Engr/Math/Physics 25
Chp5 MATLAB
Plots & Models 3
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
3
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Logarithmic Plots
y

100 1  0.01x
1  x 
2 2

2 2
 0.02 x 2
 0.1x 2
 Rectilinear Plots do Not Reveal Important
Features when one or both of the variables
range over several orders of magnitude
2
10
35
>> x = [0:0.1:100];
>> y = sqrt((100*(10.01*x.^2).^2 +
0.02*x.^2)./((1-x.^2).^2 +
0.1*x.^2));
>> plot(x,y), xlabel('x'),
ylabel('y');
25
y
20
15
1
10
0
y
30
10
>>
loglog(x,y),
xlabel('x'),
ylabel('y')
-1
10
10
5
-2
0
10
0
10
20
30
40
50
x
60
70
80
90
 Rectilinear Plot
100
-1
10
0
1
10
10
x
 Log-Log Plot
• LogLog Plot is MUCH More Revealing
Engineering/Math/Physics 25: Computational Methods
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
2
10
Making Logarithmic Plots

Important Points to Remember
1. 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.
Engineering/Math/Physics 25: Computational Methods
5
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
SemiLog Plot Comparisons
 Again Plot
y

100 1  0.01x
  0.02 x
2 2
1  x   0.1x
2 2
2
2
2
35
10
semilogx(x,y),
xlabel('x'),
ylabel('y')
30
25
semilogy(x,y),
xlabel('x'),
ylabel('y')
1
10
20
y
y
0
10
15
10
-1
10
5
-2
10
0
-1
10
0
1
10
10
 x → log; y → linear
x
Engineering/Math/Physics 25: Computational Methods
8
2
10
0
10
20
30
40
50
x
60
70
 x → linear; y → log
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
80
90
100
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
Engineering/Math/Physics 25: Computational Methods
9
1
V0
1
jC
Gv 


V1 R  1
1  jRC
jC
 Finding the
Magnitude of Gv
M ( ) | Gv |
1
1  RC 
 In this Case the
Time Constant, RC
  RC  4.7 103  22 109
 103.4 106  103.4 µs
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
2
Example  Low Pass Filter Plot
 Recall the Mag of G
M ( ) | Gv |

1
1  RC 
2
1
1   
2
 Lets “Center” out
the M(ω) plot at
ωτ = 1
 Thus ω = 1/τ = 9671
rad/s  104 rad/s
Engineering/Math/Physics 25: Computational Methods
10
M 9671 
1
2
 9671

1 
103.4 S 
 S

1
1


 70.7%
2
2
1  1
 Thus Make a log-log
Plot for M(ω) (called
a “Bode” Plot) with
the Domain
• 102 ≤ ω ≤ 106
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
4.7 kΩ
Low Pass Filter Plot
Bode Plot for RC LowPass Filter
0
22 nF
10
• This Ckt
Leaves
UNCHANGED,
or PASSES,
Low
Frequency
signals, but
attenuates
High
Frequency
Versions
Voltage Gain (unitless
70.7% left at
ω = 1/τ
-1
10
-2
10
1% left at 106
-3
10
2
10
3
10
4
Engineering/Math/Physics 25: Computational Methods
11
5
10
10
Angular Frequency, w (rad/sec)
6
10
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
12
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
13
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive Plotting
 Recall the Sagging
Cantilever Beam
• Plot Sag vs Time
Using Interactive to
 Go From This
12
 To
This
Polystrene Cantilever Beam Creep-Test
12
10
Vertical Deflection (mm)
10
8
6
4
8
6
4
2
2
Significant "Kink"
931 mN Load
0
0
0
5
10
15
20
Engineering/Math/Physics 25: Computational Methods
14
25
0
5
10
15
20
Load Application Time (minutes)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
25
Styrofoam Beam Creep Test
12
Vertical Deflection (mm)
10
8
6
4
Significant Kink
2
931 mN Load
0
0
5
10
15
20
Load Application Time (min)
Engineering/Math/Physics 25: Computational Methods
15
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
25
Format Plots by Coding
 A Tedious Process for ONE-Time Use
• HELP must be consulted a LOT to
implement Complex Formatting
4
2
y = f(x)
 Useful for
Constructing
a Personal
“Standard
Format” for
Plots
MTH15 • Bruce Mayer, PE
6
0
-2
-4
-6
-6
Engineering/Math/Physics 25: Computational Methods
16
XY f cnGraph6x6BlueGreenBkGndTemplate1306.m
-4
-2
0
x
2
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
6
Code for Previous Plot
% Bruce Mayer, PE
% MTH-15 • 23Jun13
% XY_fcn_Graph_6x6_BlueGreen_BkGnd_Template_1306.m
%
% The FUNCTION
x = linspace(-6,6,500); y = -x.^2/3 +5.5;
%
% The ZERO Lines
zxh = [-6 6]; zyh = [0 0]; zxv = [0 0]; zyv = [-6 6];
%
% the 6x6 Plot
axes; set(gca,'FontSize',12);
whitebg([0.8 1 1]); % Chg Plot BackGround to Blue-Green
plot(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)
Engineering/Math/Physics 25: Computational Methods
17
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
18
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Patent 5,078,922 Bubbler in Operation
Water Surface
Bubble
6.35 mm
Engineering/Math/Physics 25: Computational Methods
19
Carrier N2
Flow Rate in
slpm
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Bubbler-OutPut Physics
 The Details of Bubbler Operation Found in
 Chemical Vapor Output
 Pv 

Qv  QN 2 
 Phs  Pv 
• Phs  Absolute Pressure in
Bubbler HeadSpace
• Pv = Thermodynamic Vapor Pressure
Engineering/Math/Physics 25: Computational Methods
20
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Bubbler Physics
 B 
 Over a substantial
ln Pv   A  

Range of
T C 
 Where
Temperatures
• T  Absolute
Between Freezing &
Temperature
Boiling The
• A, B, C are
ThermoDyamic
CONSTANTS in
Vapor Pressure of
Units consistent with
the Liquid Chemical
T & Pv
Can be described by
the Antoine Eqn1
1. R. C. Reid, J. M. Prausnitz, B. E. Poling, Properties of Gases & Liquids,
4th Ed., New York, McGraw-Hill, 1987, pg 208
Engineering/Math/Physics 25: Computational Methods
21
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Bubbler Physics cont
 In many cases C  0
 In This Case The
Antione Eqn
Reduces to the
Clapeyron Eqn2
ln Pv   A  B T
 Thus Pv(T)
Pv  e
A B T
 e e
A
 De
B T
B T
Engineering/Math/Physics 25: Computational Methods
22
 Then the Bubbler
Eqn in terms of the
Independent Vars
QN2, Phs & T
 De  B / T
Qv  QN 2 
B /T
P

De
 hs



 or
Qv
De  B / T
 Qo Phs , T  
QN 2
Phs  De  B / T
2. R. C. Reid, J. M. Prausnitz, B. E. Poling,
Properties of Gases & Liquids, 4th Ed., New
York, McGraw-Hill, 1987, pg 206
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
23
 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
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
TEOS Chemical/Physical Data
• 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
Engineering/Math/Physics 25: Computational Methods
24
 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)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
http://ptcl.chem.ox.ac.uk/MSDS/TE/tetraethyl_orthosilicate.html
 General
Bubbler OutPut - TEOS
 Thus for TEOS the
Clapeyron Eqn
Pv ,TEOS  e19.31975562.3 T


 2.457 108 Torr e 5562.3 T
 Now the TEOS
Bubbler Normally
Operates under
these Conditions
• T: 60-85 °C
= 333-358 K
• Phs: 250-750 Torr
Engineering/Math/Physics 25: Computational Methods
25
 We Now Want to
Make a MATLAB
Plot of Qo,TEOS for
these Conditions
B /T
Qo ,TEOS
De

B /T
Phs  De

Pv ,TEOS T 
Phs  Pv ,TEOS T 
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
mesh Plot Example
 The Command Session
>> Trng = linspace(333,358,25);
>> Prng = linspace(250,750,25);
>> [T,Phs] = meshgrid(Trng,Prng);
SQUARE XY
Grid of 252
>> A = 19.3197; B = 5562.30;
(225) points
>> 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')
Bubbler_Qo_of_TPhs_1010.m
Engineering/Math/Physics 25: Computational Methods
26
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
mesh Plot Result
Qo (slpm-TEOS/Slpm-N2)
Vapor Output From TEOS Bubbler
0.25
0.2
0.15
0.1
0.05
0
700
85
600
80
500
75
400
70
300
Phs (Torr)
Engineering/Math/Physics 25: Computational Methods
27
65
60
T (°C)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
mesh Plot Result: Swap X↔Y
Qo (slpm-TEOS/Slpm-N2)
Vapor Output From TEOS Bubbler
mesh(Phs,(T-273),Qo),
xlabel('Phs (Torr)'),
ylabel('T (°C)'),...
zlabel('Qo (slpm-TEOS/SlpmN2)'), grid on,...
title('Vapor Output From
TEOS Bubbler')
0.25
0.2
0.15
0.1
0.05
0
85
80
750
75
650
550
70
450
65
T (°C)
60
350
250
Engineering/Math/Physics 25: Computational Methods
28
Phs (Torr)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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”)
Engineering/Math/Physics 25: Computational Methods
29
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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')
Engineering/Math/Physics 25: Computational Methods
30
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
contour Plot Result
 X → Phs
 X→T
Vapor Output From TEOS Bubbler
700
6
0.0
0.
14
650
600
06
0.
450
400
65
08
0.
06
0.
500
4
0.0
0.
08
70
550
0.
04
T (°C)
0.
1
4
0.0
Phs (Torr)
6
0.0
08
0.
75
04
0.
0.1
8
0.0
6
0.0
2
0.1
350
04
0.
0.
06
60
250
0.
06
8
0.0
1
0.
0.
04
0.1
8
0.
16
12
0.
0.
12
80
Vapor Output From TEOS Bubbler
750
0.0
2
85
300
350
400
300
450
550
500
Phs (Torr)
600
650
2
0.0
750
700
Engineering/Math/Physics 25: Computational Methods
31
250
60
0.1
8
0.0
6
0.0
65
70
4
0.1 6
0.1
8
0.1
2
0.1
75
T (°C)
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
80
85
Other 3D Plot Commands
Command
[X,Y] =
meshgrid(x,y)
[X,Y] =
meshgrid(x)
mesh(x,y,z)
meshc(x,y,z)
meshz(x,y,z)
Plot Description
Creates the matrices X and Y from the
vectors x and y to define a rectangular
grid
Same as [X,Y]= meshgrid(x,x).
Creates a 3D mesh surface plot
Same as mesh but draws contours under
the surface
Same as mesh but draws vertical
reference lines under the surface
Engineering/Math/Physics 25: Computational Methods
32
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Other 3D Plot Commands cont
Command
contour(x,y,z)
surf(x,y,z)
Plot Description
Creates a contour plot.
Creates a shaded 3D mesh surface plot
Same as surf but draws contours
surfc(x,y,z)
under the surface
Same as mesh but draws mesh lines in
waterfall(x,y,z)
one direction only
meshz
Qmin = 0.0186
Qmax = 0.2132
0.2
Vapor Output From TEOS Bubbler
0.15
0.1
0.05
0
85
80
750
75
650
550
70
450
65
T (°C)
60
0.2
0.15
0.1
0.05
0
90
800
80
600
350
250
70
Phs (Torr)
Engineering/Math/Physics 25: Computational Methods
33
surf
0.25
Qo (slpm-TEOS/Slpm-N2)
Qo (slpm-TEOS/Slpm-N2)
Vapor Output From TEOS Bubbler
T (°C)
400
60
200
Bruce Mayer, PE
Phs (Torr)
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Caveat on 3D Surface Plots
 3D Surfaces are Difficult for Many
ENGINEERS/SCIENTISTS to
Quickly Interpret
TEOS Bubbler Vapor Generator Temp Sensitivity
• If you have a
NonTechnical
Audience for
your Plots,
I suggest Sticking
with 2D, Cartesian
Plots
6.8%
6.6%
6.2%
6.0%
5.8%
5.6%
5.4%
5.2%
5.0%
4.8%
200
250
300
350
400
450
500
Chamber
550
Pressure (Torr)
600
650
700
4.6%
4.4%
50
60
70
80
90
Bubbler Temperature (°C)
100
Engineering/Math/Physics 25: Computational Methods
34
Change in Bubbler Output (%/°C)
6.4%
file =VapGen_T-P_Se
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
All Done for Today
TEOS Bubbler Vapor Output (1 slpm Carrier N2)
Excel Plot:
Bubbler
OutPut
300
275
225
200
175
150
125
100
75
TEOS Vapor Output (sccm)
250
50
25
Engineering/Math/Physics 25: Computational Methods
35
75
650
80
Bubbler
Temperature (°C)
85
700
550
HeadSpace
Pressure (Torr)
65
70
600
200
250
300
350
400
450
500
0
60
file =VapGen_T-P_Se
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Engr/Math/Physics 25
Appendix
f x   2 x  7 x  9 x  6
3
2
Bruce Mayer, PE
Licensed Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
Engineering/Math/Physics 25: Computational Methods
36
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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)
Engineering/Math/Physics 25: Computational Methods
37
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-2
Engineering/Math/Physics 25: Computational Methods
38
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-3
Engineering/Math/Physics 25: Computational Methods
39
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-4
Engineering/Math/Physics 25: Computational Methods
40
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-5
Engineering/Math/Physics 25: Computational Methods
41
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-6
Engineering/Math/Physics 25: Computational Methods
42
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-7
Engineering/Math/Physics 25: Computational Methods
43
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-8
 Activate the
FIGURE
PALETTE
Double
Click
Engineering/Math/Physics 25: Computational Methods
44
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-9
Engineering/Math/Physics 25: Computational Methods
45
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive 10
 Activate AxisTitle Format
Box by
DoubleClicking the
Title
Engineering/Math/Physics 25: Computational Methods
46
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive-11
 Change the
Plot
BackGround
Color to
Match the
PowerPoint
BackGround
Engineering/Math/Physics 25: Computational Methods
47
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive 12
Engineering/Math/Physics 25: Computational Methods
48
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Interactive 13
Engineering/Math/Physics 25: Computational Methods
49
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
COPY FIGURE result
Polystrene Cantilever Beam Creep-Test
12
Vertical Deflection (mm)
10
8
6
4
2
Significant "Kink"
931 mN Load
0
0
5
10
15
20
25
Load Application Time (minutes)
Engineering/Math/Physics 25: Computational Methods
50
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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)
Engineering/Math/Physics 25: Computational Methods
51
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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.
Engineering/Math/Physics 25: Computational Methods
52
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Graphics from [Mayer96]
Engineering/Math/Physics 25: Computational Methods
53
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
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
Engineering/Math/Physics 25: Computational Methods
54
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Sys3 2X200 MultiBlok, 997671 250-13.8 PreWeld Pi Tube-1
200
Individual Hole  P (10X Torr)
175
Tic Mark Label
150
125
Connecting Line
Axis UNITS
Data Symbol
100
Tic Mark
75
50
25
PARAMETERS
• For Single Tube Manifold
• Flow = ??/0.24 slpm/hole
• Exh to Atm Pressure (~750Torr)
• Test Engr = DNStoddard, BMayer
• Test Date = 09Mar00/10Mar
DNS Tube-1
BMayer Tube1
DNS Normalized
BMayer Normalized
0
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)
file = HbH997671PreW09Mar00.xls
Engineering/Math/Physics 25: Computational Methods
55
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
Polystyrene Creep Test
12
Vertical Deflection (mm)
10
8
6
4
2
Significant Kink
931 mN Load
0
0
5
10
15
Load Application Time (min)
Engineering/Math/Physics 25: Computational Methods
56
20
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt
25
Polystyrene Beam Creep
12
Vertical Deflection (mm)
10
8
6
4
Significa nt "Kink"
2
931 mN Load
0
0
5
10
15
20
25
Load Application Time (min)
Engineering/Math/Physics 25: Computational Methods
57
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Plot_Model-3.ppt