论连续性方程的推导及几种形式转换的方法

连续性方程是流体力学中的一个重要基本方程,在教学过程中往往侧重于其在工程中的应用而忽视了基本概念和物理意义。本文提出了一种系统性的教学方法,对连续性方程的相关基本概念进行串联整合,将雷诺输运定理应用到不同的流动模型来推导出四种不同形式的连续性方程,并通过演算证明它们可以相互转换,本质上是同一个方程。该教学方法能帮助学生加深对流体动力学基本公式物理意义的理解,构建起研究流体力学的基本思路。

ON THE DERIVATION OF CONTINUITY EQUATION AND SEVERAL FORMS OF TRANSFORMATION

Continuity equation is an important basic equation in fluid mechanics. In the teaching process, it is often focused on the application in engineering, the basic concepts and physical significance are ignored. This paper presents a systematic teaching method, which integrates the basic concepts of continuity equation in series. Reynolds transport theorem is applied to different flow models to derive four different forms of continuity equations to prove that they can be transformed into each other and are essentially the same equation. This teaching method helps students to deepen their understanding of the physical meaning of the basic formulas of fluid dynamics and builds a basic idea for the study of fluid mechanics.