流体運動の基本方程式
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概要
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N.S. equations are unsuitable for the investigation of the fluid motion in a boundary layer of a body, owing to the fact that the velocity of deformation varies widely. So the author has tried to get the fundamental equations of fluid motion; the equation of continuity, the equations of motion and the equation of energy in a most general form so far as we consider the fluid as a continuous medium, ignoring its atomic structure. The relation between the stress and the velocity of deformation is generalized, assuming that the proportional constant between them is a function of the time and the space coordinates. The author considers the breadth of boundary layer as an important characteristic parameter of fluid motion. Expanding functions in fundamental equations of fluid motion into series of the breadth of boundary layer, the author has obtained a system of differential equations which can be solved easily. Neglecting terms of the order of the square of the breadth of boundary layer, the author obtained approximate solutions which has sufficient accuracy for practical purpose. The fundamental equations of fluid motion in an orthogonal curvelenear coordinates are derived for convenience to discuss problems of the flow about a body of any shape. The velocity distribution in a boundary layer varies with Mach number. So the range of application of Reynolds' law of similarity must be limited by Mach number. The reason is presumably that Reynolds' law can not be applied to bodies of great scale difference.
- 明治大学の論文
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