Fluid Mechanics
• Fluids essential to life• Human body 65% water• Earth’s surface is 2/3 water• Atmosphere extends 17km above the earth’s surface
• History shaped by fluid mechanics• Geomorphology• Human migration and civilization• Modern scientific and mathematical theories and methods• Warfare
• Affects every part of our lives
57:020 Fluid Mechanics 2
• Fluids essential to life• Human body 65% water• Earth’s surface is 2/3 water• Atmosphere extends 17km above the earth’s surface
• History shaped by fluid mechanics• Geomorphology• Human migration and civilization• Modern scientific and mathematical theories and methods• Warfare
• Affects every part of our lives
HistoryFaces of Fluid Mechanics
57:020 Fluid Mechanics 3
Archimedes(C. 287-212 BC)
Newton(1642-1727)
Leibniz(1646-1716)
Euler(1707-1783)
Navier(1785-1836) Stokes
(1819-1903)Reynolds(1842-1912)
Prandtl(1875-1953)
Bernoulli(1667-1748)
Taylor(1886-1975)
Significance
• Fluids omnipresent• Weather & climate• Vehicles: automobiles, trains, ships, and
planes, etc.• Environment• Physiology and medicine• Sports & recreation• Many other examples!
57:020 Fluid Mechanics 4
• Fluids omnipresent• Weather & climate• Vehicles: automobiles, trains, ships, and
planes, etc.• Environment• Physiology and medicine• Sports & recreation• Many other examples!
Sports & Recreation
Water sports Offshore racingCycling
57:020 Fluid Mechanics 9
Auto racing Surfing
Fluids Engineering
Reality
Fluids Engineering System Components Idealized
57:020 Fluid Mechanics 10
22 PBUD
2 2s SM SNU U U
EFD, Mathematical Physics Problem Formulation
AFD, CFD,mU
Analytical Fluid Dynamics
• The theory of mathematical physicsproblem formulation
• Control volume & differential analysis• Exact solutions only exist for simple
geometry and conditions• Approximate solutions for practical
applications• Linear• Empirical relations using EFD data
57:020 Fluid Mechanics 11
• The theory of mathematical physicsproblem formulation
• Control volume & differential analysis• Exact solutions only exist for simple
geometry and conditions• Approximate solutions for practical
applications• Linear• Empirical relations using EFD data
Analytical Fluid Dynamics
• Lecture Part of Fluid Class• Definition and fluids properties• Fluid statics• Fluids in motion• Continuity, momentum, and energy principles• Dimensional analysis and similitude• Surface resistance• Flow in conduits• Drag and lift
57:020 Fluid Mechanics 12
• Lecture Part of Fluid Class• Definition and fluids properties• Fluid statics• Fluids in motion• Continuity, momentum, and energy principles• Dimensional analysis and similitude• Surface resistance• Flow in conduits• Drag and lift
Analytical Fluid Dynamics
Schematic
• Example: laminar pipe flowAssumptions: Fully developed, LowApproach: Simplify momentum equation,integrate, apply boundary conditions todetermine integration constants and useenergy equation to calculate head loss
UD 2000Re
00
0
57:020 Fluid Mechanics 13
Exact solution :2 21( ) ( )( )4
pu r R rx
Friction factor:88 64
Re2 2w
dudywf
V V
xgyu
xu
xp
DtDu
2
2
2
2
Head loss:1 2
1 2 fp pz z h
2
2
322fL V LVh fD g D
00
0
Analytical Fluid Dynamics• Example: turbulent flow in smooth pipe( )
0 5y
1 lnu y B
u y
Re 3000
*y yu *u u u *
wu Three layer concept (using dimensional analysis)
1. Laminar sub-layer (viscous shear dominates)
2. Overlap layer (viscous and turbulent shear important)
3. Outer layer (turbulent shear dominates)
57:020 Fluid Mechanics 14
1 lnu y B
520 10y
*0
1U u rfu r
510y
*0
*
1 lnu r r r u
Bu
Three layer concept (using dimensional analysis)
1. Laminar sub-layer (viscous shear dominates)
2. Overlap layer (viscous and turbulent shear important)
3. Outer layer (turbulent shear dominates)
Assume log-law is valid across entire pipe:
Integration for average velocity and using EFD data to adjust constants:
1 21 2log Re .8ff
( =0.41, B=5.5)
Analytical Fluid Dynamics• Example: turbulent flow in rough pipe
u u y k
1 ln yuk
Both laminar sublayer and overlap layerare affected by roughnessInner layer:
Outer layer: unaffected
Overlap layer: constant
57:020 Fluid Mechanics 15
1 ln yuk
1 2log3.7k D
f 1 ln 8.5 Reyu f
k
Three regimes of flow depending on k+
1. K+<5, hydraulically smooth (no effect of roughness)2. 5 < K+< 70, transitional roughness (Re dependent)3. K+> 70, fully rough (independent Re)
Inner layer:
Outer layer: unaffected
Overlap layer:
Friction factor:
For 3, using EFD data to adjust constants:
constant
Analytical Fluid Dynamics• Example: Moody diagram for turbulent pipe flow
Composite Log-Law for smooth and rough pipes is given by the Moody diagram:
57:020 Fluid Mechanics 16
1 1 22
1 2.512log3.7 Rek D
ff
Experimental Fluid Dynamics (EFD)
Definition:Use of experimental methodology and procedures for solving fluidsengineering systems, including full and model scales, large and tabletop facilities, measurement systems (instrumentation, data acquisitionand data reduction), uncertainty analysis, and dimensional analysis andsimilarity.
EFD philosophy:• Decisions on conducting experiments are governed by the ability of the
expected test outcome, to achieve the test objectives within allowableuncertainties.
• Integration of UA into all test phases should be a key part of entireexperimental program• test design• determination of error sources• estimation of uncertainty• documentation of the results
57:020 Fluid Mechanics 17
Definition:Use of experimental methodology and procedures for solving fluidsengineering systems, including full and model scales, large and tabletop facilities, measurement systems (instrumentation, data acquisitionand data reduction), uncertainty analysis, and dimensional analysis andsimilarity.
EFD philosophy:• Decisions on conducting experiments are governed by the ability of the
expected test outcome, to achieve the test objectives within allowableuncertainties.
• Integration of UA into all test phases should be a key part of entireexperimental program• test design• determination of error sources• estimation of uncertainty• documentation of the results
Purpose
• Science & Technology: understand and investigate aphenomenon/process, substantiate and validate a theory(hypothesis)
• Research & Development: document a process/system,provide benchmark data (standard procedures,validations), calibrate instruments, equipment, andfacilities
• Industry: design optimization and analysis, provide datafor direct use, product liability, and acceptance
• Teaching: instruction/demonstration
57:020 Fluid Mechanics 18
• Science & Technology: understand and investigate aphenomenon/process, substantiate and validate a theory(hypothesis)
• Research & Development: document a process/system,provide benchmark data (standard procedures,validations), calibrate instruments, equipment, andfacilities
• Industry: design optimization and analysis, provide datafor direct use, product liability, and acceptance
• Teaching: instruction/demonstration
Applications of EFD
57:020 Fluid Mechanics 19
Application in research & development
Tropic Wind Tunnel has the ability to createtemperatures ranging from 0 to 165 degreesFahrenheit and simulate rain
Application in science & technology
Picture of Karman vortex shedding
Applications of EFD (cont’d)
57:020 Fluid Mechanics 20
Example of industrial application
NASA's cryogenic wind tunnel simulates flightconditions for scale models--a critical tool indesigning airplanes.
Application in teaching
Fluid dynamics laboratory
Full and model scale
57:020 Fluid Mechanics 21
• Scales: model, and full-scale
• Selection of the model scale: governed by dimensional analysis and similarity
Measurement systems
• Instrumentation• Load cell to measure forces and moments• Pressure transducers• Pitot tubes• Hotwire anemometry• PIV, LDV
• Data acquisition• Serial port devices• Desktop PC’s• Plug-in data acquisition boards• Data Acquisition software - Labview
• Data analysis and data reduction• Data reduction equations• Spectral analysis
57:020 Fluid Mechanics 22
• Instrumentation• Load cell to measure forces and moments• Pressure transducers• Pitot tubes• Hotwire anemometry• PIV, LDV
• Data acquisition• Serial port devices• Desktop PC’s• Plug-in data acquisition boards• Data Acquisition software - Labview
• Data analysis and data reduction• Data reduction equations• Spectral analysis
Data reduction methods
EXPERIMENTALRESULTS
EXPERIMENTAL ERROR SOURCES
INDIVIDUALMEASUREMENT
SYSTEMS
MEASUREMENTOF INDIVIDUAL
VARIABLES
DATA REDUCTIONEQUATIONS
TEMPERATUREWATER
TEMPERATUREAIR
fB , P
VENTURIPRESSURE
PIPEPRESSURE
f = F( , , z , Q = )a a
wg D8LQ
Q = F( z )
w
w
T
TB T, Pz
zB , P
f f
SM
SMww
DM
SM
2
2
5
aT
TB T, Paa zSM
z
zB , PDM
DM zDM
= F(T )
( )
w
= F(T )a
zSM i
- zSM j
w
a
• Data reduction equations
• Spectral analysis
57:020 Fluid Mechanics 25
EXPERIMENTALRESULTS
EXPERIMENTAL ERROR SOURCES
INDIVIDUALMEASUREMENT
SYSTEMS
MEASUREMENTOF INDIVIDUAL
VARIABLES
DATA REDUCTIONEQUATIONS
TEMPERATUREWATER
TEMPERATUREAIR
fB , P
VENTURIPRESSURE
PIPEPRESSURE
f = F( , , z , Q = )a a
wg D8LQ
Q = F( z )
w
w
T
TB T, Pz
zB , P
f f
SM
SMww
DM
SM
2
2
5
aT
TB T, Paa zSM
z
zB , PDM
DM zDM
= F(T )
( )
w
= F(T )a
zSM i
- zSM j
w
a
Example of data reduction equations
StatSMStagSMa
w zrzgru2
)(
Spectral analysisFFT: Converts a function from amplitude as function
of time to amplitude as function of frequencyAim: To analyze the naturalunsteadiness of the separated flow,around a surface piercingstrut, using FFT.
Fast Fourier Transform
57:020 Fluid Mechanics 26
Surface piercing strut Power spectral densityof wave elevation
Free-surface waveelevation contours
FFT of wave elevation
Time history of waveelevation
Uncertainty analysis
r = r (X , X ,......, X )1 2 J
1 2 J
MEASUREMENTOF INDIVIDUALVARIABLES
INDIVIDUALMEASUREMENTSYSTEMS
ELEMENTALERROR SOURCES
DATA REDUCTIONEQUATION
EXPERIMENTALRESULT
XB , P
1
1 1
XB , P
2
2 2
XB , P
J
J J
rB , P
r r
Rigorous methodology for uncertainty assessmentusing statistical and engineering concepts
57:020 Fluid Mechanics 27
r = r (X , X ,......, X )1 2 J
1 2 J
MEASUREMENTOF INDIVIDUALVARIABLES
INDIVIDUALMEASUREMENTSYSTEMS
ELEMENTALERROR SOURCES
DATA REDUCTIONEQUATION
EXPERIMENTALRESULT
XB , P
1
1 1
XB , P
2
2 2
XB , P
J
J J
rB , P
r r
Dimensional analysis• Definition : Dimensional analysis is a process of formulating fluid mechanics problems in
in terms of non-dimensional variables and parameters.• Why is it used :
• Reduction in variables ( If F(A1, A2, … , An) = 0, then f( 1, 2, … r < n) = 0,where, F = functional form, Ai = dimensional variables, j = non-dimensionalparameters, m = number of important dimensions, n = number of dimensional variables, r= n – m ). Thereby the number of experiments required to determine f vs. F is reduced.
• Helps in understanding physics• Useful in data analysis and modeling• Enables scaling of different physical dimensions and fluid properties
57:020 Fluid Mechanics 28
• Definition : Dimensional analysis is a process of formulating fluid mechanics problems inin terms of non-dimensional variables and parameters.
• Why is it used :• Reduction in variables ( If F(A1, A2, … , An) = 0, then f( 1, 2, … r < n) = 0,
where, F = functional form, Ai = dimensional variables, j = non-dimensionalparameters, m = number of important dimensions, n = number of dimensional variables, r= n – m ). Thereby the number of experiments required to determine f vs. F is reduced.
• Helps in understanding physics• Useful in data analysis and modeling• Enables scaling of different physical dimensions and fluid properties
Example
Vortex shedding behind cylinder
Drag = f(V, L, r, m, c, t, e, T, etc.)
From dimensional analysis,
Examples of dimensionless quantities : Reynolds number, FroudeNumber, Strouhal number, Euler number, etc.
Similarity and model testing• Definition : Flow conditions for a model test are completely similar if all relevantdimensionless parameters have the same corresponding values for model and prototype.
• i model = i prototype i = 1• Enables extrapolation from model to full scale• However, complete similarity usually not possible. Therefore, often it is necessary to
use Re, or Fr, or Ma scaling, i.e., select most important and accommodate othersas best possible.
• Types of similarity:• Geometric Similarity : all body dimensions in all three coordinates have the same
linear-scale ratios.• Kinematic Similarity : homologous (same relative position) particles lie at homologous
points at homologous times.• Dynamic Similarity : in addition to the requirements for kinematic similarity the model
and prototype forces must be in a constant ratio.
57:020 Fluid Mechanics 29
• Definition : Flow conditions for a model test are completely similar if all relevantdimensionless parameters have the same corresponding values for model and prototype.
• i model = i prototype i = 1• Enables extrapolation from model to full scale• However, complete similarity usually not possible. Therefore, often it is necessary to
use Re, or Fr, or Ma scaling, i.e., select most important and accommodate othersas best possible.
• Types of similarity:• Geometric Similarity : all body dimensions in all three coordinates have the same
linear-scale ratios.• Kinematic Similarity : homologous (same relative position) particles lie at homologous
points at homologous times.• Dynamic Similarity : in addition to the requirements for kinematic similarity the model
and prototype forces must be in a constant ratio.
EFD process
• “EFD process” is the steps to set up an experiment andtake data
TestSet-up
Facility &conditions
Install model
Preparemeasurement
systems
DataAcquisition
DataReduction
UncertaintyAnalysis
DataAnalysis
Initialize dataacquisitionsoftware
Run tests &acquire data
Store data
Statisticalanalysis
Estimate biaslimits
Compare resultswith benchmarkdata, CFD, and
/or AFD
Evaluate fluidphysics
Calibration
Prepareexperimentalprocedures
Data reductionequations
Estimateprecision limits
Estimate totaluncertainty
Prepare report
57:020 Fluid Mechanics 30
TestSet-up
Facility &conditions
Install model
Preparemeasurement
systems
DataAcquisition
DataReduction
UncertaintyAnalysis
DataAnalysis
Initialize dataacquisitionsoftware
Run tests &acquire data
Store data
Statisticalanalysis
Estimate biaslimits
Compare resultswith benchmarkdata, CFD, and
/or AFD
Evaluate fluidphysics
Calibration
Prepareexperimentalprocedures
Data reductionequations
Estimateprecision limits
Estimate totaluncertainty
Prepare report
EFD – “hands on” experience
Lab1: Measurement of density andkinematic viscosity of a fluid Lab2: Measurement of
flow rate, friction factor andvelocity profiles in smooth andrough pipes.
ToScanivalve
Chord-wisePressure
TapsTygonTubing
Load Cell
Load CellL
D
57:020 Fluid Mechanics 31
Lab1: Measurement of density andkinematic viscosity of a fluid Lab2: Measurement of
flow rate, friction factor andvelocity profiles in smooth andrough pipes.
Lab3: Measurement of surface pressureDistribution, lift and drag coefficient for an airfoil
ToScanivalve
Chord-wisePressure
TapsTygonTubing
Load Cell
Load CellL
D
Computational Fluid Dynamics• CFD is use of computational methods for
solving fluid engineering systems, includingmodeling (mathematical & Physics) andnumerical methods (solvers, finite differences,and grid generations, etc.).
• Rapid growth in CFD technology since adventof computer
57:020 Fluid Mechanics 32
• CFD is use of computational methods forsolving fluid engineering systems, includingmodeling (mathematical & Physics) andnumerical methods (solvers, finite differences,and grid generations, etc.).
• Rapid growth in CFD technology since adventof computer
ENIAC 1, 1946 IBM WorkStation
Purpose• The objective of CFD is to model the continuous fluids
with Partial Differential Equations (PDEs) anddiscretize PDEs into an algebra problem, solve it,validate it and achieve simulation based designinstead of “build & test”
• Simulation of physical fluid phenomena that aredifficult to be measured by experiments: scalesimulations (full-scale ships, airplanes), hazards(explosions,radiations,pollution), physics (weatherprediction, planetary boundary layer, stellarevolution).
57:020 Fluid Mechanics 33
• The objective of CFD is to model the continuous fluidswith Partial Differential Equations (PDEs) anddiscretize PDEs into an algebra problem, solve it,validate it and achieve simulation based designinstead of “build & test”
• Simulation of physical fluid phenomena that aredifficult to be measured by experiments: scalesimulations (full-scale ships, airplanes), hazards(explosions,radiations,pollution), physics (weatherprediction, planetary boundary layer, stellarevolution).
Modeling• Mathematical physics problem formulation of fluid
engineering system• Governing equations: Navier-Stokes equations (momentum),
continuity equation, pressure Poisson equation, energyequation, ideal gas law, combustions (chemical reactionequation), multi-phase flows(e.g. Rayleigh equation), andturbulent models (RANS, LES, DES).
• Coordinates: Cartesian, cylindrical and spherical coordinatesresult in different form of governing equations
• Initial conditions(initial guess of the solution) and BoundaryConditions (no-slip wall, free-surface, zero-gradient,symmetry, velocity/pressure inlet/outlet)
• Flow conditions: Geometry approximation, domain, ReynoldsNumber, and Mach Number, etc.
57:020 Fluid Mechanics 34
• Mathematical physics problem formulation of fluidengineering system
• Governing equations: Navier-Stokes equations (momentum),continuity equation, pressure Poisson equation, energyequation, ideal gas law, combustions (chemical reactionequation), multi-phase flows(e.g. Rayleigh equation), andturbulent models (RANS, LES, DES).
• Coordinates: Cartesian, cylindrical and spherical coordinatesresult in different form of governing equations
• Initial conditions(initial guess of the solution) and BoundaryConditions (no-slip wall, free-surface, zero-gradient,symmetry, velocity/pressure inlet/outlet)
• Flow conditions: Geometry approximation, domain, ReynoldsNumber, and Mach Number, etc.
Modeling (examples)
Free surface animation for ship inregular waves
Developing flame surface (Bell et al., 2001)
57:020 Fluid Mechanics 35
Evolution of a 2D mixing layer laden with particles of StokesNumber 0.3 with respect to the vortex time scale (C.Narayanan)
Modeling (examples, cont’d)
3D vortex shedding behind a circular cylinder(Re=100,DNS,J.Dijkstra)
57:020 Fluid Mechanics 36
3D vortex shedding behind a circular cylinder(Re=100,DNS,J.Dijkstra)
DES,Re=105, Iso-surface of Qcriterion (0.4)for turbulentflow aroundNACA12 withangle of attack60 degrees
LES of a turbulent jet. Back wall shows a slice of the dissipation rate and thebottom wall shows a carpet plot of the mixture fraction in a slice through the jetcenterline, Re=21,000 (D. Glaze).
Numerical methods• Finite difference methods:
using numerical scheme toapproximate the exact derivativesin the PDEs
• Finite volume methods• Grid generation: conformal
mapping, algebraic methods anddifferential equation methods
• Grid types: structured,unstructured
• Solvers: direct methods (Cramer’srule, Gauss elimination, LUdecomposition) and iterativemethods (Jacobi, Gauss-Seidel,SOR)
o x
y
i i+1i-1
j+1j
j-1
imax
jmax x
y
21 1
2 2
2i i iP P PPx x
2
1 12 2
2j j jP P PPy y
57:020 Fluid Mechanics 37
• Finite difference methods:using numerical scheme toapproximate the exact derivativesin the PDEs
• Finite volume methods• Grid generation: conformal
mapping, algebraic methods anddifferential equation methods
• Grid types: structured,unstructured
• Solvers: direct methods (Cramer’srule, Gauss elimination, LUdecomposition) and iterativemethods (Jacobi, Gauss-Seidel,SOR)
Slice of 3D mesh of a fighter aircraft
CFD process
ConvergentLimit
Contours
Vectors
StreamlinesVerification
Geometry
SelectGeometry
GeometryParameters
Physics Mesh Solve Post-Processing
CompressibleON/OFF
Flowproperties
Unstructured(automatic/
manual)
Steady/Unsteady
Forces Report(lift/drag, shearstress, etc)
XY Plot
Domain Shapeand Size
Heat TransferON/OFF
Structured(automatic/
manual)
Iterations/Steps
Reports
57:020 Fluid Mechanics 38
Viscous Model
BoundaryConditions
InitialConditions
ConvergentLimit
Precisions(single/double)
NumericalScheme
Flowproperties
Domain Shapeand Size
Validation
Commercial software• CFD software
1. FLUENT: http://www.fluent.com2. FLOWLAB: http://www.flowlab.fluent.com3. CFDRC: http://www.cfdrc.com4. STAR-CD: http://www.cd-adapco.com5. CFX/AEA: http://www.software.aeat.com/cfx
• Grid Generation software1. Gridgen: http://www.pointwise.com2. GridPro: http://www.gridpro.com
• Visualization software1. Tecplot: http://www.amtec.com2. Fieldview: http://www.ilight.com
57:020 Fluid Mechanics 39
• CFD software1. FLUENT: http://www.fluent.com2. FLOWLAB: http://www.flowlab.fluent.com3. CFDRC: http://www.cfdrc.com4. STAR-CD: http://www.cd-adapco.com5. CFX/AEA: http://www.software.aeat.com/cfx
• Grid Generation software1. Gridgen: http://www.pointwise.com2. GridPro: http://www.gridpro.com
• Visualization software1. Tecplot: http://www.amtec.com2. Fieldview: http://www.ilight.com
57:020 Fluid Mechanics• Lectures cover basic concepts in fluid statics,
kinematics, and dynamics, control-volume, anddifferential-equation analysis methods. Homeworkassignments, tests, and complementary EFD/CFDlabs
• This class provides an introduction to all three tools:AFD through lecture and CFD and EFD through labs
• ISTUE Teaching Modules(http://www.iihr.uiowa.edu/~istue) (next two slides)
57:020 Fluid Mechanics 42
• Lectures cover basic concepts in fluid statics,kinematics, and dynamics, control-volume, anddifferential-equation analysis methods. Homeworkassignments, tests, and complementary EFD/CFDlabs
• This class provides an introduction to all three tools:AFD through lecture and CFD and EFD through labs
• ISTUE Teaching Modules(http://www.iihr.uiowa.edu/~istue) (next two slides)
TM DescriptionsTable 1: ISTUE Teaching Modules for Introductory Level Fluid Mechanics at Iowa
Teaching Modules TM for FluidProperty
TM for Pipe Flow TM for Airfoil Flow
Overall Purpose Hands-on studentexperience with table-topfacility and simple MS forfluid propertymeasurement, includingcomparison manufacturervalues and rigorousimplementation standardEFD UA
Hands-on student experiencewith complementary EFD, CFD,and UA for Introductory PipeFlow, including friction factorand mean velocity measurementsand comparisons benchmarkdata, laminar and turbulent flowCFD simulations, modeling andverification studies, andvalidation using AFD and EFD.
Hands-on student experience withcomplementary EFD, CFD, and UAfor Introductory Airfoil Flow,including lift and drag, surfacepressure, and mean and turbulentwake velocity profile measurementsand comparisons benchmark data,inviscid and turbulent flowsimulations, modeling and verificationstudies, and validation using AFD andEFD.
57:020 Fluid Mechanics 43
http://css.engineering.uiowa.edu/~fluids
Hands-on student experience withcomplementary EFD, CFD, and UAfor Introductory Airfoil Flow,including lift and drag, surfacepressure, and mean and turbulentwake velocity profile measurementsand comparisons benchmark data,inviscid and turbulent flowsimulations, modeling and verificationstudies, and validation using AFD andEFD.
Educational Materials FM and EFD lecture; labreport instructions; pre labquestions, and EFDexercise notes.
FM, EFD and CFD lectures; labreport instructions; pre labquestions, and EFD and CFDexercise notes.
FM, EFD and CFD lectures; labreport instructions; pre lab questions,and EFD and CFD exercise notes.
ISTUE ASEE papers Paper 1 Paper2
FM Lecture Introduction to Fluid Mechanics
Lab Report Instructions EFD lab report Instructions CFD lab report Instructions
Continued in next slide…
TM Descriptions, cont’dTeaching Modules TM for Fluid
PropertyTM for Pipe Flow TM for Airfoil Flow
CFD CFD Lecture Introduction to CFD
Exercise Notes None CFD Prelab1PreLab1 QuestionsCFD Lab 1Lab Concepts
EFD Data
CFD Prelab2PreLab 2 QuestionsCFD Lab2Lab Concepts
EFD Data
EFD EFDLecture
EFD and UA
Exercise Notes PreLab1 QuestionsLab1 LectureLab 1 exercise notesLab 1 datareduction sheetLab concepts
PreLab2 QuestionsLab2 LectureLab 2 exercise notesLab2 Data reductionsheet (smooth & rough)Lab concepts
PreLab3 QuestionsLab3 LectureLab 3 exercise notesData Reduction SheetLab concepts
57:020 Fluid Mechanics 44
Exercise Notes PreLab1 QuestionsLab1 LectureLab 1 exercise notesLab 1 datareduction sheetLab concepts
PreLab2 QuestionsLab2 LectureLab 2 exercise notesLab2 Data reductionsheet (smooth & rough)Lab concepts
PreLab3 QuestionsLab3 LectureLab 3 exercise notesData Reduction SheetLab concepts
UA(EFD) Lecture EFD UA Report
Exercise Notes Instructions UA
UA(CFD) Lecture
Exercise Notes None