量纲理论与量纲分析法的教学方案的探讨

DISCUSSION ON THE TEACHING SCHEME OF DIMENSIONAL THEORY AND DIMENSIONAL ANALYSIS METHOD

本文基于在大学物理教学中加强科学思维与科学方法教育的教学理念,针对目前在物理教学中仍被忽视的量纲分析法,由物理量的量纲和基本单位制等基本概念出发,依次介绍了量纲和谐原理、瑞利分析法及其优缺点、无量纲量的构造及∏定理的基本意义、工程技术中模型与原型之间的相似模拟的理论依据。同时,基于量纲分析理论重要的教育教学价值,作者提出了“完整且有深度的介绍量纲理论”的教学目标,并通过3个典型例题阐述了关于量纲理论与量纲分析的三层次教学方案。

To strengthen the concept of scientific thinking and scientific methods in university physics education,this paper focuses on the topic of dimensional analysis which has long been less involved in university physics education.Beginning with the fundamental concepts of units and dimensions of physical quantities,several key issues about dimensional analysis are discussed in detail,including the theory of dimensional homogeneity,Rayleigh's method of dimensional analysis,construction of dimensionless parameters,and the theoretical basis of similarity simulation in engineering.In addition,based on the significant teaching value of dimensional analysis theory,we put forward the teaching goal of“introducing dimensional analysis in a complete and in-depth manner”in university physics courses,and a three-level teaching approach is further elaborated by three typical examples of dimensional analysis.