量纲理论与量纲分析法的教学方案的探讨
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摘要
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.
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.
引文
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[14]朱如曾.从量纲分析观点看气体物态方程[J].大学物理,2004,23(2):15-16.ZHU R Z.Viewing the equations of state for gases with the viewpoint of dimensional analysis[J].College Physics,2004,23(2):15-16.(in Chinese)
[15]魏环,常锦才,薄惠丰.量纲分析理论在气淬钢渣问题中的运用[J].华北理工大学学报(自然科学版),2016,38(6):14-19.WEI H,CHANG J C,BO H F.Application of dimensional analysis in granulation degree of steel slag by gas quenching[J].Journal of North China University of Science and Technology,(Natural Science Edition),2016,38(6):14-19.(in Chinese)
[16]邢红军.物理教学论[M].北京:北京大学出版社,2015:179-180.
[17]石中英.知识转型与教育改革[M].北京:教育科学出版社,2005:239.
[2]赵凯华.定性与半定量物理学[M].北京:高等教育出版社,1994:63-100.
[3]梁灿彬,曹周键,陈陟陶.量纲分析简介[J].大学物理,2017,36(12):1-5.LIANG C B,CAO Z J,CHEN Z T.Introduction to dimensional analysis[J].College Physics,2017,36(12):1-5.(in Chinese)
[4]谈庆明.量纲分析[M].合肥:中国科学技术大学出版社,2007.
[5]梁灿彬,曹周键,陈陟陶.量纲分析简介(续1)[J].大学物理,2018,37(1):4-10.LIANG C B,CAO Z J,CHEN Z T.Introduction to dimensional analysis(continuation-1)[J].College Physics,2018,37(1):4-10.(in Chinese)
[6]严导淦.量纲分析及其应用[J].物理与工程,2012,22(6):21-26.YAN D G.Dimensional analysis and applidation[J].Physics and Engineering,2012,22(6):21-26.(in Chinese)
[7]RAYLEIGH L.The principle of similitude[J].Nature,1915,95:66-68.
[8]BUCKINGHAM E.On physically similar systems:Illustrations of the use of dimensional equations[J].Physical Review,1914,4(4):345-376.
[9]杨世铭,陶文栓.传热学[M].北京:高等教育出版社,2006:229-242.
[10]王丰.相似理论及其在传热学中的应用[M].北京:高等教育出版社,1990:58-96.
[11]梁灿彬,曹周键,陈陟陶.量纲分析简介(续2)[J].大学物理,2018,37(2):12-17.LIANG C B,CAO Z J,CHEN Z T.Introduction to dimensional analysis(continuation-2)[J].College Physics,2018,37(2):12-17.(in Chinese)
[12]周国全,祁宁,潘玮深.量纲方法与Π定理之应用一例---低阻尼RLC电磁振荡周期的二级修正[J].大学物理,2018,37(9):11-16.ZHOU G Q,QI N,PAN W S.An application example of the dimension method andΠ-theorem[J].College Physics,2018,37(9):11-16.(in Chinese)
[13]胡云.基于量纲分析的建模研究[J].大学物理,2006,25(12):18-22.HU Y.Dimension analysis based modeling research[J].College Physics,2006,25(12):18-22.(in Chinese)
[14]朱如曾.从量纲分析观点看气体物态方程[J].大学物理,2004,23(2):15-16.ZHU R Z.Viewing the equations of state for gases with the viewpoint of dimensional analysis[J].College Physics,2004,23(2):15-16.(in Chinese)
[15]魏环,常锦才,薄惠丰.量纲分析理论在气淬钢渣问题中的运用[J].华北理工大学学报(自然科学版),2016,38(6):14-19.WEI H,CHANG J C,BO H F.Application of dimensional analysis in granulation degree of steel slag by gas quenching[J].Journal of North China University of Science and Technology,(Natural Science Edition),2016,38(6):14-19.(in Chinese)
[16]邢红军.物理教学论[M].北京:北京大学出版社,2015:179-180.
[17]石中英.知识转型与教育改革[M].北京:教育科学出版社,2005:239.