Fluid Mechanics
General Fluid Mechanics
Physics Contributors
Baker
NavierStokes Equations
The NavierStokes equations are the fundamental partial differentials equations that describe the flow of incompressible
fluids. Using the rate of stress and rate o
LECTURE NOTES ON
INTERMEDIATE FLUID MECHANICS
Joseph M. Powers
Department of Aerospace and Mechanical Engineering
University of Notre Dame
Notre Dame, Indiana 465565637
USA
updated
03 May 2015, 5:47pm
2
CC BYNCND. 03 May 2015, J. M. Powers.
Contents
Pr
http:/moffatt.tc
Reprinted without change of pagination from the
Journal of Fluid Mechanics, volume 18, part 1, pp. 118
Viscous and resistive eddies near a sharp corner
By H. K . MOFFATT
Trinity College, Cambridge
(Received 20 June 1963)

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Some s
6
Typical Vortex Solutions
In Chap. 4 we have studied attached and free vortex layers, and seen that
the rolling up of a free vortex layer forms a vortex which has the highest
possible vorticity concentration as mentioned in the beginning of Sect. 1.3
(th
Extended Lubrication Theory: Estimation of Fluid Flow in Channels with Variable
Geometry
Behrouz Tavakol and Douglas P. Holmes
Department of Engineering Science & Mechanics, Virginia Tech, Blacksburg, VA 24061
Guillaume Froehlicher and Howard A. Stone
arX
57:020 Fluid Mechanics
Professor Fred Stern Fall 2005
Chapter 4
1
Chapter 4: Fluids Kinematics
4.1 Velocity and Description Methods
Primary dependent variable is fluid velocity vector
V = V ( r ); where r is the position vector
If V is known then pressure
1
Icampus project
Schoolwide Program on Fluid Mechanics
Modules on High Reynolds Number Flows
K. P. Burr, T. R. Akylas & C. C. Mei
CHAPTER TWO
TWODIMENSIONAL LAMINAR BOUNDARY LAYERS
1
Introduction.
When a viscous fluid flows along a fixed impermeable w
CBE 6333, R. Levicky
1
Examples of Laminar Flows
In laminar flows the fluid moves in "layers" or laminae, in contrast to the apparently chaotic motion of
turbulent flow. Laminar flows in many different geometries have been investigated with the help of
tr
20
Creeping flow
Viscosity may be so large that a fluid only flows with difficulty. Heavy oils, honey,
even tight crowds of people, show insignificant effects of inertia, and are instead
dominated by internal friction. Such fluids do not make spinning vor
The Material Derivative
The equations above apply to a fluid element which is a small
blob of fluid that contains the same material at all times as
the fluid moves.
Figure 1. A fluid element, often
called a material element. Fluid
elements are small blobs
5
Euler and Lagrange descriptions
Euler approach The fluid properties p, , v are
written as functions of space and times. The
flow is determined by the analyzing the behavior
of the functions.
Lagrange approach Pieces of the fluid are
tagged. The fluid fl
School of Mechanical Aerospace and Civil Engineering
Introduction
3rd Year Fluid Mechanics
When studying inviscid flows we simplified the NavierStokes equations
to be applicable to situations where viscous effects could be neglected.
For irrotational inv
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1.1 Lagrangian vs. Eulerian points of View
In ﬂuid mechanics we describe the motion of liquids and gases (such as water and air) using
the approach of continuum mechanics, wherein the ﬂuid is characteriz
Todays Objectives 01072015
Welcome to ME 475 Advanced Topics in
Thermodynamics and Heat Transfer: Internal
Combustion Engines!
Describe the components of internal combustion
engines using the proper terminology
Describe the fourstroke cycle for both co
Review 01072015
Course overview
Brief history of engines
Engine terminology
What are the following terms?
aBDC
rc
WOT
OHV
Todays Objectives 01122015
Describe the fourstroke cycle for both compression
and spark ignition engines
Explain key opera
Review 01212015
BSFC
FA, AF ratios
Thermal efficiency
Fuel conversion efficiency
Combustion efficiency
Volumetric efficiency
What are the main emissions from a SI engine?
What are the main emissions from a CI engine?
What would you expect the main emiss
Review 01122015
Engine terminology
What are the following terms? aBDC, rc, WOT
Engine components
What are the following components and where are the located in
the engine in relation to other components?
Crankshaft, wrist pin, main bearing
Four stroke
Review 01142015
What are the requirements for a CI engine
to run?
Twostroke cycle operation
Pros/cons of the twostroke cycle
VC
TC
B
S
L
Pros?
Cons?
Engine geometry bore, stroke,
connecting rod length, crank offset, piston
position, crank angle
Pist
Review 01262015
Airstandard, Const. V Cycle (Otto) see next slide
Airstandard, Const. P Cycle (Diesel) see next slide
AirStandard, Const. P Cycle
AirStandard, Const. V Cycle
61: constant pressure intake
12: isentropic compression
Assuming con
Capacitors and Inductors
Capacitors
I
+
V

+

I
+
v
CF
Q
here, F stands for Farads
dv
v
p=v
p=v
p dt = C v dv
= C
W(t)  = 
W(t) =
5 F
inductors
H
Where H stands for Henrie
v
d
p=v
p=
p dt = Ld
= L
W(t)  = 
W(t) =
3H
Capacitors in Parallel:
Capacitor
Review 01162015
Torque
Power = torque * angular velocity, paying respect to proper
units recall that revolutions is a unit, whereas
radians is really just a space saver, it disappears when
multiplied by something else
Indicated work the work that is
Structural Element Design
In order to select the sizes of structural elements, it is first
necessary to calculate the stresses induced from applied loads.
Normal stress is induced by bending moments and axial forces
Shear stress is induced by torsional
Example 1. Calculate the weight of 6A1 4V Titanium relative to 2024T3 Aluminum in
Tension, Bending, and Buckling.
The properties for 6Al4V Titanium are as follows:
Density = 0.16 Ib/in3
Modulus ofElasticity = 16 x 106
Ultimate Stress = 150 ksi
pep”, (E
Example Problem 1
Find the maximum normal stress and the shear stress distribution
over the cross section of the beam shown below.
Air/1.x", WM 51.17 Lx/tLL. 6‘36: mm: ('3') FIK‘EVB 5"“3
r' 3 t '2 7 4
. ,.  :2
,3}: 1,’r(27AL)+ 35*}3 ‘al Fr (
MAE 598/426 Design of Aerospace Structures
Course Objectives
Loading Conditions & Procedures
Metallic & Composite Aerospace Materials
Procedures for Sizing Aerospace Structures
 Design of Structural Members in Bending & Torsion
 Buckling Design of St
4cAo s
I
Problem
Example
of
l
e
W h e nl a n d i n g n a c a r r i e ra 1 0 , 0 0 0b a i r p l a n i s g i v e na d e c e l e r a t i o n 3 9
o
,
by meansof an anestinghookas shownin the flgurebelow.
( a ) F j n dt h e t e n s i o nn t h e c a b l e t h e
Flight Vehicle Imposed Loads
All loading conditions imposed on a structure must be known before the
flight vehicle structure can be designed. The load conditions are those
encountered both in flight and on the ground.
Since it is impossible to investigate
Composite Laminates
A useful structure will require that fibers be oriented in more
than one direction. A common approach to creating such a
structure is by stacking layers, or plies, to form a laminate.
Ply orientations are defined using the angle (12 a