California State Polytechnic University, PomonaChemical & Materials Engineering

CHE 333L

TRANSPORT LABORATORY IILABORATORY GUIDE

This manual was prepared from the materials and information provided by the Cal Poly Pomona

Chemical Engineering Faculty and Staff

Revised December, 2009 by K.H. Pang

TABLE OF CONTENTSPage

Pre-Laboratory Preparation 3Laboratory Rules 3Make the Most Out of Your Time in the Laboratory 4 Collection and Analysis of Experimental Data 5Error Analysis of Experimental Data 9 Linear Regression and Matrix Algebra 11Laboratory Notebook 16Laboratory Report 17Oral Presentation 23

EXPERIMENTS

Experiment #1 – Gas Absorption Column, Pressure Drop 25

Experiment #2 - Extended Surface Heat Transfer 29

Heat Transfer Along a Cylindrical Fin

Experiment #3 - Gas Membrane Separation 35

Experiment #4 - Double Pipe Heat Exchanger 42

Experiment #5 – Boiling Heat Transfer 47

Experiment #6 – Unsteady State Heat Transfer 54

Experiment #7 – Batch Reactor 58

Appendix A – Newton’s Method for Systems of Nonlinear Algebraic Equations 63

Appendix B – Temperature Measurements with Labview 68

Appendix C – DAC Express Operation Procedure 74

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PARTICIPATION IN CHEMICAL ENGINEERING LABORATORY

The Chemical Engineering Laboratory course has been set up as an open-ended learning experience rather than the traditional data sheet oriented laboratories you may have had in other courses. You will normally receive assignments in the form of memos, and you are expected to respond with reports as might be written if you were working in industry.

Pre-Lab Preparation

Each laboratory experiment has a well-defined objective. This objective will be represented by a numerical value, or a correlation allowing the calculation of this value, for the unit operation under study. This objective is accomplished through data taking, reduction, and analysis. The student should know the desired result before the experiment is undertaken. Otherwise insufficient data may be taken, the results may be incorrectly analyzed, or preposterous results may be reported.

Read your current assignment. Familiarize yourself with the theory relevant to the experiment and the equipment necessary to take the required data. Read the appropriate sections of your textbook and references. When you are sure you understand the problem, prepare in writing, a Pre-Lab Plan. This exercise is intended to provide the preparation necessary to undertake a successful experimental study.

The written plan should include a sketch of the experimental equipment, showing vessels, interconnecting piping, valves, and relevant instrumentation. Make sure you understand the purpose and safe operation of each of these equipment items before you start the experiment. The correct analysis of data, its accuracy, and correction for nonstandard operating conditions all require a thorough understanding of the instrumentation. The written plan should discuss the independent and dependent variables and how and over what range these independent variables will be measured (experimental grid)The plan should address the experimental procedure and the sequence of operations undertaken during the experiment. The plan should describe how the data would be correlated, based on what models and which literature information. This pre-lab must be completed before coming to lab. Bring the completed plan to the lab and have the instructor approve your work before undertaking any experimental work. Include the exercise as an appendix in your laboratory report.

Laboratory Rules

Attendance: All students are to report to the lab at the start of the period. Attendance in all sessions for the full 2 hours 50 minutes of each period is required, unless you are excused by the instructor. Unauthorized absences for part or all of any laboratory session will result in a reduced course grade. Normally work will be performed in the lab. Work in another area requires prior approval by the instructor.

Appropriate Clothing and Footwear: Good safety practices must be observed at all times in the laboratory. This practice includes the wearing of proper clothing, footwear, and eye

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protection. Wear shoes that cover the feet. Long pants are required. No sleeveless shirts or tank tops are permitted. Long sleeve shirts are preferred. Do not wear a hat. Do not wear long flowing clothes (that includes a tie). Long, loose hair must be restrained.

Safety Glasses must be worn in the laboratory at all times for those sessions in which experiments are being performed. A face shield and gloves must be worn when required.

Good Housekeeping. All equipment must be safely operated and all chemicals must be safely handled. Broken or damaged equipment should be reported to the instructor immediately. You are reminded that all equipment is to be cleaned and returned to its proper location after you finish the day's work. A clean laboratory is the responsibility of all group members. Do not leave the lab until it is clean. Refer to “Laboratory Safety Rules”

Safety Test Each student must pass a safety test during week 1

Making the most out of your time in the lab

- Good experimental work demands that data and runs be replicated. Since we cannot duplicate all conditions exactly, we make replicate runs, meaning that the conditions are almost the same but not necessarily identical. Not only should individual data be replicated (for instance a second, third, and fourth measurement of a flow rate) but also the whole run (something from which you can calculate an experimental result) should be replicated.

- When first doing a new experiment, try different things and become familiar with the experiment and the equipment. Then determine the widest possible ranges of the independent variables. In almost all cases you will want to take data over wide ranges of the independent variables. If the independent variables can easily be changed over a wide range, it is often good practice to conduct the first three experimental runs at the lowest, intermediate, and highest levels of the independent variable.

- Summarize and record in your laboratory notebook the information obtained from automatic data collection (by computer, by recorder, or whatever) as soon as possible.

- Get in the habit of working up your data as you go. Sometimes you can plot preliminary data to see trends. Other times you can calculate the experimental values and see if you are in the ballpark.

- In almost all cases you will be able to compare experimental calculations with theoretical and/or correlated values. In presenting your data and comparisons plan to use graphs if at all possible. If you are using tables, aim to make them concise, clear, and informative.

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- Acquire the habit of clearly identifying your experimental runs. Run 1, then 2, then 3 is appropriate. Or you can use letters; A. B. C. etc. If a run is a failure (this sometimes happens) the next run is still given a new number or letter.

- Most of the reference books listed for the experiments, as well as other reference books, will be available for perusal during the laboratory period.

Collection and Analysis of Experimental Data

The fundamental basis for a good laboratory report is data collection and record keeping. It is not uncommon that a considerable amount of time elapses between the data collection phase of an experiment and the eventual presentation of the results. The data, therefore, must be well defined and recorded accurately in a permanent bound laboratory notebook. An important requirement is that the notebook, “should be so clear and complete that any intelligent person familiar with the field to which it relates but unfamiliar with the specific investigation could, from the notebook alone, write a satisfactory report on the experimental work”1, 2.

1. Always use your data as you are taking it to make sample calculations of your results, dimensioning all numbers with their correct units. This simple step will insure that all the information is being recorded that will be necessary for you to make subsequent calculations for the report. Graph your results, with units, as the experiment progresses, not after you have taken all the data. Graph your data in the same way you intend to present it in your report, although it is not always necessary to make all unit conversions for an initial plot done in the lab. This plot may then be used to determine if the current experimental conditions are in the desired range, if the equipment is being incorrectly operated or is not functioning properly, or if the degree of experimental scatter is unacceptable. The plot may also be used to determine experimental conditions for subsequent data points. More data should be taken under conditions where the dependent variable changes more rapidly and less where the changes are smaller. The independent variable(s) should be changed sufficiently to make noticeable changes in the dependent variable.

Example:

1 Rhodes, F. H., “Technical Report Writing”, Mc Graw-Hill.22 Hanesian, D. and Perna A. J., “A Laboratory Manual for Fundamentals of Engineering Design”, NJIT.

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Figure 1. Pressure drop in a bed of particulate solids.

Data can be collected evenly, however the important point of fluidization should not be lost because the gas flow settings, hence Reynolds number, were not properly chosen.

2. Always indicate units of quantities that are measured.

3. Never record a calculation, dimension or note on a loose sheet of paper.

4. Sketches of experimental apparatus should be part of notebook. All important dimensions should be recorded.

5. Data from recorders should be put into a laboratory notebook. Label the data with a title, data, and description of the data. Prepare your data sheet based on your Pre-Lab plan. In many experiments you will be taking a series of readings. Record more data rather than less and, of course, include units with all numerical values. The original data sheet and any graphs should appear in the appendix of your report, and the data sheet carbon copy should be turned in to the instructor at the end of each data taking session. The complete data notebook should be turned in to the instructor at the end of the course for a grade.

Example:

UNSTEADY STATE HEAT TRANSFERJanuary 18, 1999Heating curve for water with aluminum cube

6. Always record the reading that you actual measure.

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Example:Manometer

Record left and right readings, not only the derived quantity P = 11 in.

Each table should be numbered, have a title and show all units.

Example:Table 1.

PRESSURE DROP IN PACKED COLUMNColumn diameter: 2 inchesPacked height:24 inchesColumn packing: 1/4 inch Raschig ring

Flow Rate of Flow Rate of Pressure DropWater Air Inches of water per

kg/m2.s kg/m2.s foot of packing

0 0.202 0.0750 0.279 0.1570 0.387 0.2750 0.436 0.3010 0.558 0.4030 0.610 0.4710.86 0.164 0.1070.86 0.199 0.1590.86 0.297 0.2620.86 0.362 0.4710.86 0.501 0.7850.86 0.597 1.247

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All graphs should have a Figure number, have clearly labeled coordinates and all parameters labeled. Label symbols should be used for different parameters.

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Example:

Figure 1 Pressure drop in packed column.

Dimensionless numbers should be used if possible. For example: a plot of friction factor versus Reynolds number is better than a plot of P versus velocity.

7. Notebooks become legal evidence in patent cases. Therefore, always date, sign and witness.

Example:

Experiment #1 January 18, 1999Extended Surface Heat Transfer

Signed ____________________ 10/1/02 ____________________ 10/1/02 ____________________ 10/1/02

Witness (instructor) ____________________ 10/1/02

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8. Notebooks should be neat. Write in ink. Do not erase. If necessary line out with one line.

Error Analysis of Experimental Data

An error analysis should always be an integral part of your data analysis. It is important to take sufficient replicate data points, where possible, to enable you to perform a subsequent error analysis of the results. The ultimate objective of this analysis is to minimize this error.

The treatment of experimental data does not end when the desired numerical results have been obtained. An important part of the treatment is the determination of the uncertainty associated with the numerical results3 . Every measurement of data is subject to error that can not be determined exactly. If the exact error were known it would be equivalent to measuring the quantity without error, since correction can be made for any known error. But it is possible to specify the highest amount by which the quantity might be in error.

Inaccuracies in measurements can occur due to mistakes and errors2. A mistake is the recording of a wrong reading (215 recorded as 251). An error can be consistent or random. A consistent error that usually can be corrected might come from a defect in the measuring device or the improper use of an instrument. For example: the use of a flow meter calibrated for air but used for ammonia or the use of a wrong scale on a wet test meter. Random errors are caused by fluctuations and sensitivity of the instrument or the inconsistent judgment of the experimenter. An example would be a fluctuating manometer.

Treatment of random errors.

The more measurements we take the more likely the average will be the most probable value. Let consider six measurements for the flow rate of a process stream.

Reading Flow rate F, cm3/s1 139.12 142.33 138.44 140.65 139.06 141.5

The estimate mean for the flow rate F is

33 Shoemaker, D. P. et al, “Experiments in Physical Chemistry”, McGraw-Hill, (1981)

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F= 1N ∑

i=1

N

F i = 140.15 where N = 6

If N is very large (N --> ) then the mean for the flow rate will be the true mean average m. The estimate standard deviation is given by

s = [ 1

N−1 (∑i=1

N

Fi2−N F2) ]

1/2

= 1.5579

Note: The estimate standard deviation can be obtained by the Matlab function std(F) where F = [139.1 142.3 138.4 140.6 139.0 141.5].

Since F is an estimated mean from a finite measurement, how confident are we that this is a true mean? The confidence level, (1 - ) is defined as the probability that the measured mean for a small sample F lies between a certain confidence interval. A 95 percent confidence means that = 0.05. The lower confidence interval is

F - c/2

and the upper confidence interval is

F + c/2

where c/2 =

tα /2 s

√N and t/2 is given from the Student-t distribution for small, finite sample size (N < 30). Student-t distribution and Student-t statistic were developed by W.S. Gosset in 1908 who used the pen name of “Student”. Table 1 gives values of t/2 for various confidence levels and N-1.

Table 1. Values of t/2

N-1 /2 = .05 /2 = .025 /2 = .01 1 6.314 12.706 31.8212 2.920 4.303 6.9653 2.353 3.182 4.5414 2.132 2.776 3.7475 2.015 2.571 3.3656 1.943 2.447 3.1437 1.894 2.365 2.9988 1.860 2.306 2.8969 1.833 2.262 2.821

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10 1.812 2.228 2.764

In this example, let = 0.05 which is the normal practice of giving 95 percent confidence limits for random errors based on small sample. Then

t/2 = 2.571 for N -1 = 5 from Table 1.

Therefore the lower confidence interval is

140.15 - (2.571)*(1.5579)/61/2 = 138.51

and the upper confidence interval is

140.15 + (2.571)*(1.5579)/61/2 = 141.79

Hence, 138.51 ¿ F ¿ 141.79

and, we are 95 percent confident that the true flow rate mean, F m, lies between 138.51

cm3/s and 141.79 cm3/s and F = 140.15 cm3/s is an estimate of the true mean. It must be emphasized, however, that systematic errors may be much higher than the random errors in unfavorable conditions. Therefore the sources of systematic errors must be identified and eliminated if possible.

Linear Regression

The following section provides you with the background of linear regression. You may use EXCEL/Tool/Data Analysis/Regression to perform your data analysis.

Error is inherent in data. When data exhibits substantial error rigorous techniques must be used to fit the "best" curve to the data. Otherwise prediction of intermediate values, or the derivatives of values, may yield unsatisfactory results.

Visual inspection may be used to fit the "best" line through data points, but this method is very subjective. Some criterion must be devised as a basis for the fit. One criterion would be to derive a curve that minimizes the discrepancy between the data points and the curve. Least-squares regression is one technique for accomplishing this objective.

It is easiest to interpolate between data points, and to develop correlation, when the dependent variable is linearly related to the independent variable. While individual variables may not be linearly related, they may be grouped together or mathematically manipulated, such as having their log or square root taken, to yield a linear relationship. Often theory serves as a guide for such manipulations. Since we are mainly interested in these linear relationships, we will discuss only the technique for linear least-squares regression.

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We wish to fit the "best" straight line to the set of paired data points: (x1,Y1), (x2,Y2), …, (xi,Yi). The mathematical expression for the calculated values is:

yi = a1 + a2 xi

where yi is the calculated (linear) value approximating the experimental value Yi. The model error, or residual, ei can be represented as

ei = Yi a1 a2 xi

where ei is discrepancy between the measured value Yi and the approximated value yi as predicted by the linear equation and shown in Figure 1.

Figure 1. Relationship between the model equation and the data

We wish to find values for a1 and a2 to give the "best" fit for all the data. One strategy is to minimize the sum of the squares of the errors or residuals, between the measured Yi's and the yi's calculated from the linear model.

MICROSOFT EXCEL provides you with the data analysis tool. Click on Tool/ Data Analysis/Regress and fill in the x-y data. The following example shows you how to interpret the regression results from EXCEL.

The objective in the example is to find a relationship between pressure drop in a column and the gas velocity. Table (1) tabulates pressure drop versus gas velocity data. Table (2) shows results of the regression analysis. The objective is to determine whether there is a significant correlation between pressure drop and gas velocity. There are many indicators in Table (2). The simplest indicator is the 95% confidence limits of the slope. The last two rows of the Table (2) show “Intercept” and “X Variable 1”. Under the column,”Coefficients”, the first number is the intercept and the second number is the slope. The column “Standard Error” shows the standard deviation of the intercept and the slope. If you follow the row “X Variable 1”, you will find the 95% confidence limits of the slope. If the limits do not change in sign, that is from negative to positive or vice versa, then the slope is “significantly” different from zero and you can conclude that there is a significant correlation at the 95% confidence level. You will get the same

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conclusion if you compare the “t-stat” of the slope, in this case, 8.2723, with the tabulated t-value from the student-t table. If the “t-stat” is larger than the tabulated values, then the correlation is significant. In this latter test the “t-stat” is the ratio of the absolute value of (slope – 0)/( standard error of slope). You are using the student-t test to see whether the slope is significantly different from zero.

Figure (1) shows a plot of Pressure Drop versus Gas Velocity and the straight line relationship.

Table (1) Pressure Drop versus Gas Velocity Data

X YGas Velocity Pressure Dropft/sec inches water

1 42 53 74 85 66 97 118 109 14

10 15

Table (2) Regression Analysis Results

SUMMARY OUTPUT

Regression Statistics

Multiple R0.94621904

2

R Square0.89533047

6Adjusted R Square

0.882246785

Standard Error

1.257703535

Observations 10

ANOVA

  df SS MS FSignificanc

e F

Regression 1108.245454

5108.24545

568.431034

5 3.43E-05

Residual 812.6545454

51.5818181

8Total 9 120.9      

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  CoefficientsStandard

Error t Stat P-value Lower 95% Upper 95%Intercept 2.6000 0.8592 3.0262 0.0164 0.6187 4.5813X Variable 1 1.1455 0.1385 8.2723 0.0000 0.8261 1.4648

Figure 1 Pressure Drop Vs Gas Velocity

4

6

8

10

12

14

16

0 2 4 6 8 10 12

Velocity, ft/sec

Pres

sure

Dro

p, in

ches

wat

er

Another useful method of data analysis is to determine whether a set of measured data agree with calculated values. The following example shows how regression analysis can be used for this determination. Table (3) tabulates measured and calculated pressure drop. Regression analysis is used to determine the relationship between these two set of values.. Table (2) shows results of the regression analysis. If the measured values agree perfectly with the calculated values, the regression would yield a straight line with a slope equal to 1. If the 95% confidence limits of the slope include the slope of 1, then it can be concluded that the slope is not significantly different from 1 at the 95% confidence level and the measured data agree with the calculated values. Table (3) Measured and Calculated Pressure Drops

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Measured Calculated Pressure Drop Pressure Dropinches water inches water

4 45 67 88 96 109 11

11 1210 1314 1415 15

Table (4) Results of Regression Analysis- Example 2

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.9314R Square 0.8676Adjusted R Square 0.8511Standard Error 1.3585Observations 10

ANOVA

  df SS MS FSignificance

FRegression 1 96.83 96.834 52.467 8.86E-05Residual 8 14.76 1.845Total 9 111.6      

 Coefficient

sStandard Error t Stat P-value Lower 95% Upper 95%

Intercept 2.2349 1.1806 1.8930 0.0950 -0.4876 4.9574X Variable 1 0.8950 0.1236 7.2432 0.0001 0.6100 1.1799

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Calculated Vs Measured Pressure Drops

4

6

8

10

12

14

16

4 6 8 10 12 14 16

Measured Pressure Drop, inches of water

Calc

ulat

ed P

ress

ure

Dro

p, in

ches

of w

ater

Series1

Linear (Series1)

Figure (2) Calculated versus Measured Pressure Drops

Lab Notebook

Every group must have a lab notebook (with duplicate numbered pages). During each lab make notes of everything you are doing and every measurement you make. Your notebook will be evaluated so make sure it is legible and understandable. Each page of the notebook should be signed by the data taker and witnessed by a group member and the instructor. Original data sheets should appear in the lab report appendix while the carbon copies should be given to the instructor at the end of each data taking session. In your lab notebook:

Write in ink and record all observations directly in the notebookDo not erase. If necessary line out errors with one lineAt the top of each page put the date and the experiment nameWhen you finish a page, sign and witness your name with dateNever write on a page after you have signed it

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Rotate recording among group members

Laboratory Report

Unless given other instructions, students will submit group laboratory reports. Each group member is responsible for the entire written report. Inclusion of work from others or non-referenced sources will result in an "F" grade. Reports must be written according to the format described in the Laboratory Manual. All reports must be double-spaced, typed. A sample of the title page is given.

Laboratory reports are due one week after the scheduled completion of experimental work, at the beginning of the laboratory period. Late reports will not be accepted. Reports will be graded both on technical content and on the presentation of the content. A laboratory report should include the following sections:

Title PageExecutive SummaryIntroductionObjectives ScopeProcedure Results and DiscussionsConclusions and RecommendationsAppendix

Title Page

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California State Polytechnic University, PomonaChemical and Materials Engineering

CHE 3221L- TRANSPORT LABORATORY IFALL SEMESTER, 2018

EXPERIMENT #1

Column Operating Characteristics

INSTRUCTOR:Lloyd L. Lee

SECTION 11

GROUP AMEMBERS: Brady, Tom

Brees, DrewRogers, Aaron

DUE DATE: September 27, 2018

EXECUTIVE SUMMARY (10) ______INTRODUCTION/OBJECTIVES (10) ______RESULTS & DISCUSSION (30) ______ a) Background & Procedure b) Treatment of data c) Presentation of relevant information (including results on graphical, tabular or equation forms)CONCLUSIONS & RECOMMENDATIONS (10) ______APPENDIX a) Sample calculations (10) ______ b) Error analysis (10) ______ c) Original raw data (from Notebook) (10) ______GENERAL COMPLETENESS, CONCISENESS AND NEATNESS (10) ______TOTAL (100) ______

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Executive Summary should be written in concise language fitted on a single page. It is written for an executive who is too busy to read the entire report and yet could make decisions based on the summary page. See Executive Summary below

Introduction. Research on industrial applications of the experiment and write a summary of your research. Objectives. One to two sentences to state why the experiment is performed. For example, “Determine operating characteristics of columns containing various packings” Scope. Describe how you intend to accomplish the above objectives. For example,” Determine pressure drop across the column; determine flooding conditions etc

Procedure. Write a step-by-step procedure that you follow to complete the experiment. For example, “ 1. Open the valve to allow water to run through the packing at X cc/min. 2. Open the valve slowly to allow air to run through the column making sure that water does not overflow…”In your procedure, you must include an experimental grid, a table showing all experiments you intend to run. For example,

Packing type Experiments Air flow rate liter/sec

Water flow rate liter/min

Raschig Rings 1 1 2Raschig Rings 2 1 4Raschig Rings 3 2 2Raschig Rings 4 2 4

Results and Discussions. Results are usually presented in Tables and Figures, which must be numbered and titled such as Table (1) Heat Exchanger Network Summary. All figures and tables must be referenced in the Discussion Section. If not, they should not be included. Graphs must be labeled and must have convenient scales on both the x- and y- axis. Hand-drawn graphs are acceptable. In this section you also discuss problems encountered and how you solve them.

Conclusions and Recommendations. State what conclusions you can draw from this lab. You can make any recommendations concerning this lab from scope to inaccuracies of measurements.

Appendix. In this section, you include all data sheets, calculations and any relevant materials that are too voluminous to be part of the main report. However, you must reference these contents in your main report. For example, in the Results section of the main report, you must state ” Data sheets for this experiment can be found in Appendix A”.

Executive Summaries/Abstracts

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(Excerpt from unknown source, CHE Department, Stanford University)

An abstract is a condensation of important information from a report or technical summary. It is usually one paragraph in length (approximately 200 words). It contains no equations, figures, tables, or graphs, and rarely contains references. It should be able to stand on its own, without either the title or the text, and should contain key words for referencing. An abstract should be written so that the maximum amount of information is contained in the minimum amount of space. There are two types of abstracts, those which describe the report and those which describe the work about which the report was written. The latter type is much more informative and will be used in this class.

An abstract should be written after the report is complete. It should be able to answer what was done, why it was done, how it was done, the outcome, and the significance of the results. Several general rules about abstracts are as follows.

1) Delete any sentence that does not make a positive contribution.2) The first sentence should say what was done.3) Address the general approach.4) Quote the most general results.5) State conclusions and significance

The first sentence should inform the reader of what was done, and sometimes why it was done. Examples of first sentences could be:

A materials balance approach was used to determine the location of the flame front for an in-situ oil shale retort.

The drag on a sphere in a viscous fluid was measured as a function of sphere size and flow rate.

The diffusivity of bovine serum albumin (BSA) in K-quark electrophoretic gel was measured and compared to literature values for BSA diffusivity in the major competing gels.

The next sentence or two should describe the method that was used to make the evaluations or comparisons raised in the first sentence. For example:

Off gases from an Occidental Oil (OXY-9) oil shale retort were analyzed by gas chromatography. The resultant values were used in a computer model that calculated the mass of oil shale combusted as a function of off-gas production and the location of the flame front.

Sphere of various sizes were attached to an apparatus designed to measure torque and placed in a channel of fluid that could be pumped at different rates. The torque measurements were converted into drag for each of the experiments and compared to predictions calculated according to the Sangani method.

Concentrated radiolabeled BSA was applied to one side of the gel. Strips of the gel were removed at hourly intervals. Radiolabel content was analyzed as a function of distance from the source. The diffusivity was calculated from this information based on a one-dimensional model.

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The next part of the abstract states the results. See the examples below:

The flame front predicted by the off-gas analysis lagged that indicated by the buried thermocouples.

The experimental results agreed well with the Sangani calculations at low flow rates (Re < 1) but deviated significantly at higher flow rates (Re > 10).

The measured diffusivity of BSA in K-quark gel was less than half that of the competing gels.

Finally, the significance of the results is stated:

Later mine analysis showed this to be the result of significant tunneling of the flame front. Both in-place thermocouples and off-gas analysis gave useful information about the location of a flame from in an in-situ oil shale retort.

The Sangani approach is quite effective for the prediction of the drag on a sphere for creeping flow conditions but must be used carefully at higher Reynold’s number flow.

Thus the K-quark gels will give better separation of components for lengthy separations than will the competing gels.

How to put together a laboratory report

1. ORGANIZE !!

2. Get good laboratory data and lots of it. (Read the section: Collection and Analysis of Experimental Data)

a. What is the error in the measurement of the variables?b. Identify runs as 1, 2, 3, etc. a different number for each run.c. Do all of this during the laboratory period.

3. Manipulate laboratory data. Perform calculations in the laboratory.

4. Calculate results; for example Diameter, T, k, Cp.a. What is the error of a replicated experiment?b. Do it in laboratory.

5. Note that data and sample calculations go in the Appendix.

6. Correlate experimental results with each other and with the literature or theoretical values.

a. Graphs are best if appropriate. b. If not a graph, then a table.c. Draw a curve through the data points of the graph. Draw the appropriate graph

(straight line or curve) according to what you know about the phenomenon. It is almost

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always incorrect to connect the data points by straight line. When drawing a curve, draw the proper one. If there is no inflection point do not show one.

d. Note that we usually compare experimental results to literature values. These are different from theoretical or correlated values that are calculated from a (probably very valid) theoretical or correlated equation.

e. Do as much of this as you can in the laboratory period.

7. Read the prescribed laboratory report format and FOLLOW IT.

8. Reports are prepared backwards!I) Do the Appendices and the experimental procedureII) Prepare result graphs or tables

a) Show consistency of experimental runsb) Compare and correlate experimental results with each otherc) Compare and correlate experimental results with literature data or with

theoretical results.d) Note that one of the best comparison is % error (be certain to show sign)

III) Discuss results. Place graphs or tables after their discussion.IV) Draw conclusions and make recommendationsV) Prepare the executive summary.

9. You are writing a technical report on a technical subject for a technical audience. Don't waste space and your reader's time with simplistic statements.

10. Number pages.

11. Number and title Graphs, Tables, Figures, and Appendix items

12. Aim to be "complete and concise" in the body of the report.

13. Watch significant figures. Usually three or four are appropriate. We are rarely justified in using more than four!

14. Prepare a Table of Contents.

15. The texts in reports will be read first. So any graph, table, figure or Appendix item should first be mentioned in the text. Be specific and state; for instance, "see Figure 3 for ∆T vs. time". Figure 3 should then appear on the next possible page.

16. Raw data tables or spreadsheets are generally too voluminous to be included in the main part of the report and should go to the Appendix.

Oral Presentation:

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Each laboratory group will present one oral report (20 minutes) during the quarter. In this presentation you will discuss your last experimental. The oral report will be graded according the following criteria:

Equal participation of all group membersTalk within time limit.Clarity and organization of the talk.Good speaking voice (clear, loud , well paced) with a dynamic

presentation.Rapport and interest developed in audience.Technical accuracy, correctness, and completeness.Appropriateness of technical level.Quality of visual aids.

Class Participation

To receive points for class participation, you must ask questions. Each person asking questions will receive from 1-5 points to maximum of 10 points.

The ability to speak before an audience is an invaluable asset that you must develop. This development, like writing, is a lifetime endeavor to reach perfection. Each presentation should be an improvement over the preceding one. A good presentation has the following structure:

1. Introduce the major points2. Explain each point in detail3. Review and summarize the major points

A good presentation requires that you start the preparation ahead of time and:

Produce uncluttered visual aidsOrganize the material well so that it is easy and logical to followPractice the presentation, if possible in front of an audienceSpeak to the entire audience instead of only to key peopleUse a conversational speaking style

Suggested content of your presentation:

* Define your problem. Explain the objective of your investigation. Discuss your experimental plan.* Describe your experimental system. Show a drawing (schematic) of your apparatus and explain how it was operated.* Describe the difficulties you encountered. Recommend how you would overcome these difficulties.* Discuss measurements that were made, or should be taken. Recommend the best operating range for your independent variables.* Discuss how the experimental data were, or should have been, analyzed.

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* Compare actual with the anticipated results. Discuss your conclusions.* Make recommendations for the next group performing the experiment

Appendix A

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Newton’s Method for Systems of Nonlinear Algebraic Equations

Consider two equations f1(x1, x2) and f2(x1, x2) for which the roots are desired. Let p10

, p20

be the guessed values for the roots. f1(x1, x2) and f2(x1, x2) can be expanded about point (p1

0, p2

0) to obtain

f1(x1, x2) = f1( p10

, p20

) +

∂ f 1

∂ x1 (x1 p10

) +

∂ f 1

∂ x2 (x2 p20

) = 0

f2(x1, x2) = f2( p10

, p20

) +

∂ f 2

∂ x1 (x1 p10

) +

∂ f 2

∂ x2 (x2 p20

) = 0

Let y10

= (x1 p10

) and = (x2 p20

), the above set can be written in the matrix form

[ ∂ f 1

∂ x1

∂ f 1

∂ x2

∂ f 2

∂ x1

∂ f 2

∂ x2][ y1

0

y20 ]

= [ f 1 ( p1

0 , p20 )

f 1 ( p10 , p2

0 )]or

J(p(0))y(0) = F(p(0))

In general, the superscript (0) can be replaced by (k1)

J(p(k-1))y(k-1) = F(p(k-1))

J(p(k-1)) is the Jacobian matrix of the system. The new guessed values x at iteration k are given by

x = p(k) = p(k-1) + y(k-1)

Example

Use Newton’s method with the initial guess x = [0.1 0.1 0.1] to obtain the solutions to the following equations2

f1(x1, x2, x3) = 3x1 cos(x2 x3)

12 = 0

f2(x1, x2, x3) = x12 81(x2 + 0.1)2 + sin x3 + 1.06 = 0

22 Numerical Analysis by Burden and Faires

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f2(x1, x2, x3) = e− x1 x2 + 20x3 +

10 π−33 = 0

Solution

The following two formulas can be applied to obtain the roots

J(p(k-1))y(k-1) = F(p(k-1))

J(p(k-1)) is the Jacobian matrix of the system.

J(p(k-1)) =

[∂ f 1

∂ x1

∂ f 1

∂ x2

∂ f 1

∂ x3

∂ f 2

∂ x1

∂ f 2

∂ x2

∂ f 2

∂ x3∂ f 3

∂ x1

∂ f 3

∂ x2

∂ f 3

∂ x3

]F(p(k-1)) is the column vector of the given functions

F(p(k-1)) = [ f 1 ( x1 , x2 , x3)f 2 ( x1 , x2 , x3)f 3 ( x1 , x2 , x3)

]The new guessed values x at iteration k are given by

x = p(k) = p(k-1) + y(k-1)

Table 1 lists the Matlab program to evaluate the roots from the given initial guesses.

Table 1 Matlab program for the example -------------% Newton Method% f1='3*x(1)-cos(x(2)*x(3))-.5';f2='x(1)*x(1)-81*(x(2)+.1)^2+sin(x(3))+1.06';f3= 'exp(-x(1)*x(2))+20*x(3)+10*pi/3-1' ;% Initial guess%x=[0.1 0.1 -0.1];for i=1:5f=[eval(f1) eval(f2) eval(f3)];Jt=[3 2*x(1) -x(2)*exp(-x(1)*x(2)) x(3)*sin(x(2)*x(3)) -162*(x(2)+.1) -x(1)*exp(-x(1)*x(2))

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x(2)*sin(x(2)*x(3)) cos(x(3)) 20]';%dx=Jt\f';x=x-dx';fprintf('x = ');disp(x)end

The Matlab program to solve equations (13-16) can be download from T.K. Nguyen website (http://www.csupomona.edu/~tknguyen/che333/home.htm). Make sure you understand the program. The system can be solved with measured values of xF, xR, yP, and r, leaving yi, , *, and KR as unknowns in the solution.

xF = xR( 1 ) + yP (13)

yi

1− y i = *

xR r− y i

(1−x R)r−(1− yi ) (14)

yPKR = (1 )*(xr y)lm (15)

(1yP) KR = (1 )[(1x)r (1y))]lm (16)

% Gas membrane separation calculation%Ph=[15 25 35 45 55];xf=.21;ypv=[.342 .394 .415 .431 .427;.367 .411 .456 .472 .476;.374 .436 .478 .510 .518]

;xrv=[.115 .101 .081 .075 .060;.178 .153 .135 .125 .111;.200 .189 .180 .174 .161];Kr=2;a=6;yi=0.2;theta=0.5;dy=.01;f1='yi*((1-xr)*r-(1-yi))-a*(1-yi)*(xr*r-yi)';f2='xr*(1-theta)+yp*theta-xf';dt1='((xf*r-yp)*(xr*r-yi)*(xf*r-yp+xr*r-yi)/2)^(1/3)';f3='yp*Kr*theta-(1-theta)*a*eval(dt1)';dt2='(((1-xf)*r-(1-yp))*((1-xr)*r-(1-yi))*((1-xf)*r-(1-yp)+(1-xr)*r-(1-yi))/2)^(1/3)';f4='(1-yp)*Kr*theta-(1-theta)*eval(dt2)';%df1dk=0;df1dt=0;df2dk=0;df2da=0;df2dy=0;df4da=0;

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for ni=1:3;for nj=1:5; xr=xrv(ni,nj);yp=ypv(ni,nj);r=(Ph(nj)+14.7)/14.7;%x=[Kr a yi theta];disp('Guessed values')fprintf('KR = %8.3f, alfa = %8.3f, yi = %8.3f, theta = %8.3f\n',Kr,a,yi,theta)for i=1:20%f=[eval(f1) eval(f2) eval(f3) eval(f4)];df1da=-(1-yi)*(xr*r-yi);df1dy=(1-xr)*r-(1-yi)+yi+a*(xr*r-yi)+a*(1-yi);df2dt=-xr+yp;dlm1=eval(dt1);dlm2=eval(dt2);df3dk=yp*theta;df3da=-(1-theta)*dlm1;df3dt=yp*Kr+a*dlm1;df4dk=(1-yp)*theta;df4dt=(1-yp)*Kr+dlm2;yi=yi+dy;df3dy=(eval(f3)-f(3))/dy;df4dy=(eval(f4)-f(4))/dy;yi=yi-dy;Jt=[df1dk df1da df1dy df1dt; df2dk df2da df2dy df2dt; df3dk df3da df3dy df3dt; df4dk df4da df4dy df4dt;];dx=Jt\f';x=x-dx';Kr=x(1);a=x(2);yi=x(3);theta=x(4);a_exp=yp*(1-xr)/xr/(1-yp);if max(abs(dx))<.001, break, endendfprintf('For P/p = %8.3f,Calculated values from %g iterations\n',r,i)fprintf('KR = %8.3f, alfa = %8.3f, alfa exp = %8.3f, yi = %8.3f, theta = %8.3f\

n',Kr,a,a_exp,yi,theta)

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disp(' ')endend

Appendix B

29

Temperature Measurements with Labview

Run the program Labview 6.1 located on the desktop. The following dialog box will appears

Click OK to arrive at this screen

Click “DAQ Solution” to obtain

30

Click “Next”

Click “Next” to arrive at the following screen

31

In the dialog box “Gallery Categories”, the highlight should be on Transducer Measurement. Choose Continuous Thermocouple Measurement in the dialog box “Common Solutions”. Click “Next” to arrive at the following screen

Click “Open Solution” to open up the following screen

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Click the down arrow on the right side of the dialog “Channels” and pick hp1. Next place the cursor after hp1 and type , hp4, hp5, and hp7 as shown below

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Click the right white arrow on the top left of the screen (under “Edit”) to run the program. You will receive the following display. You should note that the right arrow becomes black, the graph shows the three thermocouple temperatures with the numerical values shown on the right (you will likely have different values displayed).

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You can right click on the graph to open a dialog box for graphic control. You can choose “Auto scale Y” so that the temperatures readings will be scaled automatically and displayed on the graph.

If you choose “Auto scale Y”, the graph should look similar to the above screen.

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Appendix CDAC Express Operation Procedure

1. Go to Start Menu, Program, VT DAC Express, DAC Express. The following screen should appear.

2. Open the program testtemp in My Documents folder and go to step 5. If you cannot find testtemp in My Documents or you want to set up the DAC Express yourself then go to the next step.

3. Enable the channel connected to the board, which are channel 0 – 5. Channel 0 is the reference channel that uses an on-board thermistor. The channels that are not used will have to be manually disabled since the DAC program always enables channels 1 thru 31. This is shown in the screen below.

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4. Change the Function on Channel 1:0 to Temperature and change Transducer to TC-Reference Terminal Block (RT1) (122uA source). The EU will automatically change to Degree C. Change the Function on all other channels enabled to Temperature and change Transducer to Thermocouple K. The EU will also automatically change to Degree C.

5. Click on Timebase on the left hand side. Change the Scan Period to 1 second (or any appropriate time period). The Scan Rate will then change to 1 Scan/s. Fill in the time needed to record the data at Stop Recording. For example, 10 minutes of data acquisition equals to 600 seconds of recording.

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6. Click on Data Recorder on the left hand side. Click OK on the reminder. The following screen should appear.

7. Click on Show Display Wizard.

8. Select One Channel per Display and click Next.

9. Select All Current on Tab and click Next.

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10. Select all the channels listed and click Next.

11. Select the display type wanted (Readout, Bar Graph, Meter, or Stripchart) and click Create Displays.

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4. Start Recording the data by clicking on the Record button at the bottom of the screen.

5. When data recording is finish, provide the recording name and click OK.

6. Click on the data name on the left hand side under Data Viewer. The following screen should appear.

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7. Drag the green line in the bottom box to select all your data. Afterward, right click on the box and select Export Data.

8. Export the Data as a text file (*.txt) and click Export. After that, provide a file name and save it.

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9. Open Microsoft Excel. Click on Data, Import External Data, and Import Data

10. Select the file saved before and click Next.

11. After that, the following screen should appear. Click Finish.

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12. Select the cell to place the data and click OK.

13. Spreadsheet of sample run is shown in the screen below.

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