INTRODUCTORY FLUID MECHANICS

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MAE 101 A

INTRODUCTORY FLUID MECHANICS

Winter 2006


Instructor:
Professor Juan C. Lasheras. (
lasheras@ucsd.edu
)





Teaching Assistants:


Kyle Brucker,
kbrucker@ucsd.edu
, 550
-
2057

Julie Vanderhoff,
jcrockett@ucsd.edu
, 822
-
0129

Baldomero Alonso
-
Latorre,
balonsol@ucsd.edu
,

534
-
3959


Rubing Tang,
r1tang@ucsd.edu
, 455
-
0417




Lecture Room

:

PETER 110
Time:

Tuesdays and Thursdays 5:00
PM

6:20 PM


TA Discussion Sessions:

TAs will hold weekly (optional) discussion
sessions to solve sample problems and answer student questions.



Course Description:


Fluid statics; fluid kinematics; integral and differential forms of the
conservation laws of mass, momentum and energy; Bernoulli equation;
potential flows; dimensional analysis and similitude.



Textbook
: INTRODUCTION TO FLUID MECHANICS. Fox,
McDonald and Pritchard. John Wiley and Sons, Inc. 2004 (6th edition)

Tentative Class Schedule



Week




Topics



Week 1
,



Introduction. Fundamental Concepts.






(Chapter 1, 2)


Week 2
,




Fluid Properties

(Chapter 2)


Week 3
,



Fluid Statics.

Pressure Variation,






Hydrostatic Forces, Buoyancy

(Chapter 3)


Week 4
,



Basic Equations in Integral Form for





Control Volume

(Chapter 4)


Week 5
,



Control Volume Analysis and






Application

(Chapter 4).


Week 6
,



Midterm Exam






Kinematics . Motion of a Fluid Particle

(Chapter 5).


Week 7
,



Differential Analysis of Fluid Motion.






(Chapter 5)


Week 8
,



Conservation of Mass and Momentum.






(Chapter 5)


Week 9
,



Incompressible Inviscid Flow. Euler’s





Equation.


Bernoulli Equation.


(Chapter 6)


Week 10
,



Dimensional Analysis.

(Chapter 7)


Week 11
,



Final Exam



Homework:


Homework will be assigned each week and collected on specific due date.
Late homework will not be accepted under any circumstances.


Questions regarding the homework scores


see TAs in person. Re
-
grades
will not be considered beyond 1 week after the graded homework has been
returned.



Grading:


Homework:





10%


In class quizzes (2) (30min/each):


10%


Midterm Exam (1):




35%


Final Exam:





45%



Academic Policy on Integrity and Scholarship.


Students are encouraged to discuss course topics and homework with each
other. However, each student must submit his/her own work.


Refer to Student Link website:
UCSD Policy on Integrity and Scholarship
.




Fluid Mechanics
, physical science dealing with the action of
fluids at rest (fluid statics) or in motion (fluid dynamics), and their
interaction with flow devices and applications in engineering.



The subject branches out into sub
-
disciplines such as:
Aerodynamics

-

deals with the motion of air and other gases, and
their interactions with bodies in motion such as lift and drag;



Hydraulics

-

application of fluid mechanics to engineering devices
involving liquids such as flow through pipes, weir and dam
design;



Geophysical fluid dynamics
-

fluid phenomena associated with the
dynamics of the atmosphere and the oceans such as hurricane and
weather systems,

Bio
-
fluid mechanics
-

fluid mechanics involved in biophysical
processes such as blood flow in arteries, and many others.


Fluid dynamics has a wide range of applications, including
calculating
forces

and
moments

on
aircraft
, determining the
mass
flow rate

of
petroleum

through pipelines, predicting
weather

patterns.


Fluid
: A continuous, amorphous substance
whose molecules move freely past one another
and that has the tendency to assume the shape
of its container; a liquid or gas.



A substance that deforms continuously (flows)
under the application of a shear (tangential)
stress


Fluids

share the properties of not resisting deformation
and the ability to flow (perhaps otherwise described as
their ability to take on the shape of their containers).


These properties are typically a function of their
inability to support a
shear stress

in static
equilibrium
. While in a solid, stress is a function of
strain, in a fluid stress is a function of rate of strain.

dynamic viscosity,




in a fluid stress is a function of rate of strain


MECHANICS
: That science, or branch of Physics, which
treats of the action of forces on bodies.



That part of mechanics which considers the action of forces
in producing rest or equilibrium is called
statics
; that which
relates to such action in producing motion is called
dynamics
.


The term mechanics includes the action of forces on all
bodies, whether solid, liquid, or gaseous. It is sometimes,
however, and formerly was often, used distinctively of
solid bodies only



FLUID MECHANICS
: The branch of Physics, which
treats of the action of forces on fluids.



In the case of liquid is called also
hydrostatics
, or
hydrodynamics
,
according as the laws of rest or of motion are considered.


Aerodynamics
: The mechanics of bodies moving in the atmosphere


The mechanics of gaseous bodies is called also
pneumatics
.

Why study Fluid Mechanics?

Geophysical, Environmental Fluid Mechanics, Climatology

Why study Fluid Mechanics?

OCEANOGRAPHY

Why is the water always cold in
Southern California Pacific Coast?

Why is the water always cold in
Southern California Pacific Coast?


Upwelling

along the coast caused by Ekman transport of waters
(waters move to the right of the wind).


The waters moved offshore are replaced by waters from below. This
brings cold, nutrient rich waters to the surface.



The effect of winds on the vertical movement of water

Why study Fluid Mechanics?

The effect of winds on the vertical movement of water

Downwelling caused by Ekman transport onshore (movement of water
to the right of the wind direction).




Why study Fluid Mechanics?

Long
-
term Weather Prediction

Why study Fluid Mechanics?

Weather Forecasting, Climatology

Why study Fluid Mechanics?

Geophysical Fluid Mechanics

Why study Fluid Mechanics?

AERODYNAMICS

Why study Fluid Mechanics?

SUPERSONIC AERODYNAMICS

Why study Fluid Mechanics?

AERODYNAMICS

Why study Fluid Mechanics?

AERODYNAMICS

Why study Fluid Mechanics?

JET (aerodynamic) NOISE

Why study Fluid Mechanics?

HYDRODYNAMICS

Why study Fluid Mechanics?

Combustion, Chemically Reacting Flows, Chemical Engineering

Why study Fluid Mechanics?

Chemical Reactors

Fire Safety, Flame Propagation

Why study Fluid Mechanics?

Heat Transfer

Why study Fluid Mechanics?

Environmental Fluid Mechanics

Pollution Dispersion

Why study Fluid Mechanics?

Aerospace Propulsion

Why study Fluid Mechanics?

Industrial Gas Turbine for Power Generation


Abdominal Aortic Aneurysms (AAA)


Fusiform
:
spindle shaped, may involve considerable portion of the vessel






FIGURE 4. CT angiography showing an
terior (top) and lateral (bottom)
views of an abdominal aortic aneurysm.


BIOFLUID MECHANICS

Three
-
dimensional Volume rendering of an
Abdominal Aortic Aneurysm

R

L


AAA

Occurrence


Affected: 4
-
5 % of U.S. Population: 1,500,000
patients


250,000 new cases per year


Responsible for ~25,000 deaths per year


10
th

leading cause of death in males (>55 years)


Upon rupture death is often sudden


Mortality rate as high as 80
-
90 %


A

A

A
-
A cross cut:

Flow in the transverse plane

Flow in the longitudinal plane

-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
0
0.2
0.4
0.6
0.8
1
t/T
Normalized flow rate
L
Recirculation eddies

Jet detached from the walls

Magnitude of 2
-
Dimensional

Velocity Field

Sinusoidal pressure waveform



Pressure and shear exerted by the blood flow on the vessel wall

BIFURCATING VESSEL:
PCommA

ICA

PComm A
.

MCA

ACA

Silicon model of the Posterior Communicating
Artery Aneurysm

BIFURCATING VESSEL:
PCommA

DPIV MEASUREMENTS

Internal Carotid Artery

Posterior Communicating
Artery

Anterior Cerebral Artery

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
Flow separation region

VELOCITY FIELD

Qpeak= 10 ml/s Repeak= 740 Remean= 225 Wo = 1.2


Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
Three
-
dimensional
counter
-
clockwise vortex

VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
The vortex seems to break
down into two, or even three
vortices

VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
Flow separation region

VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

Carotid flow rate
0
2
4
6
8
10
12
0
200
400
600
800
1000
Time (ms)
Flow rate (ml/s)
VELOCITY FIELD

COMPARISON OF PRESSURE
MEASUREMENTS

26.5
31.5
36.5
41.5
46.5
51.5
56.5
61.5
66.5
71.5
0.0
0.1
0.3
0.4
0.5
0.7
0.8
0.9
1.1
1.2
1.3
1.4
1.6
t (s)
P (mmHg)
Parent Vessel
Pcom Aneurysm
Why study Fluid Mechanics?

Why study Fluid Mechanics?

Why study Fluid Mechanics?

Why study Fluid Mechanics?

Aerodynamics of a Football