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  2. List of equations in fluid mechanics - Wikipedia

    en.wikipedia.org/wiki/List_of_equations_in_fluid...

    This article summarizes equations in the theory of fluid mechanics. Definitions. Flux F through a surface, dS is the differential vector area element, ...

  3. Derivation of the Navier–Stokes equations - Wikipedia

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

    The Navier–Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum – a continuous substance rather than discrete particles. Another necessary assumption is that all the fields of interest including pressure, flow velocity, density, and temperature are at least weakly differentiable.

  4. Fluid mechanics - Wikipedia

    en.wikipedia.org/wiki/Fluid_mechanics

    Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. [ 1 ] : 3 It has applications in a wide range of disciplines, including mechanical , aerospace , civil , chemical , and biomedical engineering , as well as geophysics , oceanography , meteorology , astrophysics ...

  5. Navier–Stokes equations - Wikipedia

    en.wikipedia.org/wiki/Navier–Stokes_equations

    The Navier–Stokes equations assume that the fluid being studied is a continuum (it is infinitely divisible and not composed of particles such as atoms or molecules), and is not moving at relativistic velocities. At very small scales or under extreme conditions, real fluids made out of discrete molecules will produce results different from the ...

  6. Bernoulli's principle - Wikipedia

    en.wikipedia.org/wiki/Bernoulli's_principle

    If the fluid flow is irrotational, the total pressure is uniform and Bernoulli's principle can be summarized as "total pressure is constant everywhere in the fluid flow". [1]: Equation 3.12 It is reasonable to assume that irrotational flow exists in any situation where a large body of fluid is flowing past a solid body. Examples are aircraft in ...

  7. Hydrostatic equilibrium - Wikipedia

    en.wikipedia.org/wiki/Hydrostatic_equilibrium

    Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where = = = = Then the only non-trivial equation is the -equation, which now reads + = Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.

  8. Kelvin's circulation theorem - Wikipedia

    en.wikipedia.org/wiki/Kelvin's_circulation_theorem

    In fluid mechanics, Kelvin's circulation theorem states: [1] [2] In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. The theorem is named after William Thomson, 1st Baron Kelvin who published it in 1869.

  9. Euler equations (fluid dynamics) - Wikipedia

    en.wikipedia.org/wiki/Euler_equations_(fluid...

    For constant fluid density, the incompressible equations can be written as a quasilinear advection equation for the fluid velocity together with an elliptic Poisson's equation for the pressure. On the other hand, the compressible Euler equations form a quasilinear hyperbolic system of conservation equations .