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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 ...
The cross differentiated Navier–Stokes equation becomes two 0 = 0 equations and one meaningful equation. The remaining component ψ 3 = ψ is called the stream function. The equation for ψ can simplify since a variety of quantities will now equal zero, for example:
Navier–Stokes equation and the continuity equation [ edit ] In order to analytically find the stability of fluid flows, it is useful to note that hydrodynamic stability has a lot in common with stability in other fields, such as magnetohydrodynamics , plasma physics and elasticity ; although the physics is different in each case, the ...
The Navier–Stokes equations govern the velocity and pressure of a fluid flow. In a turbulent flow, each of these quantities may be decomposed into a mean part and a fluctuating part. Averaging the equations gives the Reynolds-averaged Navier–Stokes (RANS) equations, which govern the mean flow.
In computational fluid dynamics (CFD), the SIMPLE algorithm is a widely used numerical procedure to solve the Navier–Stokes equations. SIMPLE is an acronym for Semi-Implicit Method for Pressure Linked Equations. The SIMPLE algorithm was developed by Prof. Brian Spalding and his student Suhas Patankar at Imperial College London in the early ...
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]
Many regular fluid dynamics equations are used in astrophysical fluid dynamics. Some of these equations are: [2] Continuity equations; The Navier–Stokes equations; Euler's equations; Conservation of mass. The continuity equation is an extension of conservation of mass to fluid flow.
From the equation it is shown that for a flow with a large Reynolds Number there will be a correspondingly small convective boundary layer compared to the vessel’s characteristic length. [5] By knowing the Reynolds and Womersley numbers for a given flow it is possible to calculate both the transient and the convective boundary layer ...