What does the Navier-Stokes equation represent?
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The Navier-Stokes equations represent the conservation of momentum, while the continuity equation represents the conservation of mass.
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.
Has anyone solved the 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.
What are the three 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).
The Navier-Stokes equation is difficult to solve because it is nonlinear. This word is thrown around quite a bit, but here it means something specific. You can build up a complicated solution to a linear equation by adding up many simple solutions.
The Navier-Stokes equations consists of a time-dependent continuity equation for conservation of mass, three time-dependent conservation of momentum equations and a time-dependent conservation of energy equation.
What is Navier Stokes 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 is the problem with the Navier Stokes equation?
There are both physical and mathematical reasons why solving the Navier-Stokes equations is hard enough to deserve a million dollars. Physically, the problem with fluid flows is that they can behave chaotically and turbulently.