Last updated at 11:47 PM on 18 Mar 2007
Subscribe to the RSS feed for lecture podcasts.
Lecture on 15 March 2007
Reading: Cengel and Boles: 14.5 -- 14.7
The final exam is Tuesday, 20 March 2007, 10:15 AM to 12:05 PM. Bring a calculator and a two-sided cheat sheet.
I didn't cover as much material as I planned to cover during lecture. Here are my handwritten notes on air-conditioning process. The notes are very similar to the material in Chapter 14.
Lecture on 13 March 2007
Reading: Cengel and Boles: 14.1 -- 14.3
Slides: [one per page]
Review the Steady flow energy equation: Cengel and Boles Equation (5-37), p. 231 and study the first part of Chapter 14.
Lecture on 8 March 2007
Reading: Cengel and Boles, 13.3, 14.1 -- 14.2
I handed out this worksheet on computing the humidity ratio given the relative humidity.
Lecture on 6 March 2007
Reading: Cengel and Boles, 13.1 -- 13.2
I did not hand out this worksheet on computing the mass fraction of the constituents of air, but you may find it helpful as you study.
Chapter 12 of the book by Cengel and Boles contains definitions that are useful in subsequent chapters. The material is not difficult, but do not be deceived. As with all definitions, these formulas must be used with precision.
Lecture on 1 March 2007
Reading: 11.4
Problem Set #6 is Due on Tuesday, March 6. Do problems 11.6, 11.7, 11.32, 11.36, 11.46
Gerry will be in Salem on Monday, March 5. No office hours on Monday.
Quiz #2 will be on Tuesday, March 6. It will last 15 minutes and cover compressible flow only.
During class we worked on some example problems related to compressibility and ideal gas properties. You can download the sample problems and solutions distributed during lecture. Note that there is a typo in the worksheet. The supply temperature of the gas in problem 6 is 540 F, not 540 R. The version of the work sheet you can download has been corrected.
I did a quick derivation of a formula for computing the flow rate for compressible flow through an orifice. You can download a scanned copy of those notes to fill in the details and read additional information I didn't cover in class.
Lecture on 27 February 2007
Reading: 11.1 -- 11.3
Slides: [one per page]
The general rule of thumb is that when Ma < 0.3 a gas flow can be treated as incompressible. In the compressible flow regime, any flow with Ma > 1 is said to be supersonic. Flows with Mach numbers in the range 0.9 < Ma < 1.2 are said to be transonic. Flows with Ma > 5 are said to be hypersonic. These ranges are represented graphically in the following diagram.
Lecture on 22 February 2007
Reading: 12.4 -- 12.5
Guess Lecture by Professor Weislogel.
Lecture on 20 February 2007
Reading: 12.3 -- 12.4
Slides: [one per page]
Guest lecture by Professor Weislogel next Thursday. Regular course topics (end of pumps, beginning of compressible flow) and maybe some extra goodies.
PSU Career Fair on February 28 at SMU Ballroom. http://www.pdx.edu/careers/careerfairs.html
Part B of the podcast (for the second half of class) just ends. I must have hit the stop button by accident when the recorder was in my pocket.
During the last class (Lecture #10) we had a discussion about how gear pumps work. I gave myself the assignment to get more information. I found these web pages with gear pump animations
Detailed handwritten notes on the pump model can be downloaded here
Computational Fluid Dynamics or CFD is the use of numerical models to predict fluid flow. Centrifugal pumps have complicated geometries that can be analyzed with CFD. Here is a sample article on using CFD for water pump design
Lecture on 15 February 2007
Reading: 12.1 -- 12.4
Slides: [one per page]
PSU Career Fair on February 28 at SMU Ballroom. http://www.pdx.edu/careers/careerfairs.html
We worked on a sample problem involving the conversion of measured pump data to a pump curve.
Lecture on 8 February 2007
Reading: 9.3
Slides: [one per page]
The midterm exam is Tuesday, 13 February 2007.
Lecture on 6 February 2007
Reading: 9.2
Quiz 1 is graded. The solution is available on the web page for exams.
The midterm exam is Tuesday, 12 February 2007. It covers everything up to and including next Thursday's lecture (through lecture 9).
Lecture on 1 February 2007
Reading: 9.1 -- 9.2
Podcast: [Part A] [Part B] [Part C]
Slides: [one per page]
Quiz 1 is not graded. I'll create a web page for exams and solutions.
In the second half of class we began the solution to this in-class worksheet.
Here are Wikipedia links to Ludwig Prandtl and Theodore von Karman.
John Anderson wrote an article giving a historical account of Prandtl's boundary layer theory. Anderson has also written a textbook on the History of Aerodynamics. [Amazon Link] [Book Review from ASEE Prism]
The book refers to the boundary layer thickness as "delta" for what I called "delta_{99}". The "delta_{99}" designation is somewhat more common in the boundary layer literature.
Lecture on 30 January 2007
Reading: 8.6, 9.1
Slides: [one per page]
The bookstore now has Thermodynamics books in stock. The fifth edition (the one sold last quarter) is no longer available. The bookstore has the sixth edition of Thermodynamics: an Engineering Approach, by Cengel and Boles. You do not need to buy the new edition. However, if you don't yet have a copy of the book, and if you want to get a copy, you can buy the latest edition at the PSU Bookstore.
In an external flow the object of interest is immersed in a fluid with large extent. Examples include
Boundary layers exist when there are high velocity and/or large length scales: viscous effects are confined to a thin layer near the wall.
Caution: Not all external flows are fully explained by boundary layers. Boundary layer analysis is especially useful for streamlined objects, i.e. objects that do not cause large disruption in the streamlines of the on-coming flow. A "large disruption" occurs when the object causes the streamlines to displace by an amount equal to the size of the object.
Lecture on 25 January 2007
Reading: 8.4.3 -- 8.5
Podcast link
Slides: [one per page]
For practice, we worked on this example problem.
In class I mentioned a MATLAB Toolbox for analyzing pipe flow. I've been working on the documentation for the Toolbox and you can download an alpha version of the documentation and you can download a ZIP archive of the MATLAB programs. The class is not expected to use this toolbox and the programs. Adventurous students are encouraged to play with this code. Recognize that the documentation is "alpha" quality, meaning that it is incomplete and possibly contains errors.
Lecture on 23 January 2007
Reading: 8.4.1 -- 8.4.2
Podcast link
Slides: [one per page]
We worked the solution to problems 1 and 2 on this worksheet. You should also be able to do problems 3 and 4 on your own.
I demonstrated how to use the moody.m
function to solve the Colebrook equation with MATLAB. The steps are
moody.m
(Right-click and "Save As ...")
moody.m
ReD
and eD
and then
type f = moody(eD,ReD)
Here's a sample session
>> ReD = 5.5e6; eD=0.003; >> f = moody(eD,ReD) f = 0.0262
Lecture on 18 January 2007
Reading: 8.2 - 8.4
Podcast link
Slides: [one per page]
There was no class on Tuesday, 16 January. I'll try to make up a little time, but I can't forsee omitting an entire class worth of material from this part of the course.
Problem set 2 is available from the homework page.
I mentioned that a root-finding procedure can be used to find the friction factor from the Colebrook equation. The moody.m file is a MATLAB function for finding f when Re and epsilon/D are given.
I followed the text in section 8.2 quite closely except that I skipped section 8.2.2.
I went rather quickly over the material in sections 8.3.1 through 8.3.3. Please read those sections, but try not to get bogged down in the terminology. I skipped the material in section 8.3.4 and 8.3.5. Those sections interesting, but not essential for a first course in applied fluid mechanics.
Section 8.4 is very important for practical applications. We only covered section 8.4.1 in class today.
Lecture on 11 January 2007
Reading: 8.1 - 8.2
To motivate a physical understanding of turbulence I showed three movie clips from textbook multimedia resources.
This clip shows a modern interpretation of the famous experiment by Reynolds. The frame shows water flowing through a transparent, horizontal pipe. Dye is injected into the center of the pipe.
As the clip progresses, the velocity of the water through the pipe is increased. At very low water velocity the filament of dye-colored water is straight. As the velocity is increased, the dye streak becomes unsteady. At low speeds the dye streak is wavy or "sinuous" to use Reynolds' term. Increasing the speed further causes the dye streak to become very disordered. At the highest speeds the turbulence in the pipe causes the dye to become so well mixed that it is only visible as a slightly darker color that spans almost the entire cross section of the pipe.
From this video we conclude that turbulence is unsteady and appears to be random or chaotic. The turbulent flow has significant cross-stream velocity components which cause any convected quantity (the dye in the video clip) in the flow to be well mixed.
The video clip shows a shallow bowl of liquid being stirred by a spoon. The liquid has suspended metal flakes that make it possible to see the currents. The metal flakes change orientation, and hence reflectivity, as they move with the fluid. Although stirring the liquid in the bowl causes waves on the surface, the fine details of the flow structure is not due to waviness of the surface.
The detailed flow structure revealed by the metal flakes reveals that (1) turbulence involves motion at many length scales, (2) when the stirring stops, energy is no longer added to the system and the motion decays, and (3) the small scale motions are dissipated first, which causes the flow structure to appear more smooth as time progresses after stirring stops.
This clip shows laminar and turbulent velocity profiles in a pipe. The video frame is a view of a small length of the vertically oriented pipe. Out of the frame and below the test section is a valve that is used to start the flow. Initially the fluid is stationary. After a brief preparation sequence, the valve is opened and the velocity profile is made visible by the motion of a dye streak that starts out as a horizontal line near the top of the video frame.
At the beginning of each demonstration, a needle filled with dye is slowly withdrawn from the pipe. The needle moves horizontally from right to left. As the needle is withdrawn from the pipe, dye is injected into the stationary fluid. After the needle has been completely removed from the pipe, the valve is opened, thereby allowing the fluid to flow downward through the test section.
Two experiments are performed: one with a viscous oil and the other with water. The oil has a sufficiently high viscosity that its flow is laminar. In the bottom of the video frame is a label indicating that the Reynolds number is approximately equal to 1. The no-slip condition is clearly visible at the pipe walls. The velocity profile looks like a parabola.
The water has a low enough viscosity that when the valve is opened the flow is turbulent. Technically the flow will take time to become "fully" turbulent, but the steep gradient at the wall, the nearly flat average velocity profile in the center of the pipe, and the smearing of the dye in the center of the pipe are all characteristic of turbulent flow.
To do the homework you will need to read pp. 401 through 406. At the end of class I began a discussion of developing and fully-developed flow. Equation (8.1) and Equation (8.2) allow prediction of length of pipe necessary for the flow to become fully-developed.
Lecture on 9 January 2007
Reading: 6.1 - 6.3
I had the class work through a
problem to verify whether a vector field satisfied the
continuity equation for two-dimensional incompressible flow.
The image below shows one representation of the free vector created by
vortexVectors
MATLAB function.
Chapter 5 deals with finite control volumes: macroscopic scale regions of space. With finite control volumes, we use data on the velocity entering and leaving the control volume and the net forces acting on the control volume. Overall balances of mass, momentum and energy on the control volume do not give us detailed information on what happens inside the control volume.
Chapter 6 provides an overview to differential analysis of fluid motion. Differential analysis provides a framework for predicting the velocity field, i.e. the velocity at each point in space inside a domain of interest. In principle, differential analysis gives us much more detail than finite control volume analysis. However, the detail requires more sophisticated mathematical analysis.
In fact, very few flows can be analyzed by purely mathematical means: the equations are just too difficult to solve. Historically this meant that only highly simplified flows could be analysized using differential analysis. Now, we have numerical techniques -- usually called Computational Fluid Dynamics or CFD -- to obtain approximate solutions to the differential equations. Appendix A provides a brief introduction to CFD.
In ME 322 we will study only part of Chapter 6. The overall goal is to gain an awareness of differential analysis. Students interested in more advanced study of fluid mechanics will need to take additional courses, e.g. ME 441, to learn about differential analysis.
Although we will only be studying sections 6.1 - 6.3 and 6.8, it is helpful to get an overall picture of the chapter.