Fluid Mechanics and Applications MECN 3110

1. Fluid Mechanics and Applications MECN 3110 Inter American University of Puerto Rico Professor: Dr. Omar E. Meza Castillo

2. Course Information • Catalog Description: Analysis of fluid properties. Use of fluids static to manometry and hydrostatic forces. Application of the principles of mass and energy conservation, conservation of impulse and amount of linear movement in the solution of dynamics of fluid problems. Development of methodologies for dimensional analysis, similarity and modeling. Requires 45 hours of lecture and 45 hours of lab. • Prerequisites:MECN 3010 - Vector Mechanics for Engineers: Dynamics, MATH 3400 - Differential Equations. • Course Text: F.M. White, Fluid Mechanics, 6th Ed., McGraw-Hill, 2008.

3. Course Information • Absences:On those days when you will be absent, find a friend or an acquaintance to take notes for you or visit Blackboard. Do not call or send an e-mail the instructor and ask what went on in class, and what the homework assignment is. • Homework assignments:Homework problems will be assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on any white paper with no more than one problem written on one sheet of paper. Homework will be collected when due, with your name written legibly on the front of the title page. It is graded on a 0 to 100 points scale. Late homework (any reason) will not be accepted.

4. Course Information • Problem-Solving Technique: • Known • Find • Assumptions • Schematic • Analysis, and • Results • Quiz : There are four partial quizes during the semester. • Partial Exams and Final Exam: There are three partial exams during the semester, and a final exam at the end of the semester.

5. Course Information • Project: There is a project throughout the semester. A project will be work out by a group of three students, each group will elect a group leader. Progress reports will be required every two weeks and there will be weekly meetings of the group leaders with the instructor. At the middle and end of the semester, an oral and a written report are required. Each student will earn an individual grade which is tied to his/her progress and participation in the successful completion of the design project. Each student will also earn a group grade which is based on the reports. • Laboratory Reports: There seven or eight experimental laboratories throughout the semester. Laboratory reports must be submitted by each group, one week after the experiment is done. The report must be written in a professional format.

6. Course Grading • The total course grade is comprised of homework assignments, quizes, partial exams, final exam, and a project as follows: • Homework (9) 15% • Quiz (4) 15% • Partial Exam (3) & Final Exam 25% • Final Project 20% • Laboratory Reports 25% 100% • Cheating: You are allowed to cooperate on homework by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from others will be considered academic misconduct and will get no points.

7. Course Materials • Most Course Material (Course Notes, Handouts, and Homework) on WebPage of the course • Power Point Lectures will posted every week or two • Office Hours: • Tuesday and Thursday @ 10:00 to 11:30 PM • Email: mezacoe@gmail.com

8. Course Outline • General Principles • Fluids • Fluid Statics • Fluid Dynamics • Kinematics • Control-volume Analysis • Differential Analysis • Pipe Flow • Flow around immersed bodies • Compressible flow

9. Chapter 1 Introduction and Basic Concepts

10. Course Objectives • To describe the basic principles of fluid mechanics. Thermal Systems Design Universidad del Turabo

11. Introduction: • Fluid mechanics is the science and technology of fluids either at rest (fluid statics) or in motion (fluid dynamics) and their effects on boundaries such as solid surfaces or interfaces with other fluids.

12. Introduction: Fluid and the non-slip condition • Definition of a fluid: A substance that deforms continuously when subjected to a shear stress. • Consider a fluid between two parallel plates, which is subjected to a shear stress due to the impulsive motion of the upper plate. • No slip condition: no relative motion between fluid and boundary, i.e., fluid in contact with lower plate is stationary, whereas fluid in contact with upper plate moves at speed U. • Fluid deforms, i.e., undergoes rate of strain θ due to shear stress τ.

13. Introduction: Fluid and the non-slip condition • Newtonian Fluid • Both liquids and gases behave as fluids • Liquids: • Closely spaced molecules with large intermolecular forces. • Retain volume and take shape of container.

14. Introduction: Fluid and the non-slip condition • Gases: • Widely spaced molecules with small intermolecular forces. • Take volume and shape of container.

15. Continuum Hypothesis • In this course, the assumption is made that the fluid behaves as a continuum, i.e., the number of molecules within the smallest region of interest (a point) are sufficient that all fluid properties are point functions (single valued at a point). • The limiting volume δV* is about 10-9 mm3 for all liquids and for gases at atmospheric pressure.

16. Dimensions and Units • System International and British Gravitational Systems

17. Dimensions and Units • Secondary Dimensions in Fluid Mechanics

18. Weight and Mass

19. System, Extensive and Intensive

20. Properties Involving Mass or Weight of the Fluid Specific Gravity SG=

21. Variation in Density

22. Variation in Density

23. Properties Involving the Flow of Heat

24. Viscosity • Recall definition of a fluid (substance that deforms continuously when subjected to a shear stress) and Newtonian fluid shear / rate-of-strain relationship:

25. Viscosity

26. Viscosity

27. The Reynolds Number • The primary parameter correlating the viscous behavior of all newtonian fluids is the dimensionless Reynolds Number: • Where V and L are characteristic velocity and length scales of the flow. The second form of Re illustrates that the ratio of μ and ρ has its own name, the kinetic viscosity

28. The Reynolds Number

29. Flow between Plates • A classic problem is the flow induced between a fixed lower plate and an upper plate moving steadily at velocity V, as shown in figure. The clearance between plates is h, and the fluid is newtonian and does not slip at either plate. If the plates are large, this steady shearing motion will set up a velocity distribution u(y), as shown, with v=w=0. The fluid acceleration is zero everywhere. • With zero acceleration and assuming no pressure variation in the flow direction, you should show that a force balance on a small fluid element leads to the result that the shear stress is constant throughout the fluid.

30. Flow between Plates • Integrating we obtain

31. Flow between Plates • The velocity distribution is linear, as shown in Figure, and the constants a and b can be evaluated from the no-slip condition at the upper and lower walls: • Hence a=0 and b=V/h. Then the velocity profile between the plates is given by

32. Nonnewtonian Fluidds

33. Surface Tension and Capillarity • Two non-mixing fluids (e.g., a liquid and a gas) will form an interface. The molecules below the interface act on each other with forces equal in all directions, whereas the molecules near the surface act on each other with increased forces due to the absence of neighbors. That is, the interface acts like a stretched membrane

34. Surface Tension and Capillarity Where: • Fσ=Line force with direction normal to the cut • σ =coefficient of surface tension • L= Length of cut through the interface

35. Surface Tension and Capillarity • Effects of surface tension:

36. Surface Tension and Capillarity • Effects of surface tension:

37. Surface Tension and Capillarity • Capillary Tube Assuming θ=0o

38. Surface Tension and Capillarity • Pressure across curved interfaces • Cylindrical interface σ=Y

39. Surface Tension and Capillarity • Spherical interface • For a bubble • General case for an arbitrarily curved interface whose principal radii or curvature are R1 and R2

40. Example 1

41. Application Problems

42. Homework1  WebPage Due, Wednesday, February 02, 2011 Omar E. Meza Castillo Ph.D.