Abstract

The use of dimensional analysis to solve some problems of hydrodynamics associated with convective transport of a liquid medium is presented. In particular, this forms the basis of deriving equations of continuity, thermal conduction, diffusion, and motion of ideal (Euler) and viscous fluids (Navier–Stokes), with some complements from the field of electrohydrodynamics. In addition, the problem of the presence of two forces of viscous friction is solved, and the problems of sliding and deformation (in compression–extension in a compressible fluid). Formulas for these forces are derived.

中文翻译：

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尺寸法推导水动力方程和电流体动力学方程

摘要

提出了使用尺寸分析来解决与液体介质对流传输相关的流体动力学问题的方法。特别是，这形成了推导连续性，热传导，扩散和理想流体（Euler）和粘性流体（Navier–Stokes）方程的基础，并从电液动力学领域得到了一些补充。此外，还解决了存在两个粘滞摩擦力的问题，以及滑动和变形（在可压缩流体的压缩-扩展中）的问题。推导了这些力的公式。