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The Reynolds-averaged Navier–Stokes 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]
Fluid statics or hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium [1] and "the pressure in a fluid or exerted by a fluid on an immersed body". [ 2 ] It encompasses the study of the conditions under which fluids are at rest in stable equilibrium as opposed to fluid dynamics , the study of fluids in motion.
Quasistatic approximation(s) refers to different domains and different meanings. In the most common acceptance, quasistatic approximation refers to equations that keep a static form (do not involve time derivatives) even if some quantities are allowed to vary slowly with time.
Scheme showing the relevant variables to the problem for a positive height. The height of the liquid column in the tube is constrained by the hydrostatic pressure and by the surface tension. The following derivation is for a liquid that rises in the tube; for the opposite case when the liquid is below the reference level, the derivation is ...
Fundamentals of Hydraulic Engineering defines hydrostatics as the study of fluids at rest. [1] In a fluid at rest, there exists a force, known as pressure, that acts upon the fluid's surroundings. This pressure, measured in N/m 2, is not constant throughout the body of fluid. Pressure, p, in a given body of fluid, increases with an increase in ...
Arnold–Beltrami–Childress flow – an exact solution of the incompressible Euler equations. Two solutions of the three-dimensional Euler equations with cylindrical symmetry have been presented by Gibbon, Moore and Stuart in 2003. [29] These two solutions have infinite energy; they blow up everywhere in space in finite time.
In continuum mechanics, the Michell solution is a general solution to the elasticity equations in polar coordinates (,) developed by John Henry Michell in 1899. [1] The solution is such that the stress components are in the form of a Fourier series in θ {\displaystyle \theta } .
The primitive equations may be linearized to yield Laplace's tidal equations, an eigenvalue problem from which the analytical solution to the latitudinal structure of the flow may be determined. In general, nearly all forms of the primitive equations relate the five variables u, v, ω, T, W, and their evolution over space and time.