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1.060 Engineering Mechanics II

Spring 2006

Fluid convergence on a shore.These waves illustrate converging flow on a shoreline. (Image courtesy of cbonney.)

Course Highlights

This course features a complete set of Prof. Madsen's hand-written lecture notes, and exams and assignments that were prepared by the instructor and teaching assistant David Gonzalez-Rodriguez.

Course Description

This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from calculus and differential equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.



Syllabus

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This subject provides an introduction to fluid mechanics. You will be introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and you will learn how to solve a variety of problems of interest to civil and environmental engineers. While there will be a chance for you to put your mathematical skills obtained in 18.01, 18.02, and 18.03 to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make you think as a fluid. In addition to giving you a working knowledge of fluid mechanics, the subject will prepare you for higher-level subjects in fluid dynamics.

Lectures

Lecture notes will be distributed for each lecture, usually covering "theoretical" aspects (derivations, etc.) in more detail or in a different manner than done during class or in text. The subject content is defined by the material presented in lecture notes, recitations, and readings, so regular attendance is advisable.

Recitations

Recitations will illustrate and/or expand on concepts presented in lectures by working through example problems or conducting simple experiments. Material covered in recitations is often related to homework assignments and is considered part of the subject content, so regular attendance at one of the two weekly recitations is advisable.

Text

The following book will be used as the text for the subject, supplemented by lecture notes:

Amazon logo Young, Donald F., Bruce R. Munson, and Theodore H. Okiishi. A Brief Introduction to Fluid Mechanics. 3rd ed. New York, NY: Wiley, 2003. ISBN: 0471457574.

Reading assignments are given in the readings section.

Homework

Problem sets will be distributed at regular intervals. Each problem set is designed to build upon the material covered in the preceding lectures. Homework assignments will be prepared by teams consisting of three students. Each team will hand in one solution, with the names of team-members who contributed indicated on the cover-page. Due dates for problem sets are firm and homework assignments will be corrected and handed back (with solutions) no later than two lectures after the due date.

Exams

There will be three in-class hour exams. There will also be a three-hour scheduled final exam. The exams will be closed-book, but "cheat-sheets" will be handed out.

Grade

The grade will be based on:


ACTIVITIESPERCENTAGES
Homework25%
In-class Exams45%
Final Exam30%



In arriving at a final letter grade, two grades will be given:

The better of the two grades will be your final letter grade in 1.060.





Calendar

The calendar below provides information on the course's lecture (L), recitation (R), and exam (E) sessions.


SES #TOPICSKEY DATES
L1Subject Outline, Fluid Concepts, The Continuum Hypothesis
R1Review of Hydrostatics and Dimensional Analysis
L2Description of Fluid Flow, Conservation Laws
L3Hydrostatics, Forces on Plane and Curved SurfacesHomework 1 out
R2Stability of Floating Bodies
L4Manometry, Stability of Dams and Gates
L5Mass and Volume Conservation
L6Stream Function, Velocity Potential, Flownet ConstructionHomework 1 due

Homework 2 out
L7The Bernoulli Equation for Ideal Fluids
R3Flownet and Streamline Construction
L8Application of Mass Conservation and Bernoulli
L9Conservation Laws for Finite Control Volumes, Reynolds Transport TheoremHomework 2 due

Homework 3 out
L10Conservation of Momentum for Finite Control Volumes
R4Bernoulli Experiment
L11Applications of Momentum
L12The Bernoulli Equation from Energy ConsiderationsHomework 3 due
L13Special Forms and Interpretations of the Bernoulli Equation
E1Hour Exam 1 (Covering Material through L11)
L14Laminar Flow, Shear Stresses in FluidsHomework 4 out
L15Velocity Distribution in Laminar Flows, Turbulence, The Reynolds Number
R5Application of Conservation Principles for Finite Control
L16Pipe Friction Losses, Moody Diagram, Minor Losses
L17Pipe Flow AnalysisHomework 4 due

Homework 5 out
L18Pump Specification and Requirements
R6Pipe Flow Demonstration and Analysis
L19Turbines and Windmills
L20Drag Forces on Immersed BodiesHomework 5 due

Homework 6 out
L21Lift Forces on Immersed Bodies
R7Dynamic Response of a Floating Body
L22Fluid Mechanics of Pitching
L23Uniform Open Channel FlowHomework 6 due
L24Uniform Open Channel Flow Computations
E2Hour Exam 2 (Covering Material through L23)Homework 7 out
R8Open Channel Flow Computations
L25Bernoulli Principle in Open Channel Flow, Specific Head-Depth Diagram
L26Application of Specific Head in Open Channel Flow, Super- and Sub-critical Flows
L27Momentum Principle in Open Channel FlowHomework 7 due

Homework 8 out
L28Application of Momentum Principle in Open Channel Flow
R9Application of Energy and Momentum Principles in Open Channel Flows
L29Gradually Varied Open Channel Flow
L30Gradually Varied Flow ProfilesHomework 8 due

Homework 9 out
L31Discharge From Lakes and Under Gates
R10Determination of Gradually Varied Flow Profiles
L32Further Examples of Gradually Varied Flow
L33Unsteady Flow in Open Channels, Kinematic WavesHomework 9 due
L34Flood Routing
E3Hour Exam 3 (Covering Material through L34)
L35-L36Differential Analysis of Fluid Flow, Navier-Stokes Equations
E4Final Exam (3 Hours)




Readings

This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.

The main textbook for this course is:

Young, Donald F., Bruce R. Munson, and Theodore H. Okiishi. A Brief Introduction to Fluid Mechanics. 3rd ed. New York, NY: Wiley, 2003. ISBN: 0471457574.

Supplemental texts for the course are:

Control Volume Notes (PDF)

A Few Hints on Problem Solving (PDF)#

Readings assignments in the main textbook are shown in this table.


SES #TOPICSREADINGS
L1Subject Outline, Fluid Concepts, The Continuum Hypothesis1.1-1.6
R1Review of Hydrostatics and Dimensional Analysis
L2Description of Fluid Flow, Conservation Laws1.7-1.9, 4.1-4.2
L3Hydrostatics, Forces on Plane and Curved Surfaces2.1-2.3, 2.8-2.10
R2Stability of Floating Bodies
L4Manometry, Stability of Dams and Gates2.4-2.7, 2.11-2.12
L5Mass and Volume Conservation5.1, 6.1-6.2
L6Stream Function, Velocity Potential, Flownet Construction6.4, 6.5-6.5.1
L7The Bernoulli Equation for Ideal Fluids3.1-3.4
R3Flownet and Streamline Construction
L8Application of Mass Conservation and Bernoulli3.5-3.6
L9Conservation Laws for Finite Control Volumes, Reynolds Transport Theorem4.3-4.4
L10Conservation of Momentum for Finite Control Volumes5.2.1
R4Bernoulli Experiment
L11Applications of Momentum5.2.2
L12The Bernoulli Equation from Energy Considerations5.3-5.3.1
L13Special Forms and Interpretations of the Bernoulli Equation3.7-3.8, 5.3.2-5.3.4
E1Hour Exam 1 (Covering Material through Ses #L11)
L14Laminar Flow, Shear Stresses in Fluids1.6, 8.1
L15Velocity Distribution in Laminar Flows, Turbulence, The Reynolds Number6.9, 8.2-8.3
R5Application of Conservation Principles for Finite Control
L16Pipe Friction Losses, Moody Diagram, Minor Losses8.4
L17Pipe Flow Analysis8.5-8.6
L18Pump Specification and Requirements11.1-11.4
R6Pipe Flow Demonstration and Analysis
L19Turbines and Windmills11.6-11.8
L20Drag Forces on Immersed Bodies9.1-9.3
L21Lift Forces on Immersed Bodies9.4
R7Dynamic Response of a Floating Body
L22Fluid Mechanics of Pitching10.1, 10.4-10.4.2
L23Uniform Open Channel Flow10.4.3
L24Uniform Open Channel Flow Computations10.2

Class notes
E2Hour Exam 2 (Covering Material through Ses #L23)
R8Open Channel Flow Computations
L25Bernoulli Principle in Open Channel Flow, Specific Head-Depth Diagram10.3
L26Application of Specific Head in Open Channel Flow, Super- and Sub-critical Flows10.6.2-10.6.4
L27Momentum Principle in Open Channel Flow10.6.1

Class notes
L28Application of Momentum Principle in Open Channel FlowClass notes
R9Application of Energy and Momentum Principles in Open Channel Flows
L29Gradually Varied Open Channel Flow10.5
L30Gradually Varied Flow ProfilesClass notes
L31Discharge From Lakes and Under GatesClass notes
R10Determination of Gradually Varied Flow Profiles
L32Further Examples of Gradually Varied FlowClass notes
L33Unsteady Flow in Open Channels, Kinematic WavesClass notes
L34Flood Routing6.3, 6.8
E3Hour Exam 3 (Covering Material through Ses #L34)
L35-L36Differential Analysis of Fluid Flow, Navier-Stokes Equations8.3

Class notes
E4Final Exam (3 Hours)




Lecture Notes

This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.


SES #TOPICS
L1Subject Outline, Fluid Concepts, The Continuum Hypothesis (PDF)#
L2Description of Fluid Flow, Conservation Laws (PDF - 1.0 MB)#
L3Hydrostatics, Forces on Plane and Curved Surfaces (PDF - 1.1 MB)#
L4Manometry, Stability of Dams and Gates (PDF - 2.0 MB)#
L5Mass and Volume Conservation (PDF)#
L6Stream Function, Velocity Potential, Flownet Construction (PDF - 2.0 MB)#
L7The Bernoulli Equation for Ideal Fluids (PDF)#
L8Application of Mass Conservation and Bernoulli (PDF)#
L9Conservation Laws for Finite Control Volumes, Reynolds Transport Theorem (PDF)#
L10Conservation of Momentum for Finite Control Volumes (PDF)#
L11Applications of Momentum (PDF)#
L12The Bernoulli Equation from Energy Considerations (PDF)#
L13Special Forms and Interpretations of the Bernoulli Equation (PDF - 1.1 MB)#
L14Laminar Flow, Shear Stresses in Fluids (PDF - 1.0 MB)#
L15Velocity Distribution in Laminar Flows, Turbulence, The Reynolds Number (PDF)#
L16Pipe Friction Losses, Moody Diagram, Minor Losses (PDF - 1.2 MB)#
L17Pipe Flow Analysis (PDF)#
L18Pump Specification and Requirements (PDF - 1.2 MB)#
L19Turbines and Windmills (PDF)#
L20Drag Forces on Immersed Bodies (PDF - 1.6 MB)#
L21Lift Forces on Immersed Bodies (PDF - 1.4 MB)#
L22Fluid Mechanics of Pitching
L23Uniform Open Channel Flow (PDF - 1.0 MB)#
L24Uniform Open Channel Flow Computations (PDF)#
L25Bernoulli Principle in Open Channel Flow, Specific Head-Depth Diagram (PDF)#
L26Application of Specific Head in Open Channel Flow, Super- and Sub-critical Flows (PDF - 1.0 MB)#
L27Momentum Principle in Open Channel Flow (PDF)#
L28Application of Momentum Principle in Open Channel Flow (PDF - 1.2 MB)#
L29Gradually Varied Open Channel Flow (PDF - 1.1 MB)#
L30Gradually Varied Flow Profiles (PDF - 2.3 MB)#
L31Discharge From Lakes and Under Gates (PDF - 1.3 MB)#
L32Further Examples of Gradually Varied Flow (PDF - 1.7 MB)#
L33Unsteady Flow in Open Channels, Kinematic Waves (PDF - 1.3 MB)#
L34Flood Routing (PDF - 1.2 MB)#
L35-L36Differential Analysis of Fluid Flow, Navier-Stokes Equations (PDF - 1.8 MB)#




Recitations

This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.

The following files are notes and problems from the recitation sessions, which were led by course TA David Gonzalez-Rodriguez.


SES #TOPICSNotesProblems
R1Review of Hydrostatics and Dimensional Analysis(PDF)#
R2Stability of Floating Bodies(PDF - 1.6 MB)#
R3Flownet and Streamline Construction(PDF - 2.0 MB)#
R4Bernoulli Experiment(PDF - 1.8 MB)#
R5Application of Conservation Principles for Finite Control(PDF)#
R6Pipe Flow Demonstration and Analysis(PDF - 1.3 MB)#
R7Dynamic Response of a Floating Body(PDF - 1.3 MB)#(PDF)#
R8Open Channel Flow Computations(PDF - 1.5 MB)#(PDF)#
R9Application of Energy and Momentum Principles in Open Channel Flows(PDF)#
R10Determination of Gradually Varied Flow Profiles(PDF - 1.4 MB)#




Assignments

This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.

The assignments for this course and their solutions are listed below.  They were prepared jointly by the instructor and teaching assistant David Gonzalez-Rodriguez:


ASSIGNMENTSSOLUTIONS
Problem Set 1 (PDF)(PDF)#
Problem Set 2 (PDF)(PDF - 1.3 MB)#
Problem Set 3 (PDF)(PDF - 1.4 MB)#
Problem Set 4 (PDF)(PDF - 2.1 MB)#
Problem Set 5 (PDF)(PDF - 1.7 MB)#
Problem Set 6 (PDF)(PDF - 1.7 MB)#
Problem Set 7 (PDF)(PDF)#
Problem Set 8 (PDF)(PDF - 1.6 MB)#
Problem Set 9 (PDF)(PDF - 1.6 MB)#




Exams

This section contains documents created from scanned original files, which are inaccessible to screen reader software. A "#" symbol is used to denote such documents.

The following files are sample tests along with their solutions, as well as past final exams for the course.

Test 1 with Solutions (PDF - 1.0 MB)#

Test 2 with Solutions (PDF - 1.2 MB)#

Text 3 with Solutions (PDF - 1.1 MB)#

Final Exam with Solutions (PDF - 2.9 MB)#



Sample Exams

Sample Test 1 (PDF)#

Sample Test 2 (PDF - 1.9 MB)#

Sample Test 3 (PDF - 1.7 MB)#

Sample Test 4 (PDF - 1.0 MB)#

Study Aids for the Final Exam (PDF - 1.2 MB)#

2004 Final Exam (PDF - 2.4 MB)#

2005 Final Exam (PDF - 2.2 MB)#




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