THE EQUATIONS OF FLUID MECHANICS EXPRESSED IN CURVILINEAR COORDINATES
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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The applied science of fluid mechanics makes use of three basic equations to analyze and predict the state of a fluid in motion. These equations are the equations of motion, energy, and continuity. In most flow problems, these equations cannot be solved, or are very difficult to solve, unless they are expressed in terms of a coordinate system which conforms to the surface of the duct or body which shapes the flow. This report utilizes the methods of tensor analysis to transform the basic equations from their Cartesian forms to expressions in ten orthogonal curvilinear coordinate systems. The derivation process is outlined, and the final results are tabulated for each of the coordinate systems. Although this report assumes a Newtonian fluid model, the viscous stress components are listed separately so that, given the proper expressions for the viscous stress components, the results may also be applied to a non-Newtonian fluid.
- Numerical Mathematics
- Fluid Mechanics