Fluid Mechanics and Applications Inter - Bayamon Lecture 1 Fluid Mechanics and Applications MECN 3110 Inter American University of Puerto Rico

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon  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 Vector Mechanics for Engineers: Dynamics, MATH Differential Equations.  Course Text: F.M. White, Fluid Mechanics, 7 th Ed., McGraw-Hill, Course Information

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon  Absences  Homework assignments: Homework problems will be assigned on a regular basis. Late homework (any reason) will not be accepted. Recycled paper can be used but clean presentation is expected.  Partial Exams and Final Exam: There are two partial exams during the semester, and a final exam at the end of the semester.  Laboratory Reports: There six or seven 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. 3 Course Information

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon  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 may be required and there will be meetings of the group leaders with the instructor. At the end of the semester, a written report is 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 report. 4 Course Information

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Course Grading  The total course grade is comprised of homework assignments, quizes, partial exams, final exam, and a project as follows: Homework 10% Partial Exams (2) 34% Final Project16% Laboratory Reports20% Final exam20% 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. 5

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon  Office Hours: Monday and 2:00 to 4:00 PM  6 Course Materials

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Introduction and Basic Concepts Chapter 1 7

Fluid Mechanics and Applications Inter - Bayamon  To describe the basic principles of fluid mechanics. Thermal Systems Design Universidad del Turabo 8 Course Objectives

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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. 9

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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. 10

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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. 11

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Introduction: Fluid and the non-slip condition  Gases: Widely spaced molecules with small intermolecular forces. Take volume and shape of container. 12

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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 mm 3 for all liquids and for gases at atmospheric pressure. 13

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Dimensions and Units System International and British Gravitational Systems 14

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Dimensions and Units Secondary Dimensions in Fluid Mechanics 15

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Weight and Mass 16

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon System, Extensive and Intensive 17

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Properties Involving Mass or Weight of the Fluid 18 Specific Gravity SG=

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Variation in Density 19

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Variation in Density 20

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon The Principle of Dimensional Homogenity 21 All equations must be dimensionally homogeneous Verify dimensionality of: P.1.17

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Properties Involving the Flow of Heat 22

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Viscosity Recall definition of a fluid (substance that deforms continuously when subjected to a shear stress) and Newtonian fluid shear / rate-of- strain relationship: 23

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Viscosity 24

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Viscosity 25

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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 kinematic viscosity 26

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon The Reynolds Number 27

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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. 28

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Flow between Plates Integrating we obtain 29

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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 30 Problem 1.38

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Nonnewtonian Fluidds 31

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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 32

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon 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 33

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Surface Tension and Capillarity Effects of surface tension: 34

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Surface Tension and Capillarity Effects of surface tension: 35

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Surface Tension and Capillarity Capillary Tube 36 Assuming θ=0 o

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Surface Tension and Capillarity Pressure across curved interfaces a)Cylindrical interface 37 σ=Y

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Surface Tension and Capillarity b)Spherical interface c)For a bubble d)General case for an arbitrarily curved interface whose principal radii or curvature are R 1 and R 2 38

Chapter 1 Fluid Mechanics and Applications Inter - Bayamon Examples Prob Prob. 1.67