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  2. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Navier–Stokes_equations

    The numerical solution of the Navier–Stokes equations for turbulent flow is extremely difficult, and due to the significantly different mixing-length scales that are involved in turbulent flow, the stable solution of this requires such a fine mesh resolution that the computational time becomes significantly infeasible for calculation or ...

  3. Stokes flow - Wikipedia

    en.wikipedia.org/wiki/Stokes_flow

    The equation of motion for Stokes flow can be obtained by linearizing the steady state Navier–Stokes 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 Navier–Stokes equations reduces it to the momentum balance in the Stokes equations: [1]

  4. Stokes problem - Wikipedia

    en.wikipedia.org/wiki/Stokes_problem

    This is considered one of the simplest unsteady problems that has an exact solution for the Navier–Stokes equations. [1] [2] In turbulent flow, this is still named a Stokes boundary layer, but now one has to rely on experiments, numerical simulations or approximate methods in order to obtain useful information on the flow.

  5. Laminar flow - Wikipedia

    en.wikipedia.org/wiki/Laminar_flow

    A laminar flow reactor (LFR) is a reactor that uses laminar flow to study chemical reactions and process mechanisms. A laminar flow design for animal husbandry of rats for disease management was developed by Beall et al. 1971 and became a standard around the world [9] including in the then-Eastern Bloc. [10]

  6. Stokes' law - Wikipedia

    en.wikipedia.org/wiki/Stokes'_law

    The Stokeslet is the Green's function of the Stokes-Flow-Equations. The conservative term is equal to the dipole gradient field. The formula of vorticity is analogous to the Biot–Savart law in electromagnetism. Alternatively, in a more compact way, one can formulate the velocity field as follows:

  7. Reynolds number - Wikipedia

    en.wikipedia.org/wiki/Reynolds_number

    For flow in a pipe of diameter D, experimental observations show that for "fully developed" flow, [n 2] laminar flow occurs when Re D < 2300 and turbulent flow occurs when Re D > 2900. [13] [14] At the lower end of this range, a continuous turbulent-flow will form, but only at a very long distance from the inlet of the pipe. The flow in between ...

  8. Reynolds stress - Wikipedia

    en.wikipedia.org/wiki/Reynolds_Stress

    One splits the Euler equations (fluid dynamics) or the Navier-Stokes equations into an average and a fluctuating part. One finds that upon averaging the fluid equations, a stress on the right hand side appears of the form ρ u i ′ u j ′ ¯ {\displaystyle \rho {\overline {u'_{i}u'_{j}}}} .

  9. Navier–Stokes existence and smoothness - Wikipedia

    en.wikipedia.org/wiki/Navier–Stokes_existence...

    In mathematics, the Navier–Stokes 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 ...