MyOOPS開放式課程

2.25  高等流體力學    2002秋季

2.25 Advanced Fluid Mechanics, Fall 2002

 周 課程單元 1 連續體觀點和運動方程 Continuum Viewpoint and the Equation of Motion (PDF) 2 靜態流體Static Fluids (PDF) 3 品質守恆Mass Conservation (PDF) 4 理想流體—微分方法；歐拉方程， 伯努利積分和流線彎曲效果，伯努 利積分的一般形式 Inviscid Flow - Differential Approach: Euler's Equation, Bernoulli's Integral and the Effects of Streamline Curvature, the General Form of Bernoulli's Integral (PDF) 5 控制體理論（積分方法）；線性動 量理論，角動量理論以及熱力學第 一、第二定律 Control Volume Theorems (Integral Approach): Linear Momentum Theorem, Angular Momentum Theorem, and First and Second Laws of Thermodynamics (PDF) 6 納維－斯托克斯方程和黏性流體 Navier-Stokes Equation and Viscous Flow (PDF) 7 相似性和維度分析 Similarity and Dimensional Analysis (PDF) 8 邊界層，分離帶和拉伸、拖曳效果 Boundary Layers, Separation and the Effect on Drag and Lift (PDF) 9 渦量和環流 Vorticity and Circulation (PDF) 10 潛流，拉伸、拖曳和插入結果 Potential Flows: Lift, Drag, and Thrust Production (PDF) 11 表面張力和它對流體的效果 Surface Tension and its Effect on Flows (PDF) 12 紊流介紹 Introduction to Turbulence (PDF)

·微團運動的基本定律，物質體和控制體(PDF) 。

·關於選擇和使用控制體：在簡單問題中運用積分品質守恆定理的六種方法 (PDF) 。

·黏性流體的運動方程(PDF - 2.3 MB)。

1.連續體概念和運動方程The Continuum Viewpoint and the Equation of Motion

2.靜態流體Static Fluids

3. 流體介質中的品質守恆Mass Conservation in Flowing Media

4.理想流體ⅠInviscid Flow I

5.控制體理論Control Volume Theorems

6.黏性流體Viscous Flows

7.相似性和維度分析Similarity and Dimensional Analysis

8.邊界層，分離層和拉伸、拖曳效果Boundary Layers, Separation, and the Effect on Drag and Lift

9.渦量和環流Vorticity and Circulation

10.潛流、拉伸和拖曳Potential Flow, Lift, and Drag

11.表面張力Surface Tension

12.紊流建模裏的基本概念Basic Concepts in Turbulence Modeling

 2.25 Advanced Fluid Mechanics, Fall 2002
 Ocean Waves. (Image courtesy of ICM.)
 課程重點 This course features an entire unit of interactive problem sets, as well as lecture outlines and a selection of useful readings. 課程描述 Survey of principal concepts and methods of fluid dynamics. Mass conservation, momentum, and energy equations for continua. Navier-Stokes equation for viscous flows. Similarity and dimensional analysis. Lubrication theory. Boundary layers and separation. Circulation and vorticity theorems. Potential flow. Introduction to turbulence. Lift and drag. Surface tension and surface tension driven flows.
 師資 講師： Prof. Ain Sonin 上課時數 教師授課： 每週2節 每節1.5小時 Tutorials: 每週3節 每節1小時 程度 研究所
 教學大綱
 The syllabus for this course indicates the assignments, exams, and policies for the course. Topics Covered Continuum Viewpoint and the Equation of Motion Static Fluids Mass Conservation Inviscid Flow - Differential Approach: Euler's Equation, Bernoulli's Integral and the Effects of Streamline Curvature, the General Form of Bernoulli's Integral Control Volume Theorems (Integral Approach): Linear Momentum Theorem, Angular Momentum Theorem, and First and Second Laws of Thermodynamics Navier-Stokes Equation and Viscous Flow Similarity and Dimensional Analysis Boundary Layers, Separation and the Effect on Drag and Lift Vorticity and Circulation Potential Flows: Lift, Drag, and Thrust Production Surface Tension and its Effect on Flows Introduction to Turbulence Homework Problems and Tutorial Sessions Homework problems from Shapiro and Sonin's Advanced Fluid Mechanics Problems are indicated in the course outline for each topic. The homework problems are not to be turned in. Instead, they will be discussed in the tutorial sessions. Three tutorials are scheduled per week, but the idea is that each student should come to one session each week, usually the same one. Three sessions are scheduled, partly to accommodate a variety of student schedules and partly to reduce the class size and allow for a more informal atmosphere for discussion. The main purpose of this course is not so much to feed the students with "advanced" material (the topics covered do not in fact appear terribly advanced) as to help students develop a mastery of the underlying principles and the ability to solve, quickly and efficiently, a variety of real fluid mechanics problems from first principles. The lectures present and illustrate the fundamental laws and the methods and modeling approximations that form the basis of fluid mechanics. The problems and tutorials help the students gain a mastery of the material and to develop, by practice and trial and error, the mindset of an effective problem solver in fluid mechanics. Both the assigned problems and the tutorials are entirely voluntary. No problem sets are collected, nor is roll call taken, except perhaps to help the instructors remember the students' names. However, based on repeated experience over many years, you may take our word that your chances of doing well in this course are minimal if you do not independently do at least the assigned problems before the tutorials, and use the tutorials to repair weaknesses and develop new insights. We are ready to help you in every way to master the course material. There is, however, a profound difference between being taught and learning. Examinations and Grading There will be two one-hour quizzes during the term, announced well in advance. In order to minimize time pressures, we prefer to give the (nominally) one-hour quizzes in the evening. There will be a three-hour final exam. Quizzes and the exam will permit a limited number of pages of open notes (and a calculator and a book of mathematical formulas and tables). No other books will be allowed. The quizzes and the exam will not present you with routine problems, but will probe for mastery of the underlying material and for skill in modeling problems in the simplest possible realistic terms. Grading will be based on equal weight between the two quizzes and the final exam. You can gain extra credit by turning in, at the conclusion of the final exam, a notebook in which you have reworked and amplified your lecture notes in cohesive, clearly reasoned form. This is not obligatory, and that your grade will not suffer if you do not do it: grades will be assigned before the notebooks are examined, and only upward adjustments will be made thereafter. However, thinking through and rewriting the lecture notes, preferably on the same day as the lectures and in consultation with a text, is one of the most effective forms of study, and well worth the effort. Please do not bother to turn in a pretty version of what is on the blackboard: extra credit will be given only when it is apparent that thought has gone into the rewriting.
 教學時程
The calendar for this course is just a rough outline of the pace at which topics are covered in the class.

週       課程單元
 1 Continuum Viewpoint and the Equation of Motion 2 Static Fluids 3 Mass Conservation 4 Inviscid Flow - Differential Approach: Euler's Equation, Bernoulli's Integral and the Effects of Streamline Curvature, the General Form of Bernoulli's Integral 5 Control Volume Theorems (Integral Approach): Linear Momentum Theorem, Angular Momentum Theorem, and First and Second Laws of Thermodynamics 6 Navier-Stokes Equation and Viscous Flow 7 Similarity and Dimensional Analysis 8 Boundary Layers, Separation and the Effect on Drag and Lift 9 Vorticity and Circulation (PDF) 10 Potential Flows: Lift, Drag, and Thrust Production 11 Surface Tension and its Effect on Flows 12 Introduction to Turbulence
 相關閱讀資料
 See the lecture notes for additional information on readings. Texts The suggested text is Introduction to Fluid Mechanics by James A. Fay (MIT Press, 1994). Readings in Fay's book are recommended in the outlines for each section. Fay's book is at the advanced undergraduate level, but covers most of the topics dealt with in the lectures. The lectures will cover some material with greater rigor or different emphasis; special notes are provided for selected topics, as indicated in the outlines. Students are responsible for material covered in class or indicated in the course outlines. Knowledgeable students will be able to read equally profitably from alternative texts, provided they are in the habit of reading broadly and searching out references that satisfy them on the fundamentals. A second book, Advanced Fluid Mechanics Problems by Ascher H. Shapiro and Ain A. Sonin, is required for all students. Writings Fundamental Laws of Motion for Particles, Material Volumes, and Control Volumes (PDF) On Choosing and Using Control Volumes: Six Ways of Applying the Integral Mass Conservation Theorem to a Simple Problem (PDF) Equation of Motion for Viscous Fluids (PDF - 2.3 MB)
 課堂講稿
The lecture notes outline the topics discussed, and indicate the reading and problem set assignments that accompany each.
Course Outline
週       課程單元
 1 Continuum Viewpoint and the Equation of Motion (PDF) 2 Static Fluids (PDF) 3 Mass Conservation (PDF) 4 Inviscid Flow - Differential Approach: Euler's Equation, Bernoulli's Integral and the Effects of Streamline Curvature, the General Form of Bernoulli's Integral (PDF) 5 Control Volume Theorems (Integral Approach): Linear Momentum Theorem, Angular Momentum Theorem, and First and Second Laws of Thermodynamics (PDF) 6 Navier-Stokes Equation and Viscous Flow (PDF) 7 Similarity and Dimensional Analysis (PDF) 8 Boundary Layers, Separation and the Effect on Drag and Lift (PDF) 9 Vorticity and Circulation (PDF) 10 Potential Flows: Lift, Drag, and Thrust Production (PDF) 11 Surface Tension and its Effect on Flows (PDF) 12 Introduction to Turbulence (PDF)
 作業
 See the lecture notes for additional infomation about problem sets. Problem Sets For Section 5, Control Volume Theorems, a revised set of problems has been posted here with hints and answers as well as some full solutions and examples. This is part of an on-going updating of the problems and the way they are presented. Note that while the web-based problems seem at first sight to be similar to the ones in the problem book, they bear different numbers and are in many cases altered. The Continuum Viewpoint and the Equation of Motion Static Fluids Mass Conservation in Flowing Media Inviscid Flow I Control Volume Theorems Viscous Flows Similarity and Dimensional Analysis Boundary Layers, Separation, and the Effect on Drag and Lift Vorticity and Circulation Potential Flow, Lift, and Drag Surface Tension Basic Concepts in Turbulence Modeling
 相關資源
 This page lists links to other sites of interest on the Internet. MIT School-Wide Modular Program for Fluid Mechanics (iFluids)

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