达朗贝尔与斯托克斯佯谬的对比式教学探索  

Teaching application of comparing D′Alembert and Stokes paradox

作　　者：华蕾娜 王若愚 HUA Lei-na;WANG Ruo-yu(State Key Laboratory of Mesoscience and Engineering,Institute of Process Engineering,Chinese Academy of Sciences,Beijing.100190,China;School of Chemical Engineering,University of Chinese Academy of Sciences,Beijing 101408,China)

机构地区：[1]中国科学院过程工程研究所介科学与工程全国重点实验室,北京100190 [2]中国科学院大学化学工程学院,北京101408

出　　处：《大学物理》2025年第1期17-22,共6页College Physics

基　　金：中国科学院大学2023年管理支撑创新能力提升专项资助.

摘　　要：达朗贝尔佯谬和斯托克斯佯谬是流体力学经典内容之一,也是实际教学中较易混淆的知识点.本文以无界均匀流场中圆球绕流为例,以对比的方式给出有势流动和低雷诺数流动的核心假设、方程的导出、流场速度和压强分布的解析解等,并以云图量化两种流动的区别,厘清问题的假设如何导致了达朗贝尔佯谬和斯托克斯佯谬的产生.将生动的佯谬与繁多的公式推导紧密结合,有助于学生激发追本溯源的好奇心、进而深化对理论及其局限性的理解.D’Alembert paradox and Stokes paradox are the classical contents in fluid mechanics,which are also the confusing parts in teaching.Using a fixed sphere in a uniform flow field as an example,we present the key assumptions,governing equations,solutions of flow velocity and pressure for potential flow and low Reynolds number flow,respectively.The contours are plotted to compare the hydrodynamics of flows.The qualitative and quantitative analysis clarifies the origins of D’Alembert paradox and Stokes paradox.The combination of paradox and formula derivation could stimulate students’interesting and further improve the understanding of theory.

关 键 词：佯谬 有势流动 低雷诺数流动 教学应用 

分 类 号：O351.2[理学—流体力学]