EGM Fluid Mechanics 1 Fall 2010

Transcription

1 Instructor: Dr. Mark Sheplak, Room 7 Benton Hall, -3983, sheplak@ufl.edu, Lecture Times: MWF 3 rd period (9:35-10:40 am) in NEB 01. Office Hours: M & W -3 pm, other times by appointment. Teaching Assistant: Ms. Jessica Sockwell, TBD, Room 33 Benton Hall, -614, jsockie@ufl.edu, Office Hours: T & R 9 am -10 am, other times by appointment. Required Textbook: Incompressible Flow, 3 rd Edition, Panton, R.L., Wiley-Interscience, 005. Recommended Textbooks: An Introduction to Fluid Dynamics, Batchelor, G.K., Cambridge University Press, Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Aris, R., Dover, 196. Course Objectives: To develop a fundamental understanding of the underlying principles of fluid mechanics. Student Expectations: It is expected that this course will require at least 15 hours of effort per week when you consider time spent for lectures, reading assignments, homework, and re-writing of your class notes. I also expect that you will attend every lecture. If you cannot attend a lecture, please notify me prior to class. I strongly recommend that you implement the Five Times Strategy for learning in this class. This requires that you cover the course material at least 5 times before exams. The first time that you cover the material is when you perform your reading assignment before class. The second time that you cover the material is during lecture. The third time that you cover the material is when you re-write your lecture set of notes that includes material from lecture and the reading assignments, including all derivations and your additions. The fourth time that you cover the material is when you do your homework assignments. Finally, the fifth time that you cover the material is when you study for your exams. This technique will help you master the material and also will provide you with a comprehensive set of notes to study from for your qualifying exam. Reading Assignments: Reading assignments will be made periodically. You are responsible for the material the next class meeting. If I feel that the bulk of the class is not keeping up with the reading assignments, I reserve the right to give unannounced quizzes. Exams: There will be several exams. The final exam group is 17A, which means the exam will be held in NEB 10 on 1/17/10, from 7:30 am 9:30 am. There will be no alternative times for the exam. Student Behavior: You are expected to show up on time for class. If you are a UF campus student, you are expected to attend class. Please turn off all cell phones and pagers prior to the start of class. Please do not bring food to class. Late/Makeup Policy: No late homework assignments will be accepted. Makeup exams are not allowed. If you cannot attend an exam or cannot meet a due date, you must contact the instructor prior to the exam or due date. All policies apply to UF EDGE students as well. Accommodations: Students requesting classroom accommodation must first register with the Dean of Students Office. That office will provide the student with documentation that he/she must provide to the course instructor when requesting accommodation. Grading: Homework (see pg. 4) 10% Exam #1 (Wed., 9/9/10) 30% Exam # (Wed., 11/3/10) 30% Final Exam (Wed, 1/17/10) 30% Total 100 % 1/7

2 Grading Scale: Honesty Policy: Software Use: Course Notes: A: , A-: 87-89, B+: 84-86, B: 80-83, B-: 77-79, C+: 74-76, C: 70-73, C-: 67-69, D: 60-63, D-: 55-59, E: <55 All students admitted to the University of Florida have signed a statement of academic honesty committing themselves to be honest in all academic work and understanding that failure to comply with this commitment will result in disciplinary action. This statement is a reminder to uphold your obligation as a UF student and to be honest in all work submitted and exams taken in this course and all others. All faculty, staff and student of the University are required and expected to obey the laws and legal agreements governing software use. Failure to do so can lead to monetary damages and/or criminal penalties for the individual violator. Because such violations are also against University policies and rules, disciplinary action will be taken as appropriate. We, the members of the University of Florida community, pledge to uphold ourselves and our peers to the highest standards of honesty and integrity. The course will be taught from a Tablet PC using my typeset summary notes. These notes are meant to accompany the assigned readings from the text and reference books. They are not to be considered substitutes. You will be responsible for both the material covered in class and the assigned readings. These notes will be placed on the website in the handout section by 9 am on the day (usually, they will be posted a day early) of the lecture. If there are any subsequent revisions, they will also be posted on the website. Course Content: 1. Introduction (Ch. 1, Panton) a. Definitions b. Continuum Assumption c. Definition of Regions. Vector Calculus and Indicial Notation (Ch. 3, Panton) a. Definitions & Notation b. Vector Transformation Law c. Vector & Tensor Algebra/Calculus d. Integral Theorems 3. Kinematics (Ch. 4, Panton) a. Lagrangian and & Eulerian Methods of Description b. Streamlines, Streaklines, Pathlines c. Substantial/Material Derivative d. Decomposition of Fluid Motion 4. Basic Laws in Integral and Differential Form: (Ch 5, Panton) a. Reynolds Transport Theorem (RTT) b. Continuity i. Integral via RTT ii. Mass flux and volumetric flow rate iii. Differential in conservation and substantial derivative forms c. Momentum i. Integral via RTT ii. Differential in conservation and substantial derivative forms iii. Surface and volume forces iv. Momentum flux d. Derivation of Stress Tensor i. Symmetry of stress tensor via Angular Momentum Equation e. Review of Control Volume Problems /7

3 i. Boundary layers, wakes, s/plumes, etc. f. Energy Equations i. Integral differential forms of First Law ii. Kinetic energy equation iii. Internal energy equation iv. Interpretation of surface work terms v. Second Law/Entropy Equation 5. Newtonian Fluids and Navier-Stokes Equations: (Ch. 6, Panton) a. Newton s Viscosity Law Derivation b. Stokes Hypothesis i. Counter examples: shocks, high-frequency acoustics, etc. c. Kinetic Theory Model of Viscosity d. Non-Newtonian Fluids e. Boundary Conditions f. N-S Equations 6. Dimensional Analysis (Ch. 8, Panton) a. Variables and typical scales b. Non-dimensional formulation of governing equations and various limits c. Dynamic similarity d. Pi Theorem e. Physical interpretation of various Pi groups and various limits 7. Incompressible Flows (Ch 7, 10 and 11 Panton) a. Conditions for incompressibility b. Pressure splitting c. Exact solutions: i. channel flow: concept of entrance length, fully developed ii. Couette flow: 1-D approximation for small gap between cylinders 8. Vorticity Dynamics (Ch 13 and 17 Panton) a. Introduction to vorticity/circulation b. Vorticity Equation i. General form and sources ii. Barotropic form, discuss Lighthill s vorticity flux/source and destruction via Morten s paper. c. Helmholtz s Laws d. Kelvin s Theorem e. Helmholtz decomposition 9. Ideal Flow (Ch. 1 and 18 Panton) a. Streamfunction, velocity potential b. Bernoulli s eqn. c. Topological Notions d. Properties of Harmonic Functions e. Flow Classifications: Cyclic and Acyclic Motions f. Uniqueness of Laplace s question in Incompressible Irrotational Flows g. Two Dimensional Incompressible Irrotational Flows and Complex Potential i. Elements of complex variables (a quick review) ii. Flows represented by some simple analytic functions iii. Superposition of a uniform flow with a doublet; a vortex flow over a circular cylinder iv. Method of images h. Forces and Moments on an Arbitrary -D Body in Steady Flows i. Blasius relations ii. Kutta-Joukowski theorem i. Flow over an Airfoil and Conformal Mapping i. Basic ideas ii. Conformal mapping iii. Uniqueness of analytic transformation iv. Joukowski transformation 3/7

4 v. Flow over a Joukowski airfoil and Kutta-Joukowski condition 10. Three-Dimensional Irrotational Flows (Ch. 19 Panton) a. General Problems b. Axisymmetric Flows c. Solutions for Some Simple Flows d. Flow over a Stationary Sphere e. Butler's Sphere Theorem f. Unsteady Motion of a Sphere g. Motion of a Finite Body in a Still, Unbounded Fluid 11. Waves in Incompressible Fluids a. Basic Equations b. Small Amplitude Surface Waves i. Perturbation analysis ii. Dispersion relation iii. Interpretation of the dispersion relation iv. Limitation of the linear approximation c. Velocity field, pathlines, and pressure field d. Equipartition of energy e. Inviscid Stability Analysis f. Group Velocity 4/7

5 Notes on Homework Solutions Policies/Procedures: Format: 1. Homework is an essential element of this course.. Homework is due at the start of class on the due date assigned and late submissions will not be accepted. All policies apply to UF EDGE students as well. UF EDGE students may fax or their homework assignments to me. 3. Solutions to the homework will be available on the class website after class on the date the assignment is due. 4. Performance on the homework will comprise 10% of the student s final grade; consequently individual work must be expected on all problems. Students are encouraged to discuss the general principles involved in the homework sets with one another, but the solution of each problem must be attempted individually. 1. Use 8.5 x 11 paper and write on one side. Do not use pages torn from a spiral notebook. If your homework is excessively sloppy, it will be returned to you ungraded.. State each problem on a new page. 3. Each homework problem must be completed in a standard format, which includes the following labeled steps: GIVEN: After carefully reading the problem, state briefly and concisely what is known. Do not repeat the problem statement. FIND: State briefly and concisely what must be found. SCEMATIC: Draw a schematic of the physical problem to be considered. Note the control volumes used in the analysis by dashed lines on the sketch. Include coordinate axes when appropriate, and label relevant dimensions and velocities. BASIC EQUATIONS: Provide the appropriate assumptions and mathematical formulation for the basic laws that you consider necessary to solve the problem. SOLUTION: Provide full details of the analysis in a logical manner. Develop the analysis as far as possible before substituting numerical values. Give the answer algebraically before computing the final numerical result (if required). Clearly indicate your final answer. 4. Attach a listing of any computer program(s) used in the solution. Grading: Most problems will be graded on a 10-point scale, with points awarded in the following typical distribution: Use of proper format, paper; steps clearly labeled: 1 Schematic, complete with appropriate control volume: 1 Appropriate assumptions: 1 Clearly developed and correct analysis: 6 Algebraic expression of solution (if possible) 1 Total 10 A sample homework solution in this format is given below. Note that in grading, 10% of the score for a problem will be associated with adherence to the required format. NOTE: submitted solutions that completely ignore the format, will be returned with a grade of 0. 5/7

6 Sample Homework Solution Given: A of water issuing into a moving cart, declined at an angle as shown. Find: a) List the proper assumptions required to solve this problem. b) Draw the appropriate control volume and normal area vectors. c) What is the time rate of change of the liquid level? d) What is the thrust force acting on the car by the of water? e) What is the frictional force acting on the car? Schematic: Basic Eqns: Integral form of the continuity equation: 0 dv t CV V da Integral form of the momentum equation: CS F VdV V t V da CV CS Assumptions: 1) Incompressible flow. ) Inviscid flow. 3) Flow in cart has no velocity relative to CV. 4) Uniform area and velocity. 5) Neglect body forces. Solution: a) The proper assumptions are listed above. b) The control volume and normal area vectors are shown in the schematic. c) The components of the velocity U in the control volume are 6/7

7 Sample Homework Solution Continued U cos ˆ sin ˆ U U i U j Thus by mass continuity, which can be rearranged to D dh t d 0 U sin, 4 dt 4sin dh t d dt U d) The momentum equation in the x direction becomes D F t CV udv 3 CS u VdA Then the frictional force is d F U cos U U sin 4sin The thrust force T acting on the car is the component of the force due to the in the x direction and will be balanced by the frictional force F since the car is moving at constant speed U. Thus, d T U U cos U 4 e) The frictional force is found from part (d) to be equal and opposite to the thrust force, d F U U cos U 4 7/7