Inter - Bayamon
Lecture
Fluid Mechanics and Applications
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Fluid Mechanics and Applications
MECN 3110
Inter American University of Puerto Rico
Professor: Dr. Omar E. Meza Castillo
Inter - Bayamon
Fluid Mechanics and Applications
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:
Equations.
Dynamics,
MATH
3400
-
Differential
 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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Fluid Mechanics and Applications
Course Information
 Problem-Solving Technique:
A. Known
B. Find
C. Assumptions
D. Schematic
E. Analysis, and
F. 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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Fluid Mechanics and Applications
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 @ 10:00 to 11:30 PM
 Email: mezacoe@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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Fluid Mechanics and Applications
Chapter 1
Introduction and Basic Concepts
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Interdel
ApplicationsUniversidad
andDesign
Mechanics
Fluid
- Bayamon
Turabo
Systems
Thermal
Course Objectives
 To describe
mechanics.
the
basic
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principles
of
fluid
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Fluid Mechanics and Applications
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 θ due to shear
stress τ.
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Introduction: Fluid and the non-slip condition
Fluid Mechanics and Applications
 Both liquids and gases behave as fluids
 Newtonian Fluid
 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
intermolecular forces.
 Take volume and shape of container.
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small
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Fluid Mechanics and Applications
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).
m
  lim
V  V* V
 The limiting volume δV* 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-ofstrain 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 ρ has its own
name, the kinetic viscosity
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The Reynolds Number
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Fluid Mechanics and Applications
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.
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Fluid Mechanics and Applications
Flow between Plates
 Integrating we obtain
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Fluid Mechanics and Applications
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
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Inter - Bayamon
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
F  L
Where:
 Fσ=Line force with direction normal to the cut
 σ =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:
(R 2 ) p  2 R Cos
R h  2 RCos
2
2Cos
h
R
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Surface Tension and Capillarity
 Capillary Tube
Assuming θ=0o
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d2
 p  d 
4
d
h  
4
4
h 
d
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Fluid Mechanics and Applications
Surface Tension and Capillarity
 Pressure across curved interfaces
σ=Y
2RL p  2L
a) Cylindrical interface

p 
R
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Surface Tension and Capillarity
b) Spherical interface
R p  2R
2
2
p 
R
c) For a bubble
4
p bubble  2p droplet 
R
d) General case for an arbitrarily curved interface whose
principal radii or curvature are R1 and R2
p  R 11  R 21 
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Inter - Bayamon
Example 1
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Fluid Mechanics and Applications
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Inter - Bayamon
Fluid Mechanics and Applications
Homework1  WebPage
Due, Wednesday, February 02, 2011
Omar E. Meza Castillo Ph.D.
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