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Navier-Stokes Equations
The motion of a non-turbulent, Newtonian fluid is governed by the Navier-Stokes equation:
The above equation can also be used to model turbulent flow, where the fluid parameters are interpreted as time-averaged values.

The time-derivative of the fluid velocity in the Navier-Stokes equation is the material derivative, defined as:

The material derivative is distinct from a normal derivative because it includes a convection term, a very important term in fluid mechanics. This unique derivative will be denoted by a "dot" placed above the variable it operates on.
Navier-Stokes Background
On the most basic level, laminar (or time-averaged turbulent) fluid behavior is described by a set of fundamental equations. These equations are:
The Navier-Stokes equation is obtained by combining the fluid kinematics and constitutive relation into the fluid equation of motion, and eliminating the parameters D and T. These terms are defined below:
QuantitySymbolObjectUnits
fluid stressT2nd order tensorN/m2
strain rateD2nd order tensor1/s
unity tensorI2nd order tensor1
Glossary
3D Scanners

A white paper to assist in the evaluation of 3D scanning hardware solutions.

Negotiate Your Salary

Learn the best principles to negotiate the salary you deserve!

Essentials of Manufacturing

Information, coverage of important developments and expert commentary in manufacturing.

CNC Machining Design Guide

Optimize your designs, reduce machining time, and lower your costs.