# ME201: Fluid Mechanics

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.

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.

• 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.

• 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.

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.

• 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.

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.

• 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.

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