Fluid Mechanics and Applications MECN 3110

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Fluid Mechanics and Applications MECN 3110

• Inter American University of Puerto Rico
• Professor Dr. Omar E. Meza Castillo

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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.

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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.

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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.

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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.

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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.

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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 _at_ 1000 to 1130 PM
• Email mezacoe_at_gmail.com

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Course Outline

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

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Introduction and Basic Concepts

• Chapter 1

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Course Objectives

• To describe the basic principles of fluid
  mechanics.

Thermal Systems Design Universidad del Turabo
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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.

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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 ?
  due to shear stress t.

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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.

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Introduction Fluid and the non-slip condition

• Gases
• Widely spaced molecules with small intermolecular
  forces.
• Take volume and shape of container.

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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 dV is about 10-9 mm3 for all
  liquids and for gases at atmospheric pressure.

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Dimensions and Units

• System International and British Gravitational
  Systems

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Dimensions and Units

• Secondary Dimensions in Fluid Mechanics

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Weight and Mass
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System, Extensive and Intensive
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Properties Involving Mass or Weight of the Fluid
Specific Gravity SG
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Variation in Density
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Variation in Density
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Properties Involving the Flow of Heat
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Viscosity

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

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Viscosity
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Viscosity
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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 ? has its own
  name, the kinetic viscosity

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The Reynolds Number
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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 vw0. 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.

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Flow between Plates

• Integrating we obtain

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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 a0 and bV/h. Then the velocity profile
  between the plates is given by

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Nonnewtonian Fluidds
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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

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Surface Tension and Capillarity

• Where
• FsLine force with direction normal to the cut
• s coefficient of surface tension
• L Length of cut through the interface

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Surface Tension and Capillarity

• Effects of surface tension

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Surface Tension and Capillarity

• Effects of surface tension

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Surface Tension and Capillarity

• Capillary Tube

Assuming ?0o
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Surface Tension and Capillarity

• Pressure across curved interfaces
• Cylindrical interface

sY
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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

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Example 1
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Application Problems
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Homework1 ? WebPage
Due, Wednesday, February 02, 2011
Omar E. Meza Castillo Ph.D.