How is Navier-Stokes equation derived?
They arise from the application of Newton’s second law in combination with a fluid stress (due to viscosity) and a pressure term. The Navier-Stokes equations can be derived from the basic conservation and continuity equations applied to properties of fluids.
What assumption is used to derive the Navier-Stokes equations from the general equations of motion?
The Navier–Stokes equations are based on the assumption that the fluid, at the scale of interest, is a continuum, in other words is not made up of discrete particles but rather a continuous substance.
What is convective term in Navier-Stokes equation?
The terms on the left hand side of the momentum equations are called the convection terms of the equations. Convection is a physical process that occurs in a flow of gas in which some property is transported by the ordered motion of the flow.
When were the Navier-Stokes equations developed?
1822
The Navier-Stokes equations, developed by Claude-Louis Navier and George Gabriel Stokes in 1822, are equations which can be used to determine the velocity vector field that applies to a fluid, given some initial conditions.
What are the limitations of the Navier-Stokes equation?
The Navier-Stokes equations can technically apply to problems involving all of those variables, both compressible and incompressible. The two most important limitations on the Navier-Stokes equations is that they only apply to (a) fluids that can adequately be modeled by a continuum and (b) Newtonian fluids.
Which forces considered in Navier-Stokes equation?
There are three kinds of forces important to fluid mechanics: gravity (body force), pressure forces, and viscous forces (due to friction). Gravity force, Body forces act on the entire element, rather than merely at its surfaces.
What forces are included in Navier-Stokes equation?
Who proved Navier-Stokes equation?
John Forbes Nash Jr. in 1962 proved the existence of unique regular solutions in local time to the Navier–Stokes equation. Terence Tao in 2016 published a finite time blowup result for an averaged version of the 3-dimensional Navier–Stokes equation.
Is Navier-Stokes proven?
In particular, solutions of the Navier–Stokes equations often include turbulence, which remains one of the greatest unsolved problems in physics, despite its immense importance in science and engineering. Even more basic (and seemingly intuitive) properties of the solutions to Navier–Stokes have never been proven.
How can the Navier-Stokes equation be derived?
All non-relativistic balance equations, such as the Navier-Stokes equations, can be derived by beginning with the Cauchy equations and specifying the stress tensor through a constitutive relation. By expressing the deviatoric (shear) stress tensor in terms of viscosity and the fluid velocity gradient, and assuming constant viscosity, the
Who proved the Navier Stokes equations?
John Forbes Nash Jr. in 1962 proved the existence of unique regular solutions in local time to the Navier-Stokes equation. Terence Tao in 2016 published a finite time blowup result for an averaged version of the 3-dimensional Navier-Stokes equation.
What is the body force in the Navier Stokes equations?
The incompressible Navier Stokes equations are: ρ (∂ v i ∂ t + v j ∂ v i ∂ x j) = − ∂ p ∂ x i + μ ∂ 2 u i ∂ x j ∂ x j + f i for i = 1, 2, 3 Reading around I have gathered that the force f i is a body force which can be that due to gravity, or some other force on fluid due to the presence of a body.