# CE 304 Calibration Curve Report I uploaded the lab data and lab lecture read them to know everything about the experiment. Also I uploaded the Technical Wr

CE 304 Calibration Curve Report I uploaded the lab data and lab lecture read them to know everything about the experiment. Also I uploaded the Technical Writing for the report you MUST follow the steps in the technical writing to know exactly how to write the report. Spectrophotometer

Wavelength

Total # of test

Group A

Group B

Colorimeter

Wavelength

Total # of test

500 nm

24

Conc. (mg/L)

100

100

100

250

250

250

500

500

500

1000

1000

1000

100

100

100

250

250

250

500

500

500

1000

1000

1000

Abs

0.211

0.217

0.218

0.562

0.569

0.576

1.172

1.177

1.175

2.134

2.142

2.144

0.228

0.226

0.223

0.567

0.568

0.575

1.161

1.183

1.183

2.148

2.180

2.181

Group A

Group B

Unknown Sample

Total # of test

520 nm

24

Conc. (mg/L)

100

100

100

250

250

250

500

500

500

1000

1000

1000

100

100

100

250

250

250

500

500

500

1000

1000

1000

Abs

0.182

0.182

0.183

0.516

0.515

0.518

1.049

1.058

1.055

1.929

1.962

1.972

0.186

0.185

0.185

0.518

0.518

0.519

1.057

1.059

1.057

1.975

1.979

1.974

6

Group A, B

1

2

3

4

5

6

Average =

Abs at

500 nm

520 nm

0.873

0.817

0.876

0.821

0.874

0.820

0.918

0.826

0.919

0.825

0.919

0.827

0.897

0.823

1. Run the regresion analysis according to

tests) from each equipment.

2. Report the required values such as slope

(refer the lecture slide examples)

3. The significant digits: use the scientific e

hundredth digits for most of the factors in

value can be down to thousandth digits.

4. See the plotting example (in the next sp

value can be down to thousandth digits.

4. See the plotting example (in the next sp

to plot the calibration curve equation line

1. Convert the Abs. from each test with

the calibration curve equation.

2. Take the average of the

concentration values and calculate the

standard deviation. Report the

averagred concentration with standard

analysis according to the results (24

uipment.

ed values such as slope, intercepts… etcs.

de examples)

gits: use the scientific expression to

r most of the factors in this lab report. R^2

to thousandth digits.

example (in the next spreadsheet) for how

to thousandth digits.

example (in the next spreadsheet) for how

on curve equation line with the

Spectrophotometer

Wavelength

Total # of test

Group C

Colorimeter

Wavelength

Total # of test

500 nm

12

Conc. (mg/L)

100

100

100

250

250

250

500

500

500

1000

1000

1000

Abs

0.224

0.227

0.224

0.567

0.575

0.572

1.178

1.176

1.176

2.183

2.181

2.183

Group C

Unknown Sample

Total # of test

520 nm

12

Conc. (mg/L)

100

100

100

250

250

250

500

500

500

1000

1000

1000

Abs

0.175

0.171

0.170

0.500

0.501

0.499

1.036

1.036

1.034

1.943

1.950

1.949

6

Group C

1

2

3

Average =

Abs at

500 nm

520 nm

0.920

0.806

0.918

0.805

0.919

0.806

0.919

0.806

1. Run the regresion analysis according to the

from each equipment.

2. Report the required values such as slope, int

(refer the lecture slide examples)

3. The significant digits: use the scientific expre

hundredth digits for most of the factors in this

value can be down to thousandth digits.

4. See the plotting example (in the next sprea

to plot the calibration curve equation line with

1. Convert the Abs. from each test with

alysis according to the results (12 tests)

values such as slope, intercepts… etcs.

examples)

use the scientific expression to

ost of the factors in this lab report. R^2

housandth digits.

(in the next spreadsheet) for how

urve equation line with the

Example only

Copper metal calibration curve

Conc. (mg/L)

100

100

200

200

400

400

800

800

Abs.

0.103

0.107

0.235

0.228

0.467

0.462

0.935

0.941

From above Table, we can plot a scatter plot as shown on the right.

If after regressional analysis, we obtained the intercept and slope values as the following,

Intercept

X Variable 1 (slope)

-9.870E-03

1.186E-03

we can use them to plot the calibration curve with this equation

Y (Abs.) = slope*X(Conc.)+intercept.

With given any value of X (it should be in the range of the experimental concentrations), then we can c

X

Conc. (mg/L)

100

125

150

175

200

225

250

275

300

325

350

400

450

Y

Abs.

0.109

0.138

0.168

0.198

0.227

0.257

0.287

0.316

0.346

0.375

0.405

0.464

0.524

With the Table on the left, we can add

500

550

600

650

700

750

800

0.583

0.642

0.702

0.761

0.820

0.879

0.939

Copper calbiration curve

1

0.9

0.8

0.7

Abs.

0.6

0.5

0.4

0.3

0.2

Exp. data

0.1

0

0

200

400

600

Concentration (mg/L)

Copper calbiration curve

1

0.9

Exp. data

0.8

Calibration Curve

0.7

Abs.

0.6

0.5

0.4

0.3

800

1000

0.3

0.2

0.1

0

0

200

400

600

Concentration (mg/L)

800

1000

Lab 1 Calibration Curve and

Linear Regression Analysis

CE 304 Spring 2019

Dr. Kevin Wang

1

Outline

•

•

•

•

•

Introduction

Objectives

Equipments

Experimental Procedures

Data Analysis

– Regression analysis

– Confidence Interval

2

Introduction

The Water Cycle

3

Monitor how a fluid is transported

Groundwater Tracing

Measuring Flows in Open

Channels

http://www.openchannelflow.com/blog/article/methods-ofmeasuring-flows-in-open-channels

http://www.globalunderwaterexplorers.org/node/798

Know the residence time, flow velocities

4

How to do measurement?

• Take a series of things

whose values are known

and compare them to the

thing with the value you

want to know

• The unknown must be

within range of the

measuring device you are

using

Example

• Weight

• Length

How do we measure tracer dye?

5

Beer-Lambert Law (Beer’s Law)

A

T

I0

I

The complementary

color of the solution

(observed)

yellowish-green

yellow

organge

red

purple

violet

blue

greenish-blue

bluish-green

The transmitted The wavelength (nm) of ε

color of the

the transmitted color of

c

solution (I)

the solution

violet

400-435

d

blue

435-480

greenish-blue

480-490

bluish-green

490-500

greenish-blue

500-560

yellowish-green

560-580

yellow

580-595

organge

595-610

red

610-750

Absorption

Transmission T = I⁄I0

Intensity of the light going to the flow cell

Intensity of the light that has passed the

flow cell

extinction coefficient: how strong does a

specific substance absorb light?

concentration of the substance

length of the beam path through the cell,

cell length

http://chemistry.tutorvista.com/inorganicchemistry/concentration-of-a-solution.html

http://www.teamcag.com/support/theory/chroma/hplc_bas_at/detectors/detectio

nPrinciple.html

6

Objectives

• Develop a statistically significant calibration

curve for both a spectrophotometer and a

colorimeter to measure concentrations of a

tracer dye for use in contaminant transport

studies.

7

Equipments

Hach DR900 Colorimeter

Wavelengths: 420, 520, 560 and 610 nm

Hach DR4000-UV

Spectrophotometer

Ultraviolet and Visible spectrum

wavelength: 190 to 1100 nm.

(500 nm)

www.hach.com

http://img.medicalexpo.com/images_me/photog/84321-10100225.jpg

8

Experimental Procedures

•

•

•

•

•

http://chemistry.tutorvista.com/inorganicchemistry/concentration-of-a-solution.html

Blank solution: tap water

Standard solutions :

100, 250, 500 and 1000 mg/L

Set up the wavelength value, Calibrate

(zero) the equipment

Measure the Abs. of each concentration

(triplicates)

Measure the Abs of unknown sample

(triplicates)

Absorption spectrum of the red dye

9

Abs = m C(mg/L) + K

For many analytical

techniques, we need to

evaluate the response of

the unknown sample

against a set of standards

(known quantities).

10

Linear regression

• The coefficient of determination, R², which indicates the

percentage of variance in the dependent variable that is

accounted by variability in the independent variable

• The regression equation is the formula for the trend or fit

line which enables us to predict the dependent variable (y)

for any given value of the independent variable (x)

• The regression equation has two parts – the intercept and

the slope

• The intercept is the point on the vertical axis where the

regression line crosses.

• The slope is the change in the dependent variable for a one unit

change in the independent variable. The slope tells us the

direction and magnitude of change.

11

Regression Analysis

Dependent variable (Y)

The basic regression line concept,

DATA = FIT + RESIDUAL

Residuals

Y = mX + b

Independent variable (X)

To be precise, standard deviation is used

to represent the “error”

• Determine the the value

of m, b and their

uncertainties.

• The uncertainty (error) of

the regression, that is

Ypredict-Yexp is the function of

X*m + b

• From the regression error,

the error due to the “m”

and “b” can be further

calculated.

http://www.chem.utoronto.ca/coursenotes/analsci/stats/ErrRegr.html#errint

12

What can we do with the “error”?

13

Confidence Interval (CI)

• A 99% confidence

interval is a range of

values that you can be

99% certain contains

the true mean of the

population.

• If 99%confidence

interval contains zero,

then the effect will not

be significant at the

0.01 level.

14

Data Analysis (I)

• Use the Regression function (under Tools, Data Analysis menu

of Excel) to generate the output tables and determine the

regression equation for absorbance as a function of

concentration (these tables should be included in the

appendix of the report, but only a summary table of the

relevant information should be provided in the results section

of the main report).

• Examine the regression output table to determine whether

the intercept is significant based on the 99% confidence

interval for the intercept (if the 99% CI includes the value of

zero, the intercept is not statistically significant and should be

eliminated from the regression analysis).

15

Data Analysis (II)

• If the intercept is not significant, run the regression

analysis again by selecting the value of zero for the

intercept. Examine the regression output table to

report the final relationship, the coefficient of

determination (R2), and the 99 % CI for the slope.

• The final regression lines can be shown on the plot of

the data. For each regression, the summary tables in

the results should show the estimated values for the

slope and intercept, the 99% confidence intervals for

the slope and intercept, and the coefficient of

determination (R2).

16

Examples

Spectrophotometer Absorbance vs. Concentration (at 500 nm)

2.5

Absorbance

2

1.5

1

How to plot this line?

0.5

0

0

200

400

600

800

1000

1200

Concentration (mg/L)

Figure 1: Linear relationship between Absorbance and

Concentration using Spectrophotometer

Table 1: Summarized Regression Results for Spectrophotometer

Model

m

(99% CI)

Intercept

(99% CI)

R2

With intercept

Abs=mC+b

.00228

(.00223,.00233)

-.00748

(-.03832,.02335)

.9985

Without intercept

Abs=mC

.00227

(.00224,.00230)

N/A

.9994

17

Table A 1: Regression analysis output from Spectrophotometer data with intercept

SUMMARY OUTPUT

Regression Statistics

Multiple R

R Square

Adjusted R Square

Standard Error

Observations

0.9992

0.9985

0.9984

0.0318

24

ANOVA

df

Regression

Residual

Total

Intercept

X Variable 1

SS

1

22

23

14.545

0.022

14.568

Coefficients Standard Error

-0.00748

0.01094

0.00228

0.00002

MS

14.545

0.001

t Stat

-0.68413

119.76079

F

Significance F

14342.647

1.830E-32

P-value

0.50103

0.00000

Lower 95%

Upper 95% Lower 99.0% Upper 99.0%

-0.03017

0.01520

-0.03832

0.02335

0.00224

0.00232

0.00223

0.00233

at 500 nm

Reject intercept

18

Table A 2: Regression analysis output from Spectrophotometer data with intercept=0

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.9997

R Square

0.9994

Adjusted R Square

0.9560

Standard Error

0.0315

Observations

24

ANOVA

df

Regression

Residual

Total

Intercept

X Variable 1

SS

1

23

24

40.825

0.023

40.848

Coefficients Standard Error

0

#N/A

2.268E-03

1.117E-05

Significance

MS

F

F

40.8247 41208.50403 1.679E-37

0.0010

t Stat

#N/A

2.030E+02

P-value

Lower 95% Upper 95% Lower 99.0% Upper 99.0%

#N/A

#N/A

#N/A

#N/A

#N/A

6.327E-39 0.002245 0.002291

0.002237

0.002300

at 500 nm

Abs. = 2.268×10^-3 *Conc.

Conc. = XXXX * Abs.

19

Data Analysis (III)

• Format, significant digits

• Show how you decide the equations (with or without intercept)

based on the results of the linear regression analysis

• Apply the equations (one measure at wavelength = 500 nm and one

measure at wavelength = 520 nm) and calculate the concentration

of tracer in the unknown samples.

• Show the final equation in the form of

C (mg/L) = a Abs + b

(b can be zero or any value, depending on the results of your

regression analysis)

• These are the final equations that will be used in later experiments

for determining tracer concentrations for complete mix and plug

flow reactors.

20

Lab1 Schedule

• Group A: 2 pm (7 students)

• Group B: 2:40 pm (6 students)

• Group C: 2 pm (7 students) Friday.

• Results from Group A to C will be shared,

students in the same lab section will analyze

the same data.

21

Water Resources and Environmental

Engineering Laboratory

Writing Scientific and Engineering Reports

CE 304 SP2019

Technical Writing

Kevin Wang

Outline

•

•

•

•

Introduction

Structure of a technical report

Writing by Sections

Tips for report writing

How Engineers Spend Their Time: Early Career

25-50

______%

Engineering: Designing, measuring,

calculating, problem-solving

______%

Communicating: Writing reports, letters,

50-75

memos, proposals; giving presentations,

talking to colleagues, supervisors, and

clients

3

https://ibrahimelsawy.files.wordpress.com/2012/02/communication-engineer1.jpg

General Structure of a scientific

Writing

• In scientific writing, IMRaD (Introduction,

Methods, Results, and Discussion,

Conclusion) refers to a common organization

structure

Structure of a scientific /engineering

Report

•

•

•

•

•

•

•

•

•

Title Page

Table of Contents

Abstract

Introduction

Methods and Procedures

Results and Discussion

Summary and Conclusions

References

Appendices

Abstract

Brief trajectory (objectives, major findings, conclusion) of the report

Introduction

Background information, importance of the work,

objectives, scope of works

Methods and Procedures

Exp. Procedures

Data Analysis

The steps and equipments Equations, theories, statistic

you used in the lab

tools

Results and Discussion

Visually and textually represents research findings

Interpret the findings: Primary results vs secondary

results; Results vs. theories , Sources of error,

Conclusions

Summary of goals, results and discussion, implication of

the findings

6

Procedures and Methods

How did you do it?

• Experimental Procedures and Methods

– History of work completed

– Make use of illustrations

– Flow chart

Do not provide a step by step set of instructions

that are found in the lab manual!

• Methods of Data Analysis

– Formulas, equations, theory, statistics

Results and Discussion

• Results:

What did you find?

– Present data collected to support objectives

(Tables & Graphs)

– Use sub-headings to keep results of the same type

together, which is easier to review and read

– For the data, decide on a logical order that tells a

clear story and makes it and easy to understand

Results and Discussion

• Discussion:

What does it all mean?

– Discuss results with regard to objectives, explain the

data and significance of the information in the tables

and graphs.

– How do these results relate to the original question or

objectives outlined in the Introduction section?

– Do the data support your hypothesis? Comparison of

results with theory or accepted formulas should be

discussed.

– Sources of error should be addressed with respect to

your findings and the significance of these errors with

respect to the objectives of the lab

Results and Discussion

• Discussion:

What does it all mean?

– Discuss weaknesses and discrepancies. If your

results were unexpected, try to explain why

– Is there another way to interpret your results?

– What further research would be necessary to

answer the questions raised by your results?

– Explain what is new without exaggerating

Conclusions

• Summary of goals

• Summary of Results

– Findings from the data

You should provide a clear scientific

justification for your work in this

section

The Conclusion should concisely

provide the key message(s) the author

wishes to convey

• Implication of the findings

• Summary of recommendations

– Improve the data quality (accuracy or precision)

– Improve the experimental methods

A common error in this section is repeating the abstract, or just listing

experimental results.

Introduction

Why did you do it?

• Background (1st)

What did you do?

– Explain the importance of this lab in Engineering

practice.

• Objectives (2nd)

– State the practical objectives of the lab.

• Scope of works (3rd)

– Provide an overview of the how the objectives

were achieved, that is, what will be done in this

lab.

Move from general to specific: problem in real world / research topics

/ textbook –> your experiment.

Abstract

what you did and what the

important findings in your

research were.

• Single page alone! (requirement for the report format

in this class)

• What information should be provided in the Abstract?

– Objectives and Background Statement (1-2 sentences,

What did you investigate? Why?)

– Scope of work(1-2 sentences, What did you do?)

– Highlight Significant Findings (2 to 3 sentences, What did

you find out?)

– State major conclusions and significance. (1-2 sentences,

What do your results mean? So what?)

– One to two paragraphs total (150-300 words)

Abstract

• What to avoid:

– Do not include references to figures, tables,

equations, or sources.

– Do not include information not in report.

– Using jargon, uncommon abbreviations and

references

References and Appendix

• References

– Provide a bibliographic list of references used in the

lab report.

• Appendix (starting from an new page)

– Original data from lab, calculations (or at least one

complete set of well documented sample

calculations),

– Any other related information which supports the lab

report, but does not fit in the main report.

– All information and data needed to develop the

results of the lab or project should be presented

either in the main report or the appendix.

How to start it?

• Suggested writing order:

1.

2.

Perform all required data analysis

Have all the Figures, Tables, or Equations ready

Methods and Procedures

Write down the Exp. Steps ASAP after the lab

3.

Results and Discussion / Appendices

Put your answers for application problems in Appendices

4.

5.

6.

Conclusions

Introduction

Abstract

Major findings should be mentioned

7.

References

But we are not finished yet!

• This is just the “first draft” of your report!

Check ! Check ! Check!

Check List (attach this Table in the last page of your first two reports)

Items

Title page (format)

Table of Contents (format)

Structured abstract (Objectives, important findings and conclusion), single page alone

Introduction (Importance, objectives, scope of work)

Experimental Procedures and Data Analysis Methods

Results and discussion (rational thinking, present your data or results in a logical order, sub headings)

Conclusion

Figure legends

Captions for Figure (bottom) and Table (above)

Significant digits (round up to hundredths decimal for most of data) or scientific expression

References are superscript in text.

Text is 12 point, double-spaced.

Text is in Microsoft Word.

Acronym use is limited.

Report has been checked for spelling and grammar.

The report file name should be named in the following way: first name last name_lab#

Answers for Application questions (N/A if there is no application question)

Tips for Report Writing (I)

• Avoid vague generalizations

– “good data”, “very high temperature”, “good R2 values”

• Use Headings and Subheadings

Example: In Lab

– Spectrophotometer,

– Colorimeter

• Avoid the use of personal pronouns such as “we” or “I”

– Passive voice

– Student measured the absorbance of unknown samples with colorimeter.

– The absorbance of unknown samples were measured with colorimeter.

• Tense

–

–

–

–

Past tense to describe what was done

Past tense for results obtained

Past tense to describe findings, with present tense to interpret results

Present tense to refer to figures, tables and graphs

• Avoid long c…

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