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7/25/2019 Class 01 Handout
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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