#Vector 7 nasa meaning how to#

There are four independent variables in the problem, the x, y, and z spatial coordinates of some domain, and the time t. 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.

This area of study is called Computational Fluid Dynamics or CFD. Recently, high speed computers have been used to solve approximations to the equations using a variety of techniques like finite difference, finite volume, finite element, and spectral methods. In the past, engineers made further approximations and simplifications to the equation set until they had a group of equations that they could solve. But, in practice, these equations are too difficult to solve analytically. The equations are a set of coupled differential equations and could, in theory, be solved for a given flow problem by using methods from calculus.

#Vector 7 nasa meaning how to#

These equations are very complex, yet undergraduate engineering students are taught how to derive them in a process very similar to the derivation that we present on the conservation of momentum web page. The equations are extensions of the Euler Equations and include the effects of viscosity on the flow. The equations were derived independently by G.G. These equations describe how the velocity, pressure, temperature, and density of a moving fluid are related.

On this page we show the three-dimensional unsteady form of the Navier-Stokes Equations. Home > Beginners Guide to Aeronautics > Guide to Rockets Navier-Strokes Equation