ME351B

Fluid Mechanics

(viscous fluids)

Win 2003-04

Mechanical Engineering

Stanford University

Instructor:          Harvey S. H. Lam, lam@princeton.edu, visiting professor
Room and time:  530/127, Tuesday and Thursday, 11:00AM-12:15 PM
Office hours:       Tuesday and Thursday, 10:25-10:55AM, Room 501H in Building 500.
Students are encouraged to send me questions by emails.
TA:                     David Saintillan, dstn@stanford.edu
                            Office: Stauffer III, Room 205; phone:  723-9781
                            Office hour: Friday 4:00-5:00PM    (starting 1/9/04)
                                                Monday 4:00-5:00PM
                                        ---David will be in Building 520, Room 520-L3 for the office hour sessions.
Text Book:          F. M. White, Viscous Fluid Flow, 2nd Edition or later, McGraw Hill. (1st Edition OK).
Homework:         Normally due every Tuesday (to be collected in class).
Approximately 8-10 students are assigned to hand in their works each week to be graded. At the end of the quarter, ALL students are required to hand in all of the homeworks of the quarter in a folder. Students are encouraged to work on the homeworks and talk and discuss them together, but "copying" of other people's work is a No-No.
Grading:              Homework 30%, Midterm 30%, Final 40%.
Course outline:
  1. Review and use of dimensional analysis. Review of vector calculus. Review of experimental database.
    Read White, Chapter 1.

    Class Notes and homework assignment on Dimensional Analysis. [Homework Answers]
       Due Tuesday (1/13/04) (students assigned: Beretta, Blanquart, Buie, Kang, Kariya)
    Class Notes and homework assignment on Vector Calculus. [Homework Answers]
       Due Tuesday (1/20/04)(students assigned: Kahlighi, Khurana, Kim (HJ), Knudsen, Lee, Ni, Ong)
  2. Derivation of governing conservation equations. Assumptions. Multi-component medium issues.
    Read White, Chapter 2.
      Class Notes and homework assignment on viscous Stress Tensor. [Homework Answers]
        Due Tuesday (1/27/04) (students assigned: Barbour, Padilla, Park,Tanaka, Tang, Thomas, Walters).

      I don't like White's derivation of the energy equation in section 2-5. Here is my critique.
      Supplemental reading on elementary derivation of multi-component mass diffusion law (Fick's Law).

  3. Low Reynolds number flows. Oseen and Stokes approximations. Lubrication theory.
    Read White, Chapter 3.
            Class Notes and homework assignment on Low Reynolds Number Flows. [Homework Answers]
            Due Tuesday (2/3/04) (First student group assigned).
           Ask me, and I will tell you the physics behind the Ekman phenomena.
  4. High Reynolds number flows. The Prandtl boundary layer approximation.
  5. Read White, Chapter 4. We shall focus on 4-1 to 4-6 this week.
            Class Notes and homework assignment on Prandtl's boundary layer theory.[Homework Answers]
            Due Tuesday (2/10/04) (Second student group assigned).

  5.  More boundary layers. Review.(Mid-TermA closed book/notes take home this week!)
               Read White, Chapter 4. Include 4-10, 4-12, 4-13.
.               Class Notes on Well Known Boundary Layer Solutions. No homework assigned. Just read it.
.               Closed-book/notes mid-term will be posted saturday morning (8AM, 2/14/04). It is a two-hour take home exam, honor system. Start the clock when you download the exam, and put it in a brown manila envelop and seal it when you finish. Put your name and date on the envelop. Hand it in Tuesday  (2/17/04) in class. You can do the mid-term anytime inbetween (e.g. monday night). The reason this is not an open book exam is that there are things I want you to know without looking them up, and I want understanding. Here is my list of hints for this mid-term. I plan to take some of the mid-term question from these hints. I do not want you to memorize anything that I did not explicitly said I expect you to know by heart in my hints.
.       Download MidTerm here. This is a closed-books/notes, two-hour take-home, honor system. To be handed in Tuesday (2/17/04) when we meet in class.

   6.  Numerical marching algorithms for the boundary layer equations. Separation.
                Read White, section 4-7. Also, Chapter 7 (7-1 to 7-5).
.               Class Notes on numerical solutions of BL equations. Assignment involves Matlab.[Homework AnswersIt is highly likely that you will need to embellish a working code for the final exam.
               Download Tridiagonal-solver here. Be careful if you use cut and paste. On my computer, it made numerous errors.
.                Due Tuesday (2/24/04) (Third student group assigned).

   7.  Compressibility effects. Aerodynamics heating, recovery factor, Reynolds analogy, Busemann and Crocco energy integrals.
                 Read White, sections 7-1 to 7-4.
.                Class Notes on Compressible Boundary Layers. [Homework Answers] Assignment involves modifying your code to include compressibility effects via the Busemann Integral.
.                Due Tuesday, (3/2/04) (First student group assigned)

   8.  Stability theories.

             Read White, chapter 5. It is a relatively short chapter.
    .        Class Notes on Stabilty Theories.[Homework Answers]
    .        Due Tuesday, (3/9/04) (Second student group assigned)

   9.  Introduction to turbulent flows.
                 Read White, chapter 6. Use my class notes as a guide in reading it.
.                Class Notes on Turbulence.[Homework Answers]
.                Due Friday, (3/12/04), 2PM. (Third student group assigned). This is a relatively brief homework, and the due date has been moved up to completely free up the "final week". Please submit your homework to Room 500A (Ms. Deb Michael's office) in Building 500.


  1. The last class on 3/11/04 (friday) is devoted to review.
  2. The final will be a take-home, open-book, open-notes multiply-days final. My current intention is to have the final available for downloading sunday (3/14/04) morning, and have the finals handed back to me by 2PM of 3/19/04 (Friday), including a folder of all your homeworks of the Winter quarter. It will include an embellishment of your laminar boundary layer code.
  3. I have collected all the Typos and other comments that I have made on White's book here. It is posted here so you have a complete updated list for future references.
  4. I messed around a bit, and produced to my own satisfaction the proofs of Theorem 1 and 3 on White's page 346. It is posted for your reference. You do not need to "study" it for the final exam.You can read it after the final.
  5. Here is the take-home, open-books/notes final exam. The Friday 2PM (3/19/04) deadline is firm, including your homework folder (hand them in to Deb Michael's office in Building 500). I am available to answer questions by emails. Good luck!
  6. You can pick up the graded finals (your homeworks and your course grade) from Deb Michael' office Tuesday (3/23/04) afternoon. I will post some comments on the final exam by next sunday (3/28/04). In the mean time, enjoy this fun song that was very popular on campuses some years ago.
  7. Here are some final thoughts I have on the Final Exam. I want to thank you all for your courtesy and attention.