# ME 441/541: Advanced Fluid Mechanics

### Contents

You may also want to check out my fluid flow animation page and heat transfer animation page.

Last Update: 9 May 1997 by GWR

### Description

Advanced Fluid Mechanics is a core course in the graduate Thermal and Fluid Sciences Curriculum. It provides the fundamentals for working on fluid mechanics and convective heat transfer problems at the graduate and advanced undergraduate level.

The partial differential equations governing the conservation of mass, momentum and energy of Newtonian fluids are derived. Dimensional analysis is used to simplify the governing equations and in particular to justify the assumption of incompressible flow. Exact solution of the Navier-Stokes equations are presented. Boundary layer approximations to the governing equations are derived, and both exact and integral solutions are obtained.

### Logistics

Instructor
Gerald Recktenwald, Associate Professor, Mechanical Engineering Department
458 Science Building II, 725-4295, send me email

Textbook
F.M. White, Viscous Fluid Flow, second edition, 1991, McGraw-Hill, New York

Time and Place
Tuesdays and Thursdays, 2:00 -- 3:15 PM, Room 166, Science Building II

### Teaching Goals

The Teaching Goals are my personal activities for the quarter, which are
• Quickly derive the partial differential equations governing the conservation of mass, momentum, and energy of an incompressible Newtonian fluid.
• Obtain dimensionless forms of the governing equations, and from these extract the dimensionless parameters that determine the flow field.
• Present some exact solutions to the Navier-Stokes equations
• Describe equipment for making point measurements of velocity and pressure in a flow.
• Derive the boundary layer equations and show how to obtain exact and approximate integral solutions.

### Learning Objectives

The Learning Objectives are what I expect that you will be able to do at the end of Quarter. If you can do each of the following activities very well, then you will get an A'' grade.
• Identify the significance of each term in the governing equations.
• Simplify the governing equations for problems involving symmetry, and negligible terms.
• Specify appropriate mathematical boundary conditions given a complete physical description of a flow.
• Obtain dimensionless forms of the Navier-Stokes equations, and identify relevant dimensionless parameters.
• Perform similarity transformations for Stokes first and second problems, and obtain the exact solutions.
• Apply integral form of the boundary layer equations to derive expressions for boundary layer thickness, displacement thickness, momentum thickness and overall drag.
• Given physical interpretations of the terms boundary layer thickness'', displacement thickness'', momentum thickness'' and drag coefficient'' for flow over a flat plate.
• Utilize exact and integral solutions to the boundary layer equations to estimate boundary layer thickness and overall drag.
• Given a flow field, specify the gross characteristics of common sensors used to measure the velocity in that flow.

### Independent Projects

One quarter of the course grade will be based on your choice an independent project. Two different types of independent are allowed: design of a fluid mechanics experiment or a class portfolio. Students wishing to get design credit to meet ABET criteria must do the experiment design. Apart from the obvious difference, the design project will appeal to students who would like a specific and practical assignment, whereas the class portfolio will appeal to students who would like a broader, self-directed independent study.

#### Design Project

You will design an experiment for performing fluid mechanics measurements. You may chose from a list of projects that have already been identified, or, with instructor approval, you may create your own project. Your final design report will include citation of relevant literature, analysis to support the physical dimensions and parameter ranges for the experimental apparatus, and a specification of the instrumentation necessary to make the measurements. More details will be provided early in the quarter.

#### Class Portfolio

During the quarter you will be expected to assemble a list of independent investigations that you have undertaken to better understand the course material. These may include, but are not necessarily limited to the following
• Extra homework problems
• Annotated Journal articles you have read
• A list of references to consult for specific fluid mechanics issues
• A written summary and critique of web sites dealing with fluid mechanics
• Independent calculations on fluid mechanics problems that interest you
The portfolio is to be assembled in some tidy form, such as a three-ring binder or manila folder, and presented at the end of the class. The grading will be a subjective evaluation of the value and extent of the material you have collected. It is hoped that the portfolio will allow you to follow your own curiosity in fluid mechanics.

Cumulative grades will be based on the following weights
 25% Homework 25% Midterm 25% Independent Project (Experiment Design \emph{or} Portfolio) 25% Final Exam
The midterm exam will last one class period. The final exam will be comprehensive. Both exams are mandatory. Discuss any potential conflicts well before the exam dates. Make-up exams will not be given.