Fall, 2016
Lian Shen
ME5332
Handouts #2
Introduction
1 in the textbook.
What are fluids and fluid mechanics?
1.3 in the textbook.
A fluid is a substance that deforms continuously under an applied shear stress,
however small.
See whiteboard for discussion.
ChEM 4502
Welcome to Chem 4502
http:/www.chemteam.info/Humor/Bob-SchoolQuantum-Mech.html
ChEM 4502
What is Quantum Mechanics
a theory of matter that is based on the concept of
the possession of wave properties by elementary
particles, that affords a math
1.
2.
3.
4.
5.
6.
McQuarrie & Simon problem 3-3
McQuarrie & Simon 3-5
McQuarrie & Simon 3.9
McQuarrie & Simon 3-17
McQuarrie & Simon 3-14
McQuarrie & Simon 3.21
7. Consider a particle in a box that is 5 long, from 0 to 5
0
5
In class, we showed that the
1.
Consider a pair of wave functions, 1 and 2 that are orthonormal. Show that 3 = 1 +
2 and 4 = 1 2 can also be normalized, and that 3 and 4 are orthogonal to each
other.
2. Consider the two un-normalized wave functions 1 =
Normalize them, and then calcu
Chem 4502 Homework #1
Due 9:05 AM Jan 29th, 2016
1.
McQuarrie & Simon 1-2
2. McQuarrie & Simon 1.13
3. Human vision spans a wavelength region of 400 710 nm. How many (give a number) lines in
the hydrogen emission spectrum fall in this range, and what are
Chem 4502
Homework #5 The Hydrogen Atom
Due 3-25-2016 at 9:05 AM
1. The hydrogen atom wavefunctions are split into an angular and radial component.
Write down the Hamiltonian for the Hydrogen atom in spherical coordinates. Show that
it can be separated in
ChEM 4502
Waves Waves Waves
ChEM 4502
Shouldnt Atoms Radiate?
Gravity
Electricity and Magnetism
ChEM 4502
Black Body Radiation
Max Planck
ChEM 4502
Exercise Question:
Incandescent Bulbs made of Tungsten, which melts at ~3300 K
If solid tungsten cant be ho
Chem 4502
Homework Problem Set #4
McQuarrie & Simon
5.1
5.5
5.9
5.12
5.14
13.7
13.8
13.9
For a classical Harmonic Oscillator, the particle turns around at the points x0 and
x0 when its total energy is stored in potential energy. For the ground state of t
DAY 19: Boundary Layer
(after Couette
on the BLACKBOARD)
flat plate : let us neglect the shape of the
leading edge for now
flat plate boundary layer: in blue we highlight the region of the flow
where velocity is influenced by the presence of the solid sur
DAY 24: Flow in conduits
flow entering
a pipe
conduit: pipe, tube or duct completely filled with a flowing fluid (no free surface)
we can apply the energy equation: but, as usual, we have to estimate head losses.
Thats the challenge !
1) Flow regimes
Lam
Lift / drag
When an object is submerged in a flowing fluid, or the
object moves in a stationary fluid the fluid is forced to
flow around the object.
As a result, the object is subjected to forces
perpendicular and parallel to free stream velocity
Drag:
Day 24: Flow around objects
case 1) fluid flowing around a fixed
object (e.g. bridge pier)
case 2) object travelling within a fluid
(cars, ships planes)
two forces are exerted between the fluid and the object
related to:
Skin Friction (Ch9),
Drag, Lift (C
review pre-midterm2
Day 21
Definition of mass and volume flow rate
Q dQ Vn dA V dA
A
A
A
of course, for V normal to n and for V= constant
we come back to our first simple definition Q= VA
Generalized form for the mass flow rate
in case of constant veloc
DAY 16:
ENERGY
Chapter 7
REYNOLDS TRANSPORT
THEOREM
for a system with discrete entrances and exits
B is an extensive property
b=dB/dM is the intensive counterpart
d
bd mb OUT mb IN
dt
dt CV
dBsys
REYNOLDS TRANSPORT
THEOREM & Mass
for a system with disc
Chapter 4: description of fluids in motion
First: fluid motion is defined by the velocity vector v = v(x,y,z)
steady motion:
the flow velocity does not change in time
particular streamline
the streamline is a curve that is
parallel (or tangent) to the vel
Image from Wikipedia.com
Osborne Reynolds
(23 August 184221 February 1912)
Transition from laminar to turbulent flow
Reynolds number
Reynolds stresses
Reynolds-averaged Navier Stokes equations
Reynolds transport theorem
given u=U+u, with U=<u>
Reynold
DAY 17:
Energy Grade Lines &
Hydraulic Grade Lines
EGLs & HGLs
HYDRAULIC GRADE LINE HGL
Graphical
representation of p
(often p G z
)
Recall,
z
if we tap in piezometers,
at each point i, the fluid level will
rise to a height of
pi
zi
HGLS ARE LIKE THE
Fluid Mechanics 3502
Day 2
Fluid Properties Part 2
Solid-Liquid-Gas
Solid under shear vs Fluid under Shear
Density / Specific Weight
Compressible vs. Non-Compressible (contd)
Viscosity
Newtonian vs. Non-Newtonian Fluids
Surface Tension
Vapor Pressure
Summ
Rotation and vorticity
V magnitude increases
V direction changes
note:
the rotation of a fluid element
has to be quantified at a small scale
Consider a fluid element undergoing shear
y
under a linear velocity profile
(constant shear dU/dy)
a small fluid e
Chapter 4: description of fluids in motion
First: fluid motion is defined by the velocity vector v = v(x,y,z)
steady motion:
the flow velocity does not change in time
particular streamline
the streamline is a curve that is
parallel (or tangent) to the vel
p0
Reminder
p=p0+h
h
p p h
If A and B are on a
common horizontal line are
connected by a single liquid pA = pB
0
The pressure at a point in a fluid does
not depend on directions
In fluids, pressure always acts
normal to a solid surface.
A
B
Static pressur
Design in Construction
Prof Challou
Csci 3081W
Lecture 20
The Design Challenge
Design is hard. A wicked" problem.
Tacoma Narrows Bridge
Photos from http:/www.enm.bris.ac.uk/research/nonlinear/
tacoma/tacoma.html
The Design Challenge
Design is hard. A w
More UML, Abstract Syntax Trees
Prof. Dan Challou
Lecture 17
Fall 2013
Logistics
Iteration 2 Due Friday at 11:59pm
Iteration 3 out Thursday
First writing assignment due next Thursday
11/7
Why UML and Abstract Syntax Trees
UML is a design tool
For ite
UML Class Diagrams
Prof. Dan Challou
Lecture 16
Fall 2013
Logistics
First Writing assignment out in Lab tomorrow
Improving your Scanner and Writing about it!
Models
Software Models" are helpful in understanding many aspects
of software development.
They
More Work with UML, Abstract
Syntax Trees, and our Project
Prof. Dan Challou
Lecture 18
Fall 2013
Logistics
Iteration 2 Due Tomorrow at 11:59pm
Iteration 3 out Today! due Nov 21
First writing assignment due next Thursday
11/7
Back to Work
Recall, Selec