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Date: Around 1993


Question:
Navier-Stokes 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 Navier-Stokes 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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