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ME201: Fluid Mechanics

Unit 2: Fluid Dynamics and Kinematics   In this unit, we will take a look at fluids in motion.  In particular, we will set the stage for later applications by providing fundamental definitions and tools for flow situations. These tools include Bernoulli’s equation for the conservation of energy in this unit and equations for the conservation of mass and momentum.  In later units we will apply those tools to commons situations such as flow in conduits and around obstacles.

Unit 2 Time Advisory
This unit will take you approximately 17 hours to complete.

☐    Subunit 2.1: 5 hours

☐    Subunit 2.2: 3 hours

☐    Subunit 2.3: 2 hours

☐    Subunit 2.4: 1 hour

☐    Subunit 2.5: 3 hours

☐    Subunit 2.6: 3 hours

Unit2 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Use the Bernoulli equation to calculate simple flow conditions (e.g. flow stagnation). - Use Reynold Transport Theorem to derive conservation laws for fluid flows. - Derive equations from Eulerian and Lagrangian viewpoints.

2.1 The Bernoulli Equation   - Lecture: MIT OpenCourseWare: Professor Water Levin’s “Hydrostatics, Archimedes' Principle, and Fluid Dynamics” Link: MIT OpenCourseWare: Professor Water Levin’s “Hydrostatics, Archimedes' Principle, and Fluid Dynamics” (YouTube)
 
Also available in:
HTML/PDF Transcript. Adobe Flash, and Mp4 Download
iTunes U
 
Instructions: Please watch this video (49:00 minutes), which will introduce you to the Bernoulli equation from a classical mechanics perspective.

 Terms of Use: Walter Lewin, Physics I:Classical Mechanics, Fall
1999. (Massachusetts Institute of Technology: MIT
OpenCourseWare), [http://ocw.mit.edu](http://ocw.mit.edu/ "http://ocw.mit.edu") (Accessed
November 10, 2010). License: Creative Commons BY-NC-SA 3.0. The
original version can be found
[here](http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-28/).
  • Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 3: Bernoulli Equation” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 3: Bernoulli Equation” (PDF)
     
    Instructions: Please click on the hyperlink “Chapter 3” under “Lecture Notes” to download the PDF file for Chapter 3.  Read pages 1-27.  In this reading, you will learn about flow patterns and the Bernoulli equation.  You will learn to apply the Bernoulli equation to calculate several flow situations, including stagnation flow and flow in pilot tube.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Assessment: MIT: Course 801: “8.01 Quiz 9, Fall 1994” and “8.01 Quiz 9 Solutions, Fall 1994” Link: MIT: Course 801: “8.01 Quiz 9, Fall 1994” (PDF) and “8.01 Quiz 9 Solutions, Fall 1994” (PDF)

    Instructions: Please click on the first link to Quiz 9 Problem #3 of the Fall 1994 class.  Please solve the problem. Read the problem statement carefully and try to solve it yourself before looking up the solution in the second link.

    Terms of Use: The linked material above has been reposted by the kind permission of MIT, and can be viewed in its original form here.  Please note that this material is under copyright and cannot be reproduced in any capacity without explicit permission from the copyright holder. 

2.2 Fluid Velocity   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” (PDF)
 
Instructions: Please click on the “Chapter 4” hyperlink under the “Lecture Notes” section on the left side of the webpage to download the PDF file for Chapter 4.  Read pages 1-3 to learn about different descriptions of velocity.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Reading: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” Link: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” (PDF)
     
    Instructions: Please download the PDF file for Lecture Notes of ME330: Elementary Fluid Dynamics.  Read pages 47-52.  This reading will introduce you to Eulerian and Lagrangian views of fluid motions.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Eulerian Lagrangian Description” Link:  MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Eulerian Lagrangian Description” (RealPlayer)
     
    Instructions: Download and watch the movie “Eulerian Lagrangian Description” on the webpage. The length of the movie is 27 minutes.  Please also download and read the companion film notes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Lecture: Indian Institute of Technology (IIT) Bombay: Professor T. I. Eldho’s “Lecture 6 – Kinematics of Fluid Flow” Link: Indian Institute of Technology (IIT) Bombay:  Professor T. I. Eldho’s “Lecture 6 – Kinematics of Fluid Flow” (YouTube)
     
    Instructions: Please watch this video (51:10 minutes), which will introduce you to kinematics of fluid flow.  This lecture will cover the material that you need to know for subunits 2.2 and 2.3.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

2.3 Fluid Acceleration   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” (PDF)
 
Instructions: Please download the PDF file for Chapter 4 and read pages 4-7.  In this reading, you will learn about acceleration field and material derivative.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Web Media: MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Pressure Field and Acceleration”. Link: MIT: Professor Ascher Shapiro’s National Committee for Fluid Mechanics Films: “Pressure Field and Acceleration.” (RealPlayer)
     
    Instructions: Download and watch the movie “Pressure Field and Acceleration.”  The video is 29 minutes in length.  Please also download and read the companion film notes.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

2.4 Basic Control Volume Approach   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” (PDF)
 
Instructions: Please click on the hyperlink “Chapter 4” under the “Lecture Notes” section on the left side of the webpage to download the PDF file for Chapter 4.  Please read pages 14-15.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

2.5 Reynolds Transport Theorem   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 4: Fluids Kinematics” (PDF)
 
Instructions: Please download the PDF file for Chapter 4 and read pages 16-17.  In this reading, you will learn about Reynolds Transport Theorem, which will be used to formulate the basic conservation laws of fluid mechanics in Unit 3.
 
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Reading: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” Link: University of Kentucky: Professor J. M. McDonough’s Lectures Notes on Introduction to Fluid Mechanics: “Lectures on Elementary Fluid Dynamics” (PDF)
     
    Instructions: Please download the PDF file for Lecture Notes of ME330: Elementary Fluid Dynamics and read pages 52-58.  The reading will provide a detailed explanation and mathematical derivation of Reynolds Transport Theorem.
     
    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

  • Lecture: Indian Institute of Technology (IIT) Bombay: Professor T. I. Eldho’s “Lecture 7 – Kinematics of Fluid Flow” Link: Indian Institute of Technology (IIT) Bombay: Professor T. I. Eldho’s “Lecture 7 – Kinematics of Fluid Flow” (YouTube)
     
    Instructions: Please watch this video (51:10 minutes), which will introduce you to Reynolds Transport Theorem.

    Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.

Review Questions for Unit 2   - Assessment: The Saylor Foundation’s “ME201: Unit 2 Assessment” Link: The Saylor Foundation’s “ME201: Unit 2 Assessment” (HTML)
 
Instructions: Please perform this exercise. 

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