| Navier-Stokes Equations |
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| The motion of a non-turbulent, Newtonian fluid is governed by the Navier-Stokes equation: |
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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: |
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| 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. |
| 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 |
