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Fluid Mechanics – AS102

Class Note No: 01

July 30, 2007

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About Myself

◮   Luoyi Tao; Office: 104; Phone: 4003

Email: [email protected], [email protected]

◮  Chinese speaking English with heavy accent ...

◮  First time teaching⇒

Please STOP me if you have difficulty to understand me &

I will write on board & slides as much as I can

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About Myself

◮  Teaching philosophy:◮ Open minded, Equal & Interactive◮ Encourage questioning & Open to suggestions

Rewards – Extra points to your grades

◮ Encourage you to talk to each other◮ Entertainment? (from my side)

◮   Confession:◮ Have NO answers to all of... !!◮ Have No answers to most of... ?◮ Do my best !  and Invite you to push & help

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Grading Policy

◮  Homework assignments & Tutorials, 20%

◮  Two quizes, 20% each◮  Final exam, 40%

◮  Plus the extra points

◮   Homework assignments collected; Randomly selectproblems to grade

◮   Special Attention:

◮ key concepts, to be identified , will be repeatedly tested in

the quizes and the final;◮ problems in assignments & tutorials will appear in the

quizes and the final, with “slight” modifications

◮   Attendancy:I (!) & you (?) follow the rules

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Structure of Lectures

◮   Lecture time: W 10:00-10:50; TH 9:00-9:50; F 8:00-8:50

Tutorial time: M 1:00-1:50 (?)

◮  Assignment collected one week after

◮  Office hour ?

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Why Fluid Mechanics

◮  Suspension bridge designs

◮ The first Tacoma Narrows suspension bridge collapsed on

the 7th of November, 1940, at approximately 11:00 AM, dueto wind-induced vibrations (mechanical resonance,torsional twisting mode). Total 1524m long with a mainspan of 853m.

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Why Fluid Mechanics

Figure: http://www.civeng.carleton.ca/Exhibits/Tacoma Narrows/ DSmith/photos.htm

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Why Fluid Mechanics

Figure: http://www.civeng.carleton.ca/Exhibits/Tacoma Narrows/ DSmith/photos.htm

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Why Fluid Mechanics

Figure: http://www.civeng.carleton.ca/Exhibits/Tacoma Narrows/ DSmith/photos.htm

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Why Fluid Mechanics

◮  Boeing 787 dreamliner design

Figure:  http://en.wikipedia.org/wiki/Image:NW Boeing 787.jpg

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Why Fluid Mechanics◮  Skyscraper designs

Figure: http://www.pbs.org/wgbh/buildingbig/wonder/structure/ 

empirestate1 skyscraper.html

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Why Fluid Mechanics

◮  Hurricanes tracking

Figure:  http://en.wikipedia.org/wiki/Image:Hurricane KatrinaAugust 28 2005 NASA.JPG

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Why Fluid Mechanics

◮   Clay Institute Millennium Prize on N-S equations (US $1million)

Nash (?), Lions (?), ...

◮   Turbulence modeling – Chandrasekhar, Heisenberg,

Laudau, ..., put their hands on N-S ...

◮  Opportunities waiting for YOU ...

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Structure of the Course

◮  Main Content: (roughly following the course syllabus)◮ Vector & Tensor Calculus

◮ Cartesian tensors – indicial notations and conventions

(economical in bookkeeping and operation )

◮ Green’s & Stokes’ theorem, divergence theorem of Gauss

◮ Introduction to general curvilinear tensors(understanding how to write the motion equations in 

cylindrical and spherical coordinates...)

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Structure of the Course

◮  Main Content (ctd.):

◮ Hydrostatics & Aerostatics

◮ Stationary

◮ Rigid body motion

◮ Buoyant forces

S f h C

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Structure of the Course

◮  Main Content (ctd.):

◮ Basic concepts in describing fluid motion like

◮ Eulerian & Lagrangian

◮ Streamline, streakline, pathline

◮ Kinematics

S f h C

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Structure of the Course

◮  Main Content (ctd.):

◮ Equations of Motion (for air and water & the like)

◮ Conservation laws – mass, linear momentum, angular

momentum, energy◮ 2nd law of thermodynamics – its role in constructing the

constitutive models (& selecting solutions)

◮ Integral (global) and differential (local) forms

◮ Inertial and non-inertial rotating frames

◮ Inviscid & potential flows

St t f th C

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Structure of the Course

◮  Main Content (ctd.):

◮ Bernoulli equation

◮ derivation & applications

◮ Flow examples like Couette flow, Hagen-poiseullie flow ...

◮ (?) Sound wave and 1-D shock wave – 1-D compressiblemotion

(?) Boundary layer theory (flat plate)

St t f th C

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Structure of the Course

◮  Main Content (ctd.):

◮ Dimensional analysis

◮ The Rayleigh method

◮ Buckingham Pi theorem

◮ Similitude

Contin m Treatment

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Continuum Treatment

INTO the lecture NOW 

What is a fluid (gas, liquid)?

◮  “shape determined by its confines”?(what about the effect of gravity on liquids?)

◮  “unable to resist shearing”?

(what about the deformation of rocks during million years?)

(about scales)

Continuum Treatment

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Continuum Treatment

1st Restriction:

NOT deal with individual molecules & atoms in this courseWHY??

◮   Interests –  Macro-scale motions such as◮ Air flow around an airplane

◮ (Water or Air) Pipe flows (of large size)◮ Atmospheric & Oceanic motion, etc.,

where◮ enough number of molecules present◮ details of micro-scale motions not essential & collectively

accountable through temperature, pressure...◮ integral, differential equations of motion adequate

(continuum treatment )

Continuum Treatment

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Continuum Treatment

◮  Micro, molecular picture. Air, ∼ 1020/cm3 (under std)

◮  Hamilton’s equations:

d q

dt   =

 ∂ H 

∂ p,

  d p

dt   = −

∂ H 

∂ q

◮ Hamiltonian H  =  H (q, p) =? (monatomic, diatomic; m-m,m-w)

◮ IC’s?◮ Capacity in math & computers?

Continuum Treatment

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Continuum Treatment

◮   Covered:Fluids like air & water  under “normal” conditions

Or Newtonian fluids (to be qualified later )

◮   Not Covered:Chemical reactions like combustion or in hypersonic flow;

Phase transitions;

Materials like blood, asphalt ...;

Heat or Mass transfer