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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:
