

NavierStokes Equations
Name: Unknown
Status: N/A
Age: N/A
Location: N/A
Country: N/A
Date: Around 1993
Question:
NavierStokes equations I need to know what these equations are
and some references so that my student team can understand them. We are going
to the Cornell Super computing Contest and the FIDAP software package uses
these equations. An understanding will help us better pose and solve our
problem on wing design for paper airplanes.
Replies:
The NavierStokes equation is a standard equation that describes
the flow of continuum matter in fluid form  that can be a liquid like water,
or a gas like the air. The equation describes the change with time of the
density and velocity of the fluid. From the density, (assuming constant
temperature) you should be able to get pressure, which is needed for wing
design. The equation involves derivatives with respect to space and time of
this velocity and density, and the important thing that you need to take
account of is the boundary between the air and the wing  these boundary
conditions (and the plane's speed relative to the overall air speed) are what
determine the solution. I do not know the name of any specific text, but an
advanced aeronautical engineering text should give you more than you need.
Look in the library under aeronautics, fluid dynamics, and maybe airplane
design, or wing design.
A. Smith
Any good fluid dynamics or meteorology text will have an
explanation of the NS equations. The exact form changes with coordinate
systems and mathematical are vector notation, but I think the general idea is
that the total rate of change of the system = the local rate of change with
time + the rate at which the substance is transported by your location. So
the temperature change at your location has two components, the local
derivative as say the sun heats your air, and the advection term as hotter or
cooler air is moved past your location by the wind.
Mark Fernau
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Update: June 2012

