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The Navier–Stokes equations (/ n æ v ˈ j eɪ s t oʊ k s / nav-YAY STOHKS) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades ...
This equation is called the mass continuity equation, or simply the continuity equation. This equation generally accompanies the Navier–Stokes equation. In the case of an incompressible fluid, Dρ / Dt = 0 (the density following the path of a fluid element is constant) and the equation reduces to:
The continuity equation is an extension of conservation of mass to fluid flow. [ citation needed ] Consider a fluid flowing through a fixed volume tank having one inlet and one outlet. If the flow is steady (no accumulation of fluid within the tank), then the rate of fluid flow at entry must be equal to the rate of fluid flow at the exit for ...
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]
Kerr and Dold showed that such disturbances exist with finite amplitude, thus making the solution an exact to Navier–Stokes equations. Introducing a stream function ψ {\displaystyle \psi } for the disturbance velocity components, the equations for disturbances in vorticity-streamfunction formulation can be shown to reduce to
Chapman–Enskog theory provides a framework in which equations of hydrodynamics for a gas can be derived from the Boltzmann equation.The technique justifies the otherwise phenomenological constitutive relations appearing in hydrodynamical descriptions such as the Navier–Stokes equations.
Download as PDF; Printable version; ... move to sidebar hide. From Wikipedia, the free encyclopedia. Redirect page. ... Navier–Stokes equations; Retrieved from ...
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 ...
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