Fluid Mechanics: Navier Stokes
The time-derivative of the fluid velocity in the Navier-Stokes equation is the material derivative, defined as:
|
Fluid Mechanics: Navier Stokes
|
| 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: |
| Quantity | Symbol | Object | Units |
| fluid stress | T | 2nd order tensor | N/m2 |
| strain rate | D | 2nd order tensor | 1/s |
| unity tensor | I | 2nd order tensor | 1 |
|
Copyright © efunda.com
|
