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[email protected] • ENGR-25_Plot_Model-3.ppt1
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Engr/Math/Physics 25
Chp5 MATLABPlots &
Models 3
[email protected] • ENGR-25_Plot_Model-3.ppt2
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Learning Goals List the Elements of a COMPLETE
Plots• e.g.; axis labels, legend, units, etc.
Construct Complete Cartesian (XY) plots using MATLAB• Modify or Specify MATLAB Plot Elements:
Line Types, Data Markers,Tic Marks
Distinguish between INTERPolation and EXTRAPolation
[email protected] • ENGR-25_Plot_Model-3.ppt3
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Learning Goals cont
Construct using MATLAB SemiLog and LogLog Cartesian Plots
Use MATLAB’s InterActive Plotting Utility to Fine-Tune Plot Appearance
Use MATLAB to Produce 3-Dimensional Plots, including• Surface Plots• Contour Plots
[email protected] • ENGR-25_Plot_Model-3.ppt4
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Logarithmic Plots
Rectilinear Plots do Not Reveal Important Features when one or both of the variables range over several orders of magnitude
0 10 20 30 40 50 60 70 80 90 1000
5
10
15
20
25
30
35
x
y
10-1
100
101
102
10-2
10-1
100
101
102
x
y
>> x = [0:0.1:100];>> y = sqrt((100*(1-0.01*x.^2).^2 + 0.02*x.^2)./((1-x.^2).^2 + 0.1*x.^2));>> plot(x,y), xlabel('x'), ylabel('y');
222
222
1.01
02.001.01100
xx
xxy
>> loglog(x,y), xlabel('x'), ylabel('y')
Rectilinear Plot Log-Log Plot• LogLog Plot is MUCH More Revealing
[email protected] • ENGR-25_Plot_Model-3.ppt5
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Making Logarithmic Plots
Important Points to Remember1. You cannot plot negative numbers on a
log scale – Recall the logarithm of a negative number is
not defined as a real number
2. You cannot plot the number 0 (zero) on a log scale– Recall log10(0) = ln(0) = −
Therefore choose an appropriately small number (e.g., 10−18) as the lower limit on the plot.
3. Tick-mark labels on a log scale are the actual values being plotted; they are not logs of the No.s– The x values in the previous log-log plot
range over 10−1 = 0.1 to 102 = 100.
[email protected] • ENGR-25_Plot_Model-3.ppt6
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Making Logarithmic Plots cont
4. Gridlines and tick marks within a decade are unevenly spaced. – If 8 gridlines or tick marks occur within the
decade, they correspond to values equal to 2, 3, 4, . . . , 8, 9 times the value represented by the first gridline or tick mark of the decade.
5. Equal distances on a log scale correspond to multiplication by the same constant – as opposed to addition of the same constant
on a rectilinear scale– e.g.; all numbers that differ by a factor of 10 are
separated by the same distance on a log scale. That is, the distance between 0.3 and 3 is the same as the distance between 300 and 3000. This separation is referred to as a decade or cycle
[email protected] • ENGR-25_Plot_Model-3.ppt7
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
MATLAB Log & semiLog Plots
MATLAB has three commands for generating plots with log scales:1. Use the loglog(x,y) command to have
both scales logarithmic.
2. Use the semilogx(x,y) command to have the x scale logarithmic and the y scale RECTILINEAR.
3. Use the semilogy(x,y) command to have the y scale logarithmic and the x scale RECTILINEAR
[email protected] • ENGR-25_Plot_Model-3.ppt8
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
SemiLog Plot Comparisons
Again Plot 222
222
1.01
02.001.01100
xx
xxy
x → log; y → linear x → linear; y → log10
-110
010
110
20
5
10
15
20
25
30
35
x
y
semilogx(x,y), xlabel('x'), ylabel('y')
0 10 20 30 40 50 60 70 80 90 10010
-2
10-1
100
101
102
x
y
semilogy(x,y), xlabel('x'), ylabel('y')
[email protected] • ENGR-25_Plot_Model-3.ppt9
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Example Low Pass Filter
Consider a Simple RC “Voltage Divider”
4.7 kΩ
22 nF
By the Methods of Junior-Level EE Find the Voltage “Gain”, Gv
RCjCj
R
CjV
VGv
1
11
1
1
0
21
1||)(
RCGM v
In this Case the Time Constant, RC
µs
RC
4.103104.103
1022107.46
93
Finding the Magnitude of Gv
[email protected] • ENGR-25_Plot_Model-3.ppt10
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Example Low Pass Filter Plot
Recall the Mag of G
Lets “Center” out the M(ω) plot at ωτ = 1
Thus ω = 1/τ = 9671 rad/s 104 rad/s
2
2
1
1
1
1||)(
RCGM v
Thus Make a log-log Plot for M(ω) (called a “Bode” Plot) with the Domain• 102 ≤ ω ≤ 106
%7.70
2
1
11
1
4.1039671
1
19671
2
2
SS
M
[email protected] • ENGR-25_Plot_Model-3.ppt11
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Low Pass Filter Plot
102
103
104
105
106
10-3
10-2
10-1
100
Angular Frequency, w (rad/sec)
Vol
tage
Gai
n (u
nitle
ss
Bode Plot for RC LowPass Filter
4.7 kΩ
22 nF
1% left at 106
70.7% left at ω = 1/τ
• This Ckt Leaves UNCHANGED, or PASSES, Low Frequency signals, but attenuates High Frequency Versions
[email protected] • ENGR-25_Plot_Model-3.ppt12
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive Plotting in MATLAB The “SemiAutomatic” interface
can be very convenient when You• Need to create a large number of different
types of plots,• Construct plots involving many data sets,• Want to add annotations such as
rectangles and ellipses• Desire to change plot characteristics such
as tick spacing, fonts, bolding, italics, and colors
[email protected] • ENGR-25_Plot_Model-3.ppt13
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
MATLAB Interactive Plots cont
The interactive plotting environment in MATLAB Includes tools for• Creating different types of graphs,• Selecting variables to plot directly
from the Workspace Browser• Creating and editing subplots,• Adding annotations such as lines, arrows,
text, rectangles, and ellipses, and• Editing properties of graphics objects, such
as their color, line weight, and font
[email protected] • ENGR-25_Plot_Model-3.ppt14
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive Plotting
Go From This To This
Recall the Sagging Cantilever Beam• Plot Sag vs Time
Using Interactive to
0 5 10 15 20 250
2
4
6
8
10
12
0 5 10 15 20 250
2
4
6
8
10
12
Load Application Time (minutes)
Ver
tical
Def
lect
ion
(mm
)
Polystrene Cantilever Beam Creep-Test
931 mN LoadSignificant "Kink"
[email protected] • ENGR-25_Plot_Model-3.ppt15
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
0 5 10 15 20 250
2
4
6
8
10
12
Load Application Time (min)
Ver
tica
l Def
lect
ion
(m
m)
Styrofoam Beam Creep Test
931 mN Load
Significant Kink
[email protected] • ENGR-25_Plot_Model-3.ppt16
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Format Plots by Coding
A Tedious Process for ONE-Time Use• HELP must be consulted a LOT to
implement Complex Formatting
Useful forConstructinga Personal “Standard Format” for Plots
-6 -4 -2 0 2 4 6-6
-4
-2
0
2
4
6
x
y =
f(x)
MTH15 • Bruce Mayer, PE
XYf cnGraph6x6BlueGreenBkGndTemplate1306.m
[email protected] • ENGR-25_Plot_Model-3.ppt17
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Code for Previous Plot% Bruce Mayer, PE% MTH-15 • 23Jun13% XY_fcn_Graph_6x6_BlueGreen_BkGnd_Template_1306.m%% The FUNCTIONx = linspace(-6,6,500); y = -x.^2/3 +5.5;% % The ZERO Lineszxh = [-6 6]; zyh = [0 0]; zxv = [0 0]; zyv = [-6 6];%% the 6x6 Plotaxes; set(gca,'FontSize',12);whitebg([0.8 1 1]); % Chg Plot BackGround to Blue-Greenplot(x,y, zxv,zyv, 'k', zxh,zyh, 'k', 'LineWidth', 3),axis([-6 6 -6 6]),... grid, xlabel('\fontsize{14}x'), ylabel('\fontsize{14}y = f(x)'),... title(['\fontsize{16}MTH15 • Bruce Mayer, PE',]),... annotation('textbox',[.51 .05 .0 .1], 'FitBoxToText', 'on', 'EdgeColor', 'none', 'String', 'XYfcnGraph6x6BlueGreenBkGndTemplate1306.m','FontSize',7)
[email protected] • ENGR-25_Plot_Model-3.ppt18
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
3D Surface Plots
Example Consider a Humidification Vapor-Generator used to Fabricate Integrated Circuits A Carrier Gas, Nitrogen in this case, “bubbles” thru the Liquid Chemical, Becoming Humidified in the Process
The “Bubbler OutPut”, Qmix, is the sum of Carrier N2, QN2, and the Chem Vapor, Qv
[email protected] • ENGR-25_Plot_Model-3.ppt19
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Patent 5,078,922 Bubbler in Operation
Carrier N2 Flow Rate
in slpm
Bubble
6.35 mm
Sparger Tube
Water Surface
[email protected] • ENGR-25_Plot_Model-3.ppt20
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bubbler-OutPut Physics The Details of Bubbler Operation Found
in
Chemical Vapor Output
vhs
vNv PP
PQQ 2• Phs Absolute Pressure in
Bubbler HeadSpace• Pv = Thermodynamic Vapor Pressure
[email protected] • ENGR-25_Plot_Model-3.ppt21
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bubbler Physics
Over a substantial Range of Temperatures Between Freezing & Boiling The ThermoDyamic Vapor Pressure of the Liquid Chemical Can be described by the Antoine Eqn1
CT
BAPvln
Where• T Absolute
Temperature• A, B, C are
CONSTANTS in Units consistent with T & Pv
1. R. C. Reid, J. M. Prausnitz, B. E. Poling, Properties of Gases & Liquids, 4th Ed., New York, McGraw-Hill, 1987, pg 208
[email protected] • ENGR-25_Plot_Model-3.ppt22
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bubbler Physics cont
In many cases C 0
In This Case The Antione Eqn Reduces to the Clapeyron Eqn2
Then the Bubbler Eqn in terms of the Independent Vars QN2, Phs & T
2. R. C. Reid, J. M. Prausnitz, B. E. Poling, Properties of Gases & Liquids, 4th Ed., New York, McGraw-Hill, 1987, pg 206
TBAPv ln Thus Pv(T)
TB
TBA
TBAv
De
ee
eP
TBhs
TB
Nv DeP
DeQQ
/
/
2
or
TB
hs
TB
hsoN
v
DeP
DeTPQ
Q
Q/
/
2
,
[email protected] • ENGR-25_Plot_Model-3.ppt23
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bubbler Physics cont
Thus the Normalized Output, Qo, Can be Modulated by Pressure and Temperature Control
We would Now Like to Plot Qo(Phs,T) for The Chemical TEOS
From the Manufacturer’s Data A summarized in [Mayer96], Find the Antoine/Clapeyron Constants for Pv in Torr • A = 19.3197• B = 5562.30 Kelvins
[email protected] • ENGR-25_Plot_Model-3.ppt24
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
TEOS Chemical/Physical Data
General • Synonyms: ethyl
silicate, tetraethoxysilane, silicic acid tetraethyl ester, TEOS, tetraethyl silicate
• Molecular formula: (C2H5O)4Si
Physical data• Appearance:
colorless liquid with an alcohol-like odor
Physical data• Melting point: −86
C• Boiling point: 169
C• Vapor density: 7.2
(air = 1)• Vapor pressure:
2 mm-Hg at 20 C– H2O → 17.54 mm-
Hg
• Liquid Density (g/cm3): 0.94
• Flash point: 39 C (closed cup)
http://ptcl.chem.ox.ac.uk/M
SD
S/T
E/tetraethyl_orthosilicate.htm
l
[email protected] • ENGR-25_Plot_Model-3.ppt25
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bubbler OutPut - TEOS
Thus for TEOS the Clapeyron Eqn
We Now Want to Make a MATLAB Plot of Qo,TEOS for these Conditions
Now the TEOS Bubbler Normally Operates under these Conditions• T: 60-85 °C
= 333-358 K• Phs: 250-750 Torr
T
TTEOSv
e
eP3.55628
3.55623197.19,
Torr 10457.2
TPP
TP
DeP
DeQ
TEOSvhs
TEOSv
TBhs
TB
TEOSo
,
,
/
/
,
[email protected] • ENGR-25_Plot_Model-3.ppt26
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
mesh Plot Example
The Command Session>> Trng = linspace(333,358,25);>> Prng = linspace(250,750,25);>> [T,Phs] = meshgrid(Trng,Prng);>> A = 19.3197; B = 5562.30;>> Pv = exp(A - B./T);>> Qo = Pv./(Phs - Pv);>> mesh((T-273),Phs,Qo), xlabel('T (°C)'), ylabel('Phs (Torr)'),...zlabel('Qo (slpm-TEOS/Slpm-N2)'), grid on,...title('Vapor Output From TEOS Bubbler')
SQUARE XY Grid of 252 (225) points
Bubbler_Qo_of_TPhs_1010.m
[email protected] • ENGR-25_Plot_Model-3.ppt27
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
mesh Plot Result
6065
7075
8085
300400
500600
700
0
0.05
0.1
0.15
0.2
0.25
T (°C)
Vapor Output From TEOS Bubbler
Phs (Torr)
Qo
(slp
m-T
EO
S/S
lpm
-N2)
[email protected] • ENGR-25_Plot_Model-3.ppt28
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
mesh Plot Result: Swap X↔Y
250350
450550
650750
6065
7075
80850
0.05
0.1
0.15
0.2
0.25
Phs (Torr)
Vapor Output From TEOS Bubbler
T (°C)
Qo
(slp
m-T
EO
S/S
lpm
-N2)
mesh(Phs,(T-273),Qo), xlabel('Phs (Torr)'), ylabel('T (°C)'),...zlabel('Qo (slpm-TEOS/Slpm-N2)'), grid on,...title('Vapor Output From TEOS Bubbler')
[email protected] • ENGR-25_Plot_Model-3.ppt29
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Mesh Plot Caveats
To Make the Simple Surface Plot Shown the X-Y Grid Must be SQUARE• i.e.; [No. X-pts] = [No. Y-pts]
– 25 in this case
Do NOT make the grid too DENSE• I tried the Qo Plot with a 500x500 Grid →
250 000 Points• Along with the 250 000 Qo calc Points,
MATLAB had to operate on a Half a MILLION pts (took “forever”)
[email protected] • ENGR-25_Plot_Model-3.ppt30
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
contour Plot Example The Command Session
>> Trng = linspace(333,358,25);>> Prng = linspace(250,750,25);>> [T,Phs] = meshgrid(Trng,Prng);>> A = 19.3197; B = 5562.30;>> Pv = exp(A - B./T);>> Qo = Pv./(Phs - Pv);>> contour(Phs,(T-273),Qo), xlabel('Phs (Torr)'), ylabel('T (°C)'),...zlabel('Qo (slpm-TEOS/Slpm-N2)'), grid on,...title('Vapor Output From TEOS Bubbler')>> contour((T-273),Phs,Qo), xlabel('T (°C)'), ylabel('Phs (Torr)'),...zlabel('Qo (slpm-TEOS/Slpm-N2)'), grid on,...title('Vapor Output From TEOS Bubbler')
[email protected] • ENGR-25_Plot_Model-3.ppt31
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
contour Plot Result
X → Phs X → T
Phs (Torr)
T (°
C)
Vapor Output From TEOS Bubbler
250 300 350 400 450 500 550 600 650 700 75060
65
70
75
80
85
T (°C)
Phs
(Tor
r)
Vapor Output From TEOS Bubbler
60 65 70 75 80 85250
300
350
400
450
500
550
600
650
700
750
[email protected] • ENGR-25_Plot_Model-3.ppt32
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Other 3D Plot CommandsCommand Plot Description
[X,Y] = meshgrid(x,y)
Creates the matrices X and Y from the vectors x and y to define a rectangular grid
[X,Y] = meshgrid(x) Same as [X,Y]= meshgrid(x,x).
mesh(x,y,z) Creates a 3D mesh surface plot
meshc(x,y,z) Same as mesh but draws contours under the surface
meshz(x,y,z) Same as mesh but draws vertical reference lines under the surface
[email protected] • ENGR-25_Plot_Model-3.ppt33
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Other 3D Plot Commands cont
Command Plot Description
contour(x,y,z) Creates a contour plot.
surf(x,y,z) Creates a shaded 3D mesh surface plot
surfc(x,y,z) Same as surf but draws contours under the surface
waterfall(x,y,z) Same as mesh but draws mesh lines in one direction only
250350
450550
650750
6065
70
7580
850
0.05
0.1
0.15
0.2
Phs (Torr)
Vapor Output From TEOS Bubbler
T (°C)
Qo
(slp
m-T
EO
S/S
lpm
-N2)
Qmin = 0.0186Qmax = 0.2132
meshz
200
400
600
800
60
70
80
900
0.05
0.1
0.15
0.2
0.25
Phs (Torr)
Vapor Output From TEOS Bubbler
T (°C)
Qo
(slp
m-T
EO
S/S
lpm
-N2)
surf
[email protected] • ENGR-25_Plot_Model-3.ppt34
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Caveat on 3D Surface Plots
3D Surfaces are Difficult for Many ENGINEERS/SCIENTISTS to Quickly Interpret• If you have a
NonTechnical Audience for your Plots, I suggest Sticking with 2D, Cartesian Plots
5060
7080
90100
200250
300350
400450
500550
600650
700
4.4%
4.6%
4.8%
5.0%
5.2%
5.4%
5.6%
5.8%
6.0%
6.2%
6.4%
6.6%
6.8%
Bubbler Temperature (°C)
Chamber Pressure (Torr)
TEOS Bubbler Vapor Generator Temp Sensitivity
file =VapGen_T-P_Sens.xls
[email protected] • ENGR-25_Plot_Model-3.ppt35
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
All Done for Today
Excel Plot:BubblerOutPut
60
65
70
75
80
85
200
250
300
350
400
450
500
550
600
650
700
0
25
50
75
100
125
150
175
200
225
250
275
300
BubblerTemperature (°C)HeadSpace
Pressure (Torr)
TEOS Bubbler Vapor Output (1 slpm Carrier N2)
file =VapGen_T-P_Sens.xls
[email protected] • ENGR-25_Plot_Model-3.ppt36
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Bruce Mayer, PELicensed Electrical & Mechanical Engineer
Engr/Math/Physics 25
Appendix 6972 23 xxxxf
[email protected] • ENGR-25_Plot_Model-3.ppt37
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-1
Starting Commands
>> delY_mm = [0, 2, 4, 4.5, 5.5, 6, 6.5, 8, 9, 11];>> t_min = [0, 2, 4, 6, 9, 12, 15, 18, 21, 24];>> plot(t_min, delY_mm)
[email protected] • ENGR-25_Plot_Model-3.ppt38
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-2
[email protected] • ENGR-25_Plot_Model-3.ppt39
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-3
[email protected] • ENGR-25_Plot_Model-3.ppt40
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-4
[email protected] • ENGR-25_Plot_Model-3.ppt41
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-5
[email protected] • ENGR-25_Plot_Model-3.ppt42
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-6
[email protected] • ENGR-25_Plot_Model-3.ppt43
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-7
[email protected] • ENGR-25_Plot_Model-3.ppt44
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-8
Activate the FIGURE PALETTE
DoubleClick
[email protected] • ENGR-25_Plot_Model-3.ppt45
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-9
[email protected] • ENGR-25_Plot_Model-3.ppt46
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive 10
Activate Axis-Title Format Box by Double-Clicking the Title
[email protected] • ENGR-25_Plot_Model-3.ppt47
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive-11 Change the
Plot BackGround Color to Match the PowerPoint BackGround
[email protected] • ENGR-25_Plot_Model-3.ppt48
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive 12
[email protected] • ENGR-25_Plot_Model-3.ppt49
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Interactive 13
[email protected] • ENGR-25_Plot_Model-3.ppt50
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
COPY FIGURE result
0 5 10 15 20 250
2
4
6
8
10
12
Load Application Time (minutes)
Ver
tical
Def
lect
ion
(mm
)
Polystrene Cantilever Beam Creep-Test
931 mN LoadSignificant "Kink"
[email protected] • ENGR-25_Plot_Model-3.ppt51
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
WJ’s Patented Bubbler
C. C. Collins, M. A. Richie, F. F. Walker, B. C. Goodrich, L. B. Campbell, “Liquid Source Bubbler”, United States Patent 5,078,922 (Jan 1992)
[email protected] • ENGR-25_Plot_Model-3.ppt52
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
WJ Bubbler Design
Schematic diagram of a the WJ chemical vapor generating bubbler system used in CVD applications. Note the use of the dilution MFC to maintain constant mass flow in the output line. An automatic temperature controller sets the electric heater power level
Cut-away view of a WJ chemical source vapor bubbler. The bubbler features a total internal volume of 0.95 liters, and a 25 mm thick isothermal mass jacket with an exterior diameter of 180 mm.
[email protected] • ENGR-25_Plot_Model-3.ppt53
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Graphics from [Mayer96]
[email protected] • ENGR-25_Plot_Model-3.ppt54
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Why Plot?
Engineering, Math, and Science are QUANTITATIVE Endeavors, we want NUMBERS as Well as Words
Many times we Need to• Understand The (functional) relationship
between two or More Variables• Compare the Values of MANY Data sets
[email protected] • ENGR-25_Plot_Model-3.ppt55
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
Sys3 2X200 MultiBlok, 997671 250-13.8 PreWeld Pi Tube-1
0
25
50
75
100
125
150
175
200
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Hole Number (1 = closest to Manifold Block)
Ind
ivid
ual
Ho
le
P (
10X
To
rr)
DNS Tube-1 BMayer Tube1
DNS Normalized BMayer Normalized
PARAMETERS• For Single Tube Manifold• Flow = ??/0.24 slpm/hole• Exh to Atm Pressure (~750Torr)• Test Engr = DNStoddard, BMayer• Test Date = 09Mar00/10Mar
file = HbH997671PreW09Mar00.xls
Plot Title
Axis Title
Tic Mark
Tic Mark Label
Lege
nd
Data Symbol
Annot
atio
ns
Axis UNITS Connecting Line
[email protected] • ENGR-25_Plot_Model-3.ppt56
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
0 5 10 15 20 250
2
4
6
8
10
12
Load Application Time (min)
Ver
tica
l Def
lect
ion
(m
m)
Polystyrene Creep Test
931 mN Load
Significant Kink
[email protected] • ENGR-25_Plot_Model-3.ppt57
Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods
0 5 10 15 20 250
2
4
6
8
10
12
Load Application Time (min)
Ver
tical
Def
lect
ion
(mm
)
Polystyrene Beam Creep
931 mN Load
Significant "Kink"