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2.25  高等流體力學    2002秋季

2.25 Advanced Fluid Mechanics, Fall 2002

譯者:李豔芳

編輯:陳盈、洪曉慧

 

An image of ocean waves.

海洋波浪。(ICM提供圖像)

 

課程重點

本課程有整單元的互動式問題組以及講稿大綱和一系列有用的閱讀資料。

 

課程描述

研究流體動力學的基本概念和方法。連續體的品質守恆,動量和能量方程,黏性流體的納維-斯托克斯方程,相似性和維度分析,流體潤滑理論,邊界層和分離區,環流和渦量定理,潛流,紊流的介紹,上升和拖曳,表面張力和表面張力驅動流。

 

 

 

作業問題和輔導課

作業問題來自Shapiro和Sonin 的《高等流體力學問題》Advanced Fluid Mechanics Problems,主題由課程大綱指示。作業問題不必繳交,但要在輔導課上討論。每週安排3節輔導課,要求是每個學生應該每週參加一次輔導課,通常是同一個時段的課。安排三次課是一方面配合學生的不同時間安排,一方面減少班級規模,這樣可以有更多自由討論的機會。

本課程的主要目的不是向學生灌輸進階內容(涉及的主題實際上並不一定是進階的),而是為了幫助學生掌握基本原則,培養快速、有效地解決不同實際流體力學問題的能力。授課中介紹並說明了基本定律、方法和模擬近似值,這些形成了流體力學的基礎。問題和輔導課幫助學生藉由實踐、嘗試錯誤以掌握內容,形成有效解決流體力學問題的思維方法。

指派的問題和輔導課完全都是自願的,不用繳交問題也不用點名,除非為了幫助導師記住學生的名字。但是,根據我們多年經驗,你要相信的是,你至少要在輔導課前獨立完成指派的問題,並藉由輔導課來查漏補缺並形成新觀點,否則,你在本課程將所獲甚少。雖然在教與學之間有很大的差別,但是我們會用各種方法隨時幫助你去掌握課程內容。

 

測驗和成績

在學期中會有兩次先行通知的一個小時的小測驗,為了減少時間壓力,我們傾向於晚上進行測驗。

會有一個三個小時的期末考試。

小測驗和考試將允許限制頁數的開卷(一個計算器和有數學公式和表格的本子),不允許有其他課本之使用。小測驗和考試中不會出一般問題,而是會深入考查你對基本內容的掌握程度,以及在最簡單且有可能的現實情況中進行問題建模的技巧。

兩次小測驗和期末考試在成績中佔有相等的比例,成績則根據以上兩者的情況所得。

你可以在期末考試結束時藉由繳交你重整理的有重點性的講稿筆記得到額外的分數,這個筆記必須條理清晰,結構緊湊。這個不是必須做的,如果你不做你的分數也不會受到影響。成績在檢查筆記前已經確定了,之後只是做一些向上的調整。但是,重新整理和學習課堂講稿,最好在授課的同一天進行,並同時參考課文,這是最有效的學習方式之一,而且事半功倍。請不要繳交和黑板所寫的相同的筆記,只有在你的筆記中有你的想法的時候才會給你額外的分數。

 

 

教學大綱、教學時程、課堂講稿

本次課程的大綱說明了這次課程的作業、考試和規則。

 

本次課程的時程僅是一個根據課程涵蓋的主題列出的粗略大綱。

 

課堂講稿列出了所要討論的主題,並指示了相應的問題和閱讀材料。

 

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)

 

 

相關閱讀資料

閱讀課堂講稿獲得更多關於閱讀資料的資訊。

 

課本

建議使用由James A. Fay (麻省理工學院出版, 1994)編寫的《流體力學概論》Introduction to Fluid Mechanics,在每單元的大綱裏都建議閱讀Fay的書裏的內容。Fay的書是高年級大學生水準,但是包括了課堂中大部分討論的主題。授課中將涉及更精確或者不同重點的內容,大綱裏指出了一些精選的主題,會相應提供特殊的講稿。學生需要學習課堂上或者課程大綱裏提到的內容。

有學識的學生即使閱讀其他內容相當的書本都能獲得同樣的效果,他們能習慣性地廣泛閱讀和搜索參考資料,來滿足他們對基礎原理的需要。

要求所有學生閱讀的第二本書是由Ascher.H.shapiroAin.A.Sonin寫的《高等流體力學問題》Advanced Fluid Mechanics Problems。

寫作

·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)。

 

作業

看課堂講稿可以得到關於問題的更多資訊。

 

問題組

對於第5節-控制體理論,這裏已經張貼了一些修改過的問題,含提示和答案以及一些完整的解決方法和例子。這是一部分正在更新的問題和方法。注意,雖然網頁上的問題看起來和問題集裏的很像,但是它們的題號不一樣並且在很多地方都作了改動。

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

 

相關資源

本頁列出了其他一些相關網站。

麻省理工學院校內流體力學模組計畫(iFluidsMIT School-Wide Modular Program for Fluid Mechanics (iFluids)

 

 

 

2.25 Advanced Fluid Mechanics, Fall 2002

An image of ocean waves.
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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有關本課程的討論

課程討論
品質守恆Mass Conservation 應該是質量守恆

kundong, 2012-08-13 12:51:35
課程討論
請問有沒有相關的資料或是影音檔?
Joe, 2011-06-08 23:57:30
課程討論
該如何使用附件之pdf檔呢!?
Joe, 2011-06-07 16:51:44

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