What can the Navier Stokes equations be used for?

The Navier–Stokes equations are useful because they describe the physics of many phenomena of scientific and engineering interest. They may be used to model the weather, ocean currents, water flow in a pipe and air flow around a wing.

What will happen if Navier Stokes equation is solved?

You’d be able to perfectly model complex systems such as stellar gases. You’d be able to perfectly describe fluid flow through a pipe, and reduce turbulence such that you get maximum efficiency out of transport of fluids such as oil.

What is the problem with Navier Stokes equation?

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.

Is Navier-Stokes equation linear?

This chapter describes the Navier-Stokes (N-S) equations. The N-S equations form a quasi-linear differential system, and such systems can be studied through linearized equations.

Is the Navier Stokes equation applicable to turbulent flows?

To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier–Stokes equations are solved numerically. Thus, randomness or turbulence can apparently arise as a consequence of the structure of the Navier–Stokes equations.

How can the Navier-Stokes equation be derived?

Derivation of the Navier-Stokes equations Euler equation. Normal force acting on a fluid element. Shear force acting on a fluid element. Weight force acting on a fluid element. Substantial, local and convective acceleration. Viscous stress tensor. Taking into account the viscous normal stress. The Navier-Stokes equation for incompressible fluids.

What are the assumptions of the Navier-Stokes equations?

The stress tensor is a linear function of the strain rate tensor or equivalently the velocity gradient.

Who proved the Navier Stokes equations?

Navier-Stokes equation, in fluid mechanics, a partial differential equation that describes the flow of incompressible fluids. The equation is a generalization of the equation devised by Swiss mathematician Leonhard Euler in the 18th century to describe the flow of incompressible and frictionless fluids.