# ME201: Fluid Mechanics

Unit 4: Application of Differential Analysis   *Application of differential analysis allows the determination of how properties such as fluid velocity and pressure vary within a volume of interest.  For example, we might be interested in the details of fluid flow within a conduit, through a turbine, or over an airplane wing.

In those applications, we chose a volume of interest with appropriate boundary conditions and integrate the governing differential conservation equations to obtain distributions or profiles of quantities of interest.  *

This unit will take you approximately 13 hours to complete.

☐    Subunit 4.1: 2 hours

☐    Subunit 4.2: 2 hours

☐    Subunit 4.3: 6 hours

☐    Subunit 4.4: 3 hours

Unit4 Learning Outcomes
Upon successful completion of this unit, the student will be able to:
- Define a fluid element and its motions. - Derive the Navier-Stokes equations. - Perform differential analysis of fluid flows. - Obtain exact solutions for the Navier-Stokes equations for simplified geometries and flow conditions.

4.1 Kinematics and Deformation   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 6: Differential Analysis of Fluid Flow” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 6: Differential Analysis of Fluid Flow” (PDF)

Instructions: Please download the PDF file for Chapter 6 and read pages 1-5.  In this reading, you will learn how about motions of fluid element, which include translation, linear deformation, rotation, and angular deformation.

4.2 Mass Conservation and Linear Momentum   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 6: Differential Analysis of Fluid Flow” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 6: Differential Analysis of Fluid Flow” (PDF)

Instructions: Please download the PDF file for Chapter 6 and read pages 6-12.  In this reading, you will be introduced to the continuity and momentum balance equations in differential form.

4.3 The Navier-Stokes Equations   - Reading: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 6: Differential Analysis of Fluid Flow” Link: University of Iowa: Professor Fred Stern’s Lectures Notes on Fluid Mechanics: “Chapter 6: Differential Analysis of Fluid Flow” (PDF)

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