Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]

[email protected] • ENGR-25_Lec-29_MS_Excel-2.ppt1

Bruce Mayer, PE Engineering/Math/Physics 25: Computational Methods

Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

MS ExcelTables/Plots



The 11 MS Excel Chart Types



Graph Construction Demo

TABLE I: Vapor Pressure DataVapor pressures (mm Hg) of less than one atmosphere as a function of temperature. (All temperatures are in degrees Celsius)

Chemical 1 5 10 20 40 60 100 200 400 760 mmHg

Sodium, Na 439 511 549 589 633 662 701 758 823 892 oC

1,4-Dioxane C4H8O2 -35.8 -12.8 -1.2 12.0 25.2 33.8 45.1 62.3 81.8 101.1 oC

Acetone (CH3)2CO -59.4 -40.5 -31.1 -20.8 -9.4 -2.0 7.7 22.7 39.5 56.5 oC

Butyric Acid, C4H8O2 25.5 49.8 61.5 74.0 88.0 96.5 108.0 125.5 144.5 163.5 oC

Stannic Chloride, SnCl4 -22.7 -1.0 10.0 22.0 35.2 43.5 54.7 72.0 92.1 113.0 oC

http://research.umbc.edu/~lkelly/DAExp.htm

Given Vapor Pressure Data

Construct a Scatter Chart to Find the Clapeyron Eqn Constants m & bfor Stannic Chloride

bT

mPv 1ln



Chart Construction ResultSnCl4Vapor Pressure

ln(Pv) = -4.7201(1000/T) + 18.958R2 = 0.9992

0

1

2

3

4

5

6

7

2.5 2.75 3 3.25 3.5 3.75 41000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

12%

Fit Error = (Fit-Actual)/A

ctual

ln(Pv)(ln[Torr])Fit Error

Linear (ln(Pv)(ln[Torr]))

Demo_Excel_Table-n-Chart_Build_Fa06.xls



ln(Pv) = -4.7201*(1000/T) + 18.958R² = 0.9992

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

12%

0

1

2

3

4

5

6

7

2.5 2.75 3 3.25 3.5 3.75 4

Clapeyron Model Fit Error

ln(P

v) (

ln[T

orr]

1000/T (1/K)

SnCl4 Vapor Press by Clapeyron Eqn

ln(Pv) (ln[torr])

Model Error

Linear (ln(Pv) (ln[torr]))



All Done for Today

ExcelPlotting HbH Metering Tube P • Orifice Characteristic • 25Jan00

P = 30.471qR2 = 0.9996

0

1

2

3

4

5

6

7

8

9

0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.21 0.24 0.27 0.30MFC Flow, q (slpm)

[1

-Hol

e B

ack

Pres

sure

] ( [

Torr

])

0

10

20

30

40

50

60

70

80

90

1-Hole B

ack Pressure, P ([Torr)

1-Hole Back Pressure (SQRT{Torr})

1-Hole Back Pressure (Torr)

Bernoulli Square Law Behavior

file = Tube-Test_00.xls

PARAMETERS• Exhaust to Atmosphere• 0.312" O.D. Tube• 9.5 mil holes• Rough, 1st-cut Test• Re = 4q/(d) = 1400 @ q = 0.24 slpm



Bruce Mayer, PELicensed Electrical & Mechanical Engineer

[email protected]

Engr/Math/Physics 25

Appendix 6972 23 xxxxf

tfyyy

735

masterjslave PxhPn

1



Chart Construction Demo (1) Start

• Open File Demo_Excel_Table-n-Chart_Build_0511.xls

Copy from Table from Slide-22 → Paste into Demo Sheet • Need Vertical

Data

Horizontal table starting in Col-H

Copy Table Cells and EDIT → PASTE SPECIAL → transpose



Chart Construction Demo (2)

Result after Transpose Paste



Chart Construction Demo (3) Archive Data

• Make Scratch WorkSheet; Xfer horizontal Table to to this sheet

Edit Worksheet• Adjust Headings• Delete Cols other

Than SnCl4• Move Remaining

to Right



Chart Construction Demo (4) Place in cols A &

B• 1000/T; T in

Kelvins• Ln(Pv)

After Filling A & B

Formula for Col-B• =LN(E8)



Chart Construction Demo (5) Now need to Sort

the Data with the indep var (1000/T) in ASCENDING ORDER• DATA → SORT



Chart Construction Demo (6) Highlight/

Select Data to Plot

Invoke Chart Wizard



Chart Construction Demo (7) Continue with

Chart Wizard



Chart Construction Demo (8) Add X-Grid Lines

Remove Legend

Insert As NEW Sheet• Give Descriptive

Name



Chart Construction Demo (9)

Stannic Chloride (SnCl4) Vapor Pressure(ln[Torr])

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

1000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

Chart Wizard Result

Change• X-axis Scale: 2.5-4• Shorten Title• Clear BackGround• Lager, Sq Data Markers• GridLine & Text Colors



Chart Construction Demo (10) Select Chart Area

ThenRight-Clik

Select X-axis, Ther Right-Clik



Chart Construction Demo (11) Select Grid Lines,

Rt-Clik, Chg Colors

Select Data Series, Rt-Clik, Chg Marker



Chart Construction Demo (12) Position Labels at Page Edges →

Stretch-Out Plot Area



Chart Construction Demo (13) Chart Fine-Tuning Result

SnCl4Vapor Pressure

0

1

2

3

4

5

6

7

2.5 2.75 3 3.25 3.5 3.75 41000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

Add TrendLine to find Clapeyron m &b Constants



Chart Construction Demo (14) Select Data

Series, Rt-Clik, Add TrendLn

Select: Linear, Display Parameters



Chart Construction Demo (15) Fine Tune TrendLine Form & Display

SnCl4Vapor Pressure

y = -4.7201x + 18.958R2 = 0.99920

1

2

3

4

5

6

7

8

2.5 2.75 3 3.25 3.5 3.75 41000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

SnCl4Vapor Pressure

ln(Pv) = -4.7201(1000/T) + 18.958R2 = 0.9992

0

1

2

3

4

5

6

7

8

2.5 2.75 3 3.25 3.5 3.75 41000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

Done with Plot; and have determined m & b by Trendline• Note that the Fit is Excellent;

R2 = 99.92%



Chart Construction Demo (16) Add Fitted Data to table

Copy & Paste from Chart

Calc Using m & b

Analysis of Fit Characteristics

Calc Error=(G4-E4)/E4



Put Fitted Data on Chart• On Table: Select & Copy

Data• On chart: EDIT → PASTE

SPECIAL → dialog Box above



Chart Construction Demo (17) Fine Tune Two-Variable Display

SnCl4Vapor Pressure

ln(Pv) = -4.7201(1000/T) + 18.958R2 = 0.9992

-1

0

1

2

3

4

5

6

7

8

2.5 2.75 3 3.25 3.5 3.75 4

1000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

Error Data Series

To Make Error Data More Visible Show using SECONDARY Axis at Right



Chart Construction Demo (18)SnCl4Vapor Pressure

ln(Pv) = -4.7201(1000/T) + 18.958R2 = 0.9992

0

1

2

3

4

5

6

7

8

2.5 2.75 3 3.25 3.5 3.75 41000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

-6.0%

-4.0%

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

10.0%

12.0%



Chart Construction Demo (19) Fine Tune Two-Axes Display



Chart Construction Demo (20)SnCl4Vapor Pressure

ln(Pv) = -4.7201(1000/T) + 18.958R2 = 0.9992

0

1

2

3

4

5

6

7

2.5 2.75 3 3.25 3.5 3.75 41000/T (1/Kelvin)

ln(P

v) (l

n[To

rr])

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

12%

Fit Error = (Fit-Actual)/A

ctual

ln(Pv)(ln[Torr])Fit Error

Linear (ln(Pv)(ln[Torr]))



Nice Chart



Coefficient of Correlation The coefficient of correlation is an

indication of how well the linear relationship determined by the method of least squares fits the data set.

The equation for the coefficient of correlation is:

2i

2i

2i

2i

iiii

)y()yn()x()xn()y)(x()yxn(R



Interpretation of R If R is 0, the points are so scattered that

the regression line does not help predict y for a given x.

If R is +1 (positive slope) or –1 (negative slope), the points actually lie on a straight line so almost perfect predictions of y for a given x can be made using the regression line.



Goodness of FitR Value Correlation

0.9 to 1.0 Very high positive0.7 to 0.9 High positive0.5 to 0.7 Moderate positive0.3 to 0.5 Low positive-0.3 to 0.3 Little, if any-0.5 to -0.3 Low negative-0.7 to -0.5 Moderate negative-0.9 to -0.7 High negative-1.0 to -0.9 Very high negative

Bruce Mayer, PE Licensed Electrical & Mechanical Engineer [email protected]

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