Can anyone explain to me the navier-stokes equation for fluid ?

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Can anyone explain to me the navier-stokes equation for fluid ?

In: Engineering

There’s a few properties of fluids that explain how they move. One is called viscosity, which is a measure of how much a fluid resists being sheared (you can imagine something like honey or molasses as a high viscosity fluid – it likes to stick together and doesn’t pour very quickly.) Another property is momentum – a moving fluid has momentum based on its density and the speed it’s moving at.

We can apply Newton’s laws to describe the motion of fluids. The problem is that viscosity and momentum makes it a lot harder to apply Newton’s laws to fluids. The Navier-Stokes equations are a series of equations that try to solve the problem of conservation of momentum in a moving fluid. There are 5 equations – a time dependent conservation of mass equation, a time dependent conservation of energy equation, and three time dependent conservation of momentum equations (for momentum in the x, y, and z directions.)

Together if you can solve these equations for every set of x,y,z coordinates within a fluid, you can completely describe how it will move, where it will eddy, etc. Unfortunately the equations are very complicated, they’re partial differential equations, and you need to solve them at very very small intervals. So that’s why we can’t solve them by hand, and that’s why NASA uses super computers to run fluid simulations.