Reynolds-averaged NavierStokes equations (RANS equations) are time-averaged [a] equations of motion for fluid flow. The idea behind the equations is Reynolds decomposition , whereby an instantaneous quantity is decomposed into its time-averaged and fluctuating quantities, an idea first proposed by Osborne Reynolds . [ 1 ]