Unit 3: Finite and Differential Control Volume Analysis In Unit 2, you learned some fundamental definitions and learned to apply the conservation of energy (Bernoulli’s equation) to flow situations. In Unit 3, you will learn a systematic process for applying the conservation of mass, momentum, and energy to specific volumes (control volumes) of interest. For example, this control volume might be a section of pipe or a fluid tank. In addition, we will introduce the conservation laws over a differential or infinitesimal volume element in order to obtain differential equations representing the conservation principles. You will learn more about the application of differential analysis in Unit 4.
Unit 3 Time Advisory
This unit will take you approximately 15 hours to complete.
☐ Subunit 3.1: 4 hours
☐ Subunit 3.2: 4 hours
☐ Subunit 3.3: 4 hours
☐ Subunit 3.4: 3 hours
Unit3 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Derive the continuity, momentum, and energy equations of fluid
flows.
- Use the continuity, momentum, and energy equations to study simple
flow conditions.
3.1 Mass Conservation
- 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 58-68. This reading
will introduce you to conservation of mass and the continuity
equation. You will also learn several simple applications of the
continuity equation.
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displayed on the webpage above.
Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 5: Finite Control Volume Analysis” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 5: Finite Control Volume Analysis” (PDF)
Instructions: Please download the PDF file for Chapter 5 and read pages 1-4. In this reading, you will be introduced to the basics of finite control volume analysis. You will also learn how to apply mass conservation in the context of control volume analysis.
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 8 – Kinematics of Fluid Flow” Link: Indian Institute of Technology (IIT) Bombay: Professor T. I. Eldho’s “Lecture 8 – Kinematics of Fluid Flow” (YouTube)
Instructions: Please watch this video (55:02 minutes), which will introduce you to continuity equation.Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
3.2 Momentum Equations
- 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 69-78. This reading
will introduce you to conservation of momentum and the most
important equations in fluid mechanics, i.e. the Navier-Stokes
equations. We will examine the Navier-Stokes equations more
thoroughly in Unit 4.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
- Reading: University of Iowa: Professor Fred Stern’s Lectures Notes
on Fluid Mechanics: “Chapter 5: Finite Control Volume Analysis”
Link: University of Iowa: Professor Fred Stern’s Lectures Notes on
Fluid Mechanics: “Chapter 5: Finite Control Volume
Analysis” (PDF)
Instructions: Please download the PDF file for Chapter 5 and read pages 5-20. In this reading, you will study several practical applications of the momentum equations, including jet deflected by a plate or a vane, flow through a nozzle, and forces on bends.
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3.3 Energy Equations
- Reading: University of Iowa: Professor Fred Stern’s Lectures Notes
on Fluid Mechanics: “Chapter 5: Finite Control Volume Analysis”
Link: University of Iowa: Professor Fred Stern’s Lectures Notes on
Fluid Mechanics: “Chapter 5: Finite Control Volume
Analysis” (PDF)
Instructions: Please download the PDF file for Chapter 5 and read
pages 21-37. In this reading, you will learn how to apply the first
law of thermodynamics to derive energy equations for fluid flows.
Note that this reading will cover the material you need to know for
subunits 3.3.1-3.3.4.
Terms of Use: Please respect the copyright and terms of use
displayed on the webpage above.
- Web Media: University of Iowa: Professor Fred Stern’s Fluid
Mechanics Video Gallery
Link: University of Iowa: Professor Fred Stern’s Fluid Mechanics
Video
Gallery (Quicktime)
Instructions: At the top of the webpage, click on the link to the “Video Gallery.” Then, click on the hyperlink for Chapter 5 and watch all eight video segments on the webpage. Each video segment lasts about 1-2 minutes.
Terms of Use: Please respect the copyright and terms of use displayed on the webpage above.
3.3.1 First Law Comparisons
3.3.2 First Law Applications
3.3.3 Irreversible Flow
3.3.4 Loss Determination
Review Questions for Unit 3
- Assessment: The Saylor Foundation’s “ME201: Unit 3 Assessment”
Link: The Saylor Foundation’s “ME201: Unit 3
Assessment”
(HTML)
Instructions: Please perform this exercise.
You must be logged into your Saylor Foundation School account in
order to access this quiz. If you do not yet have an account, you
will be able to create one, free of charge, after clicking the
link.