Experiments in transport phenomena crosby

Experiments in
Transport Phenomena
A Manual for Use in Chemical Engineering 324,
Transport Phenomena Laboratory
By E.J. Crosby
Revised by Thomas W. Chapman
Updated by Rafael Chavez, 2002
Chemical Engineering Department
University of Wisconsin-Madison
Madison, Wisconsin 53706
Copyright © 1999 by T.W. Chapman

ChE 324 Lab Manual
Preface
Page I-1
ChE 324 Transport Phenomena Laboratory
Experiments in
Transport Phenomena
by E.J. Crosby
revised by T.W. Chapman
updated by Rafael Chavez
Preface
Chemical Engineering 324, Transport Phenomena Laboratory, is an important
course in the chemical engineering curriculum. It is intended to accomplish three
objectives:
a. to demonstrate experimentally the major principles of the subject,
Transport Phenomena, which are presented in the lecture course, ChE 320;
b. to develop skills in engineering experimentation and data analysis; and,
c. to provide instruction and practice in methods of technical communication.
The textbook Transport Phenomena by Bird, Stewart, and Lightfoot (2002) is the
main source for the theoretical aspects of most of the topics treated in the laboratory.
Generally the notation used in this manual will be the same as that used in that book.
In this revision of the manual, the references were updated to the Second Edition
of the Transport Phenomena book. Some content was also added or modified to make the
manual more self-contained and easier to use.
The book by William Pfeiffer (2001) provides guidance regarding technical-
communication skills. Also useful are the books by Beer and McMurrey (1997), M. Alley
(1996), and the web pages of the technical-communication courses taught in Engineering

ChE 324 Lab Manual
Preface
Page I-2
Professional Development (http://www.engr.wisc.edu/epd/tc/). The elegant little book by
Strunk and White (1959) is an extremely valuable source of advice for writers.
During the semester the students work in small groups, performing weekly
experiments. Individual reports are prepared and submitted at the subsequent class
session. Each week students will be asked to prepare either a formal technical report or a
shorter technical memo. Each student will also make one oral presentation.
This lab manual provides general guidelines regarding the operation of the course
as well as descriptions of each of the laboratory experiments. Students are expected to
review the subject of each week's laboratory prior to the class in order to understand
better the significance of the lab exercises. Also, a plan for data collection and analysis
should be prepared ahead of time. Planning prepares the students to complete many of the
necessary calculations during the lab period. Short quizzes may be given at the
beginning of the lab sessions to confirm such preparation. The course will be much less
time consuming for students who can complete most of the data analysis during the lab
session.
Each week the assigned experiment is put into context by a hypothetical memo
written by a fictitious industrial supervisor to his engineering staff. These memos,
included in Appendix 15, are intended to give the students a practical motivation for
conducting the assigned study. With a concrete context, the students should find it easier
to write a realistic and relevant report rather than simply commenting on whether their
data agreed with “theory”, that is, what they perceive as the “right” answer because it
comes from a textbook. Thus, student reports should be written in response to these
assignment memos.
References
Alley, M., The Craft of Scientific Writing, 3rd
edition, Springer-Verlag, New York (1996)
Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, 2nd
.Edition, John
Wiley & Sons, New York (2002)
Beer, D., and D. McMurrey, A Guide to Writing as an Engineer, John Wiley & Sons,
New York (1997)
Pfeiffer, William S., Pocket Guide to Technical Writing, 2nd
Edition, Prentice Hall, Upper
Saddle River, New Jersey (2001)
Strunk, W., Jr., and E.B. White, The Elements of Style, 3rd
edition, Macmillan, New York
(1972)

ChE 324 Lab Manual
Table of Contents
Page I-3
ChE 324 Transport Phenomena Laboratory
Experiments in
Transport Phenomena
by E.J. Crosby
revised by T.W. Chapman
updated by R. Chavez
Contents
Preface I-1
Introduction I-5
I. The Need for Experimentation in Chemical Engineering I-6
II. Course Guidelines for ChE 324 I-8
III. Use of Computers in ChE 324 I-11
IV. Safety in the Laboratory I-13
V. Technical Communication I-14
A. Format of Formal Reports I-14
B. Content of Memos I-19
C. Oral Reports I-20
VI. Experimental Design and Statistical Analysis of Data I-23
Part A. Measurement of Transport Properties
A.1 Viscosity of Newtonian Liquids A.1-1
A.2 Thermal Conductivity of Solids A.2-1

ChE 324 Lab Manual
Table of Contents
Page I-4
Part. B. Measurement of Profiles of Velocity, Temperature,
and Concentration
B.1 Velocity Profiles in Steady Turbulent Flow B.1-1
B.2 Temperature Profiles in Solid Rods B.2-1
B.3 Concentration Profiles in a Stagnant Film B.3-1
Part C. Measurement of Transport Coefficients
C.1 Friction Factors for Flow in Circular Tubes C.1-1
C.2. Heat-transfer Coefficients in Circular Tubes C.2-1
Part D. Analysis of Macroscopic Systems
D.2 Efflux Time for a Tank with Exit Pipe D.2-1
D.3 Heating Liquids in Tank Storage D.3-1
Appendices
Appendix 1. Sample Laboratory Report Ap.1-1
Appendix 2. (Suppressed)
Appendix 4. Density and Viscosity of Aqueous Sucrose and Glycerol
Solutions
Ap.4-1
Appendix 5. Density and Viscosity of Water Ap.5-1
Appendix 6. Eigenvalues for Experiment A.2 Ap.6-1
Appendix 8. MathCAD Program to Calculate Temperature Profiles in
Rods for Experiment B.2
Ap.8-1
Appendix 9. MathCAD Program to Calculate Unsteady-state
Concentration Profiles for Experiment B.3
Ap.9-1
Appendix 10. Vapor Pressure of Acetone Ap.10-1
Appendix 11. Excel Spreadsheet for Preliminary Data Analysis of
Friction Factors. Experiment C.1
Ap.11-1
Appendix 12. Excel Spreadsheet for Analysis of Data in Experiment
C.2, Heat Transfer Coefficients
Ap.12-1
Appendix 13. Statistical Analysis of Experimental Data Ap.13-1
Appendix 14. Experiment D.3 Benchmark Problem Ap.14-1

ChE 324 Lab Manual
I. The need for experimentation in Chemical Engineering
Page I-6
I. The Need for Experimentation in Chemical
Engineering
One of the general objectives of chemical engineers is to develop quantitative
models of chemical processes that are useful for process design, simulation, and control.
Many chemical engineering course, particularly Transport Phenomena, present
fundamental principles that lead to deterministic models of chemical and physical
processes. Combination of the basic concepts of conservation, of mass, momentum,
energy, and chemical species, with relevant rate laws leads to either macroscopic or
differential balances that, in principle, can predict the behavior of chemical processes.
Thus, it is demonstrated that such processes can be analyzed on a rational basis.
The mathematical models derived by this approach contain physical properties on
the material that is involved. Properties such as density, viscosity, heat capacity, thermal
conductivity, diffusion coefficient, etc. necessarily appear in the theoretical equations.
Thus, quantitative application of the models requires numerical values of such properties.
For pure materials, property values may or may not be available in the literature. For
mixtures or materials at extreme conditions of temperature and pressure, experimental
values are quite rare.
In principle, thermodynamic and transport properties might be calculated
theoretically from molecular properties, but at this time, only the properties of simple
molecules in the low-density gas state can be estimated theoretically with reasonable
accuracy. Therefore, one is frequently faced with the need to measure material properties
experimentally.
On the macroscopic scale, the methods of transport phenomena allow one to
compute transport rates and detailed profiles of velocity, temperature, and concentration
but only in very simple geometries and for streamline or laminar fluid flow. When
geometries or boundary conditions become complicated, the mathematics of solving the
differential equations of change may become intractable or at least require numerical
solution on a computer. A more serious obstacle arises when fluid flow is turbulent.
Turbulent flow is inherently random and chaotic; no rigorous theoretical method is yet
available for predicting velocity, temperature, and concentration profiles.
With complex geometries or with turbulent fluid flow, the macroscopic balances
of transport phenomena are still relevant, but empirical models must be used to
characterize interfacial rates. Thus, one defines fluid-film transport coefficients such as
the friction factor, the heat-transfer coefficient, and the mass-transfer coefficient.
Although dimensional analysis of the differential conservation equations can identify
what independent groups of variables should appear in the functional dependence of rate
quantities on operating conditions, the actual relationships must be determined

ChE 324 Lab Manual
I. The need for experimentation in Chemical Engineering
Page I-7
experimentally. Fortunately, results for a given geometry can be generalized as
dimensionless empirical correlations that apply to a wide range of materials.
The purpose of this course is that students recognize that the physical quantities
discussed in their transport phenomena course can indeed be measured. The experiments
are grouped into four categories: measurement of transport properties, observation of
profiles, measurements of transport coefficients, and analyses of macroscopic systems.
In each section there are experiments that deal with fluid flow, with heat transfer, and
with mass transfer.
Too often undergraduate students approach laboratory courses with the idea that
their objective is to prove basic theories or to obtain results that agree with published
information. Laboratory reports then focus on whether the experimental results agree
with the "right" answer and on explanations of why the agreement is not perfect.
Although there may be a correct value for an intrinsic property value of a material, such
as density or thermal conductivity, the same can not be said of transport characteristics.
Transport coefficients and similar efficiency factors of chemical-process systems depend
on many variables. Thus, no generalized correlation given in the literature can be
expected to predict the behavior of a particular experimental system perfectly.
Experimental data are precious. Quantitative (and qualitative) observations of the
performance of a particular system are costly in time, materials, instrumentation, and
effort. But, provided that the experiments are well designed and the measurements done
carefully, the results possess the quality of uniqueness. The results tell one how this
particular system behaves under the conditions tested. Discrepancies between direct
measurements and published results for similar systems should be analyzed to ensure that
no critical features have been overlooked in the measurements or data analysis. But,
almost always, the direct results should be taken as the best indication of that system's
operating characteristics.
In order to combat the tendency of students to view their experiments as simply
an exercise in replicating known results, each experiment is introduced to the students
with a memo that provides a hypothetical context for experiment. The students are
encouraged to imagine themselves working in the chemical industry, and their supervisor
gives them an assignment to conduct an experiment for some particular purpose in their
company. These memos are intended to present a realistic and practical motivation for
doing each experiment. Accepting this context and motivation should make it easier for
students to write interesting lab reports that address the basic questions of how the
experiment system actually behaves.

ChE 324 Lab Manual
Course Guidelines
Page I-8
II. Course Guidelines
1. WEEKLY ACTIVITIES
The course meets weekly for one four-hour period. The first hour is normally
used for instruction, discussion, oral presentations, and occasional quizzes. The
remaining three hours are devoted to measurements and calculations in the laboratory.
Students conduct the experiments in groups, as assigned by the instructor.
However, except when specifically indicated, each individual must prepare and submit a
separate report. Reports are due by class time in the following week. To minimize the
time required for this course, students should come to class prepared for the experiment
of the week. That is, they should review the experimental procedure and the underlying
theory before coming to class. Also, they should do as much data analysis as possible
during the lab session.
2. GRADING PROCEDURE
The grade for this course will be based approximately upon the following
distribution of credit:
Category Weight
Class Quizzes and Exercises 10 %
Oral reports 5 %
Laboratory Reports 80 %
Professionalism 5 %
Reports are due at the next class following the experimental session. Late reports
will be penalized 10%/day. Weekends count as two days.
3. DAMAGE TO EQUIPMENT
Fee cards with charges for costs will be issued to anyone who, in the opinion of
the instructional staff, damages or destroys equipment because of carelessness or
negligence.
4. HOUSEKEEPING
Cleanliness in the laboratory is mandatory. Because of the large number of
students using the laboratory, it is difficult to keep the laboratory clean and orderly unless
each student cleans up his or her work area at the close of each instructional period. Each

ChE 324 Lab Manual
Course Guidelines
Page I-9
group of students is responsible for its work area. All utilities are to be turned off, and all
spills are to be cleaned up before any member of the group leaves the laboratory.
5. SAFETY
All personnel are required to wear safety glasses and proper clothing when in the
laboratory in accordance with the specified safety procedures. Each individual student
must acquire his or her own safety glasses and wear them at all times in the laboratory.
Substantial footware, other than sandals, and proper clothing that provides protection
from accidental spills and burns should be worn.
6. SMOKING, EATING, AND DRINKING
As indicated in the laboratory safety procedures, no smoking, eating, or drinking
in any form is allowed in the laboratory or adjoining rooms.
7. COMPUTATIONAL AIDS
As calculations can be made while experimental measurements are in progress,
students should bring to the laboratory hand calculators, handbooks, graph paper, etc., for
the analysis of data. Computers connected to the college network and file servers are
available adjacent to the lab and should be used as needed. These computers are
available to all ChE students during open hours, but ChE 324 students have priority
during the lab period.
8. LABORATORY REPORTS
Reports are expected to be submitted in typewritten form except that sample
calculations in the appendix may be hand written. Only the the body of the main report
need be submitted on high-quality paper. Appendices may be printed on draft-quality
paper,or on paper with printing on the reverse side, in order to minimize paper costs.
Nevertheless, students who print at CAE should expect to purchase some additional paper
beyond the initial semester allotment.
The laboratory instructor will present examples of proper formats for reports and
memos and will indicate how the reports should be bound.
9. WRITING SKILLS
A primary objective of this course is to develop the students’ writing skills.
Dictionaries and other references should be used to avoid errors in spelling, punctuation,
grammar, and word usage. In addition to the books recommended with the syllabus, there
are other references available in the library. In particular, 15 relevant videotapes
produced for EPD 201, Basic Technical Writing, can be viewed at Wendt Library.
Detailed guidelines for writing technical reports are available from EPD on the web at

ChE 324 Lab Manual
Course Guidelines
Page I-10
http://fbox.vt.edu:10021/eng/mech/writing/. Students who have difficulty with basic
writing skills should consult the campus Writing Lab in the Helen C. White Building.
Use a style similar to that used in chemical engineering publications to present equations,
figures, tables and citations.
10. ORAL PRESENTATIONS
Ability in oral communciation is just as important to an engineer as effective
written communication. Therefore, among the class exercises each student will give a
short technical presentation. Individual students will be asked to present his or her results
from one of the lab experiments in the course. Alternatively, one may propose another
technical topic, such as a project from a summer job or co-op. Specific individual
assignments will be given by the instructors. Presentations should be kept short and to
the point. Effective visual aids, i.e., overhead transparencies, should be used to enhance
the presentation. Guidance on presentation methods will be given by the lab instructor.
Students should also consult the textbooks on technical communication.

ChE 324 Lab Manual
Use of Computers in ChE324
Page I-11
III. Use of Computers in ChE 324
As engineers, students in this course are expected to be computer literate. Also,
they are expected to develop the ability to produce reports of a high professional
standard. This means that data should be presented and analyzed using the most modern
tools, and reports should be presented in a polished form, typed and containing neat
graphs and tables. Therefore, it is necessary for students to use commonly accepted
computer tools in preparing their reports.
Software
The majority of students in ChE 324 use Microsoft Word for their reports and
Microsoft Excel or Mathcad for the data analysis and preparation of graphs. Use of these
particular programs is not required, but they are readily available through the Computer-
Aided Engineering (CAE) facilities in the College. Also, in general, the lab instructors
are familiar with these common programs and thus are prepared to offer assistance to
students performing specific tasks with their data or reports. It will be assumed that the
students already have a working knowledge of computers and programs of this type so
detailed instruction will not be presented. Those people who need help should see the
teaching assistants during their office hours and make use of the handouts and manuals
and of the consultants at CAE.
Computer Resources
Students are encouraged to use the many CAE computers provided in the College
to work on their reports. During the laboratory, a lab-group member or two should be
able to do much of the data analysis while others are collecting more data. There is a
satellite CAE computer room adjacent to the transport lab that now contains Windows-
based machines. These machines are connected to the CAE network so that students can
save their files directly. Of course, one can also save documents on Diskettes.
MSDS (Material Safety Data Sheet) information is available at a number of
websites, e.g., http://msds.pdc.cornell.edu. Information is provided for the safe handlling
of most chemical compounds, including toxicity, flash point, volatility, etc. It is always
wise and prudent to check on potential hazards with any chemical that one may be using.
Course Homepages
Most ChE324 instructors take advantage of internet resources to distribute materials and
to communicate with students. Materials related to ChE 324 are posted on a course
homepage at http://courses.engr.wisc.edu/ecow/get/che/324/. Students are expected to

ChE 324 Lab Manual
Use of Computers in ChE324
Page I-12
make use of this method to obtain course materials. The Appendix of this manual
contains several Excel and Mathcad programs that have been set up to facilitate the data
analysis in particular experiments. Those files are also available on the course homepage.
The materials can be accessed from off-campus computers as in the CAE labs.

ChE 324 Lab Manual
Safety in the Laboratory
Page I-13
IV. Safety in the Laboratory
The Department of Chemical Engineering and the University have provided a safe
laboratory, safe equipment, and safe experimental procedures for this course. However, safety in
any laboratory ultimately rests with each individual working there. A few specific safety
procedures will be emphasized in ChE 324 to reduce the chance of an accident or injury and to
help develop proper habits of laboratory safety. Issues of concern include
1. Safety Glasses: All persons in the laboratory will wear safety glasses whenever they are
whithin the restricted area of the laboratory.
2. Shoes: Footware must provide protection. Sandals and open-toed shoes will not be
permitted.
3. Eating, Drinking: Eating, drinking in the laboratory is not permitted.
4. Chemical Hazards: Review the hazards, toxicity, and proper disposal of any chemicals
used in the lab. Such information is available on the Cornell web site mentioned in
Section III.
5. Broken Glass: Be especially careful handling glass equipment or materials. There is a
special receptacle for disposal of broken glassware. Do not discard in any waste baskets.
6. Contact Lenses: Wearing contact lenses in a chemical laboratory is hazardous. Is is
recommended that persons avoid wearing them to the extent possible.
7. Clothing: The wearing of shorts and sleeveless shirts in the laboratory will not be
permitted. Trousers and skirts must extend below the knees. The use of a laboratory coat
is recommended.
8. Medical Insurance: The University does not carry blanket accident insurance to cover
medical costs in case of accidents involving students. Students should obtain adequate
medical or accident insurance for themselves.
9. Housekeeping: Housekeeping and safety are closely related. Sloppy housekeeping and
poor safety practices in the laboratory and workroom/classroom should be reported to the
instructor. We do not intend to allow any unsafe practices to develop. This will help
insure the safety of all.
10. Paying attention: Most accidents can be avoided by diligence, awareness, and caution. No
horseplay or practical jokes are allowed.

ChE 324 Lab Manual
Technical Communication
Formal Reports Page I-14
V. Technical Communication
A major objective of this course is to provide instruction and practice in technical
communication. Students will report on the laboratory experiments with complete,
formal technical reports, which are appropriate for archival purposes, with shorter
memoranda, which are commonly used to convey progress reports in industry, and with
oral summaries, which are also used quite often for providing overviews to colleagues
and supervisors.
This section summarizes guidelines and suggestions to help in preparing each
type of report.
A. Formal Reports
1. DEADLINE FOR SUBMISSION
Reports are due at the beginning of the period following that period during which
the experiment was performed. Late reports will be penalized 10% of the grade for each
day that submission is delayed.
2. MECHANICS OF PRESENTATION
Reports are to be word-processed (or typed) with double spacing on one side only
of standard 8 1/2" by 11" white paper. A 12-point font size is required and the Time New
Roman font is suggested. The left-hand margin should be 1-1/4". All pages, including
those with accompanying graphs and figures as well as appendices, are to be assembled
in proper order, numbered, and stapled. Figures and tables cited in the body of the report
should appear immediately following the citation, either at the end of the paragraph in the
case of tables or on the next page following. (The body of the report should be printed on
good-quality paper. If reports are printed at CAE, students may find it necessary to
purchase an additional paper allowance. Appendices may be printed, written, or drawn
on lower-quality or used paper, provided that the face side is clean.)
3. CONTENTS
There are few if any absolute rules governing the style or format of technical
reports, other than the basic requirements of clarity and neatness. The writer must adopt a
style that is appropriate for the purposes of the report and recognizes the interests and
background of the likely audience. Different formats may be appropriate for different
reports, but often a standardized format is imposed on the writer by an organization or
publication editor. For the sake of consistency in ChE 324, reports will comprise the
following designated sections in the order given. Some reports will be submitted in a

ChE 324 Lab Manual
memo format. In that case, some for the following sections may be condensed,
combined, or even eliminated. Standards for memos are summarized in Section V.B.
3.1 TITLE PAGE
This page is to be written in the following form:
(top of page, centered)
Department of Chemical Engineering
University of Wisconsin
Madison, Wisconsin
(middle of page, centered)
ChE324. Transport Phenomena Laboratory
Experiment number
Experiment title
(lower, right-hand corner)
Student's name
Partners' names
Date experiment was
completed
Date report is submitted
3.2 ABSTRACT
The abstract is a simple, clear, and concise paragraph or two covering (i) what
was done, (ii) how it was done, and (iii) what was accomplished. This differs from a
Summary of Results in that it is written as an advertisement, to interest the passing reader
in the rest of the report, or as a very general summary of the nature and scope of the
report. It should be self-contained, i.e., no references to figures, tables, or equations
should be included. The abstract should contain text only.
3.3 INTRODUCTION
Reports normally begin with an introduction that sets the context for the report.
(The format at some companies and laboratories might include an executive summary
before the introduction, either as an alternative to the abstract or in addition to it.) In
general, the introduction specifies the topic of the report and states the motivation for the
reported study, giving the objectives or purpose. Some background is given, such as
references to earlier related work or to the theoretical basis for subsequent analysis. For a

ChE 324 Lab Manual
longer report, it is helpful to the reader to give a paragraph or two outlining the structure
and content of the report and even the nature of the results.
3.4 THEORY (usually not required in ChE 324)
For a research study, there may be a separate section devoted to the development
of the relevant theoretical analysis, which provides the basis for the subsequent data
analysis and interpretation of results. In ChE 324, the theory is available in common
textbooks and references so no separate theory section is required. Reference to relevant
theory and its source should be given in the introduction or in a later section when it is
used. Equations that will be used in presenting the results might be given in the
Introduction in order to define terms. Use the textbook Transport Phenomena as a guide
to the proper format for presenting equations within the text. Equations should appear as
part of a sentence.
3.5 EXPERIMENTAL APPARATUS AND PROCEDURE (usually not required
in ChE 324)
In an original experimental study there is normally a section describing apparatus,
procedure, and methods used to obtain the results. If these are not a central point of the
presentation, or if they are fairly routine, they might appear in an appendix. In ChE 324
the apparatus and procedures are described in this lab manual so they need not be
included in the student reports; reference to the descriptions given in the manual is
sufficient. Incidental modifications in the standard procedures or any difficulties with the
equipment might be mentioned in the discussion section.
3.6 RESULTS AND DISCUSSION
This part of the report should include a summary form the specific results of the
experiment, presented in neat, clear-cut tabular and graphical form, and a thoughtful
analysis of their significance, implications, or possible applications. Pertinent discussion
of the experimental procedure (especially deviations from that suggested or possible
sources of error), theoretical analysis of the system studied as needed to interpret the
results, analysis of the data (including estimates of error), and conclusions are all given in
this section. While the earlier sections should be quite objective, this is the place where
the author can present his or her observations and interpretations. As a basis for the
analysis or to support specific conclusions, one should refer freely to relevant citations in
the literature.
In writing both the Introduction and the Discussion, the author should keep in
mind both the presumed motivation for the study and the likely interests of the reader.
For each experiment this manual presents a hypothetical context for the experiment, other
than an academic exercise. Thus, the report should be written in response to the
presumed motivation. If specific questions are posed in the manual or by the instructors,
they should be used as suggestions for topics to be discussed in the overall context of the
report.

ChE 324 Lab Manual
3.7 CONCLUSIONS AND RECOMMENDATIONS (optional in ChE 324)
Most reports lead to specific conclusions based on the reported results and the
analysis given. Recommendations for future work or applications and other implications
might be stated in a final section. In shorter reports this section may be omitted with the
relevant conclusions and recommendations given at the end of the discussion section. In
ChE 324 reports a separate conclusions section is usually not warranted.
3.8 APPENDICES
Appendices contain supplemental information that is not an integral part of the
main report but is often included for reference by the excessively curious reader (or
grader). All materials covered in the following subsections are to be located in the
appendix of the report. These particular sections are not usually included in industrial
reports or academic papers.
3.8.1 SAMPLE CALCULATIONS
This section should include one example of each calculation made in connection
with the analysis of the experimental data. Each calculation is to be accompanied by the
formula involved, written in terms of the clearly defined variables, with the item being
calculated appearing on the left-hand side of the equation. The numerical values and
units of each quantity appearing on the right-hand side of the equation are to be given
when substituted into same. The calculations must be presented in neat, logical order
with the answers either underlined or set off by blocks. Extensive arithmetic
manipulations need not be shown. Identify the part of the experiment to which each
calculation applies. Simply presenting a spreadsheet with the calculated values is not
sufficient.
3.8.2 MATHEMATICAL DERIVATIONS
Any derivations performed in connection with the data analysis and discussion are
to be demonstrated in this section. This includes analysis of errors based on equations
appearing elsewhere.
3.8.3 ORIGINAL DATA SHEET(S)
A neat, orderly data sheet, for recording the original data, is to be prepared prior
to beginning the experiment and preferably before coming to the lab. All data taken in
the laboratory are to be included in their original form. Lab partners may make
photocopies for inclusion in individual reports. For the case of computer-acquired data
files, hard copies of the files are usually not required in the report.

ChE 324 Lab Manual
4. GRAPHS AND TABLES
Key graphs and tables should be presented in the body of the reports, either in the
Summary of Results or in the Discussion. Less important ones, or those used in
intermediate calculations, should be placed in the Appendix. Graphs and tables in the
body of the report should be placed on or immediately following the page where they are
first mentioned, as is done in textbooks. Graphs, as well as drawings and diagrams, are
numbered sequentially and called “Figure x.” Tables are also numbered in a separate
series. Graphs require complete, self-explanatory captions, placed below the figure but
within the margins. Tables should include a descriptive heading at the top of the table.
The main text should say what is presented in each figure and describe the significance of
each graph and table.
Graphs are to be presented on standard 8-1/2" by 11" paper with generous
margins. Theoretical or computed functions should be shown as smooth curves without
points. Plotted experimental points, used to define empirical curves, must be clearly
indicated by some appropriate symbol. The variables plotted on the ordinate and abscissa
as well as any parameters should be indicated with the units designated. The graphs are
to be inserted in the assembly of the report pages with either the bottom or the right-hand
edge as the base of the figures as drawn. Graphs are to be lettered to read from the
"front" and "right side." Any hand-drawn curves are to be drawn with the aid of ship's
curves or French curves. If more than one set of data are shown on a graph, different
symbols should be used and defined either in a legend or in the caption. Computer-
generated graphs are preferred. Column headings in tables should include the units of the
entries.
5. GRADING
Reports will be graded on the basis of neatness, grammar, spelling, and clarity as
well as technical validity. Strive to be clear and concise.

ChE 324 Lab Manual
Memorandum Reports Page I-19
B. Memorandum Reports
Much communication within a technical or industrial organization is accomplished
with memos. Memos are short documents that can be read quickly and easily. They are
designed to convey their message clearly and concisely. Memos may be used to give a
notice, to make a request, or to provide a report. In Chemical Engineering 324 memos are
written for the latter purpose. The memos used here resemble those that an engineer in
industry would use to provide a progress report or summary of a project to supervisors and
colleagues. Typical formats for memos and guidelines for their content are provided in
technical writing textbooks and at the EPD Technical Communication web site.
The difference between a memo and a complete formal report is the greater amount
of detail contained in the latter. A report is intended for the purposes of communicating
with a wide, varied audience and of establishing a relatively permanent record of what was
done in a project. A memo is generally written for more immediate needs, such as
conveying recent results, e.g. a weekly progress report, to a knowledgeable reader such as
a supervisor. A memo is also designed to be read and understood quickly.
Thus, a memo does not need to present all the background material that goes into a
formal report. The format is a bit different, and it is obviously shorter. The emphasis is on
the results and your interpretation. Recommendations for additional work are usually
appropriate.
You may abbreviate the formal title page of a report into a memo heading such as
that used in each weekly memo to students from the ChE 324 instructor, and one may omit
an abstract. Separate sections headings may or may not be required, depending on the
length and complexity of the memo. Headings are probably appropriate and helpful if a
memo is longer than a page or two. Whether there are headings or not, several sections
appearing in a report may be combined logically within a memo. For example, the
introduction, theory, apparatus, and procedure may all be combined into several coherent
paragraphs, and the discussion and conclusions might flow together. It is a good idea to
give a summary of the most important results and conclusions in the first paragraph, which
then serves as a type of abstract or summary. This is the information that a busy reader is
most eager to obtain.
Depending on the complexity of the material in the memo, you may or may not
need an appendix. In any case, you should make liberal use of figures and tables, but make
sure that the headings and captions are thorough and descriptive. Generally, you should
include a list of references. For the purposes of this course, sample calculations are always
required as an appendix with memos.
It is conventional to provide copies to all parties with an interest in the content of a
memo, and the names of those receiving copies are listed with a copy (cc:) notation at the
bottom of the document. In ChE 324 the laboratory partners should be identified by
including them in the copy list.

ChE 324 Lab Manual
Oral Reports Page I-20
C. Oral Reports
Engineers are frequently called upon to present oral reports. These may be brief
summaries to a team of colleagues on a project in process, a proposal to senior
management for a major investment, a tutorial to other engineers on a specialized subject,
or a paper at a technical conference reporting on a completed project. Oral reports may
be presented to a small group around a conference table or delivered in an auditorium to
an audience of hundreds. The duration may be only five or ten minutes or as long as an
hour or even more. In all cases, the purpose of an oral report is to convey information to
the audience rapidly and efficiently, preferably with a sense of the speaker's attitudes and
personality that is no so readily conveyed in a written report. Although an oral report
may not be able to cover a topic in as much detail as a written document can, it allows the
speaker an opportunity to emphasize and communicate his more important points.
Another advantage of an oral report is that the audience is often able to ask questions to
clarify the speaker's intent.
Probably everyone who delivers an oral report feels some nervousness about
standing up and talking before an audience. Such nervousness should not be a cause for
concern but a source of energy for the presentation. Nervousness diminishes with
experience, but for inexperienced speakers as well as old hands, preparation is the key to
avoiding any feared awkwardness or embarrassment during the oral presentation.
Beer and McMurrey (1997) present a very sensible discussion about giving oral
reports. Some of their primary points are summarized below. Pfeiffer (2001) presents a
similar discussion.
Preparation
The key to a successful presentation is preparation. As with writing the speaker
should first analyze his or her audience. Why are you giving the talk, why is an audience
coming to hear it, what do they already know about your subject, and what do they want
to learn from you? Those are the questions that the speaker must answer and keep in
mind while preparing and delivering a talk. Of course, there are situations where the
audience is rather diverse, and there is not a single set of answers. Then the speaker faces
the challenge of balancing the talk to offer something of interest to everyone, without
baffling anyone completely nor boring others excessively.
Analyzing the audience also involves identifying the primary purpose of giving
the talk. After that purpose has been clearly stated, the speaker has a basis for selecting
and organizing the content of the talk. Another key factor, however, is the time frame
available for the presentation. If one has only 10 minutes available for the presentation,
he must select his material judiciously to be both complete and concise and to
communicate his key points. It is an unforgivable sin of technical presentations to exceed
the time allotted. The audience is busy, and each member has his own agenda for the
day. When the stated termination time comes, the audience stops listening so the entire
point of the talk may be lost. Usually, time should be left at the end of a talk for
questions and discussion. And no one will object if a technical talk ends a few minutes
early.

ChE 324 Lab Manual
After a speaker has identified her primary purpose and the key points to be
conveyed, she next must select a structure for the talk. That is, a logical sequence must
be selected as the path by which she will lead the audience through the subject at hand.
Every talk must have a beginning, a central part, and an end. The beginning is an
introduction and a preview that prepares the audience and sets the stage for what follows.
The end is the summary of what has been covered, with conclusions and perhaps
recommendations. The end should reiterate key points just as the beginning might
suggest what key issues are to be covered.
The central part of a talk is the technical development of the specific subject.
This part of the talk, just like a written report, should be organized to make the trip from
the original objective and premises to the conclusions as effortless as possible for the
audience. Designing such a path requires selecting a logical structure. As indicated by
Beer and McMurray, there are a number of alternative strategies that may be selected,
depending on the topic and the audience. One may proceed chronologically or spatially;
one may go from simple to complex or vice versa, one may organize the points in order
of decreasing or increasing importance, familiarity, difficulty, etc. Regardless of what
logical sequence is selected, the speaker should be consistent so that the audience does
not get confused. Also, it is imperative that the degree of detail presented be adjusted to
fit the time allotment for the talk and the technical level of the audience.
After the overall structure of the talk has been designed and the content selected,
the speaker should design visual aids and graphics to enhance the clarity and efficiency of
his presentation. Slides or overhead transparencies should be used to reinforce what the
speaker is saying, helping to convey the overall logic of the presentation. As a picture is
worth many words, the same is true of well-designed graphs and diagrams. Each graphic
should have a descriptive heading, summarizing the significance of the illustration. On
all sheets one should use large letters that are easy to read and avoid cluttering it up with
too much information. Each page to be displayed should be kept quite simple and
contain lots of blank space so that the observer does not get overloaded and can focus on
the key point.
In preparation for the presentation, the speaker should give special thought to
what will be said in the introduction and in the conclusion. These portions of a talk
should appear to be ad lib, but they should be quite polished to make a good impression
on the audience. A speaker may want to make some notes as an aid in the presentation,
but for most of the talk, the visuals themselves should be sufficient reminders of what
needs to be said and in what order.
Finally, in preparation for an oral presentation, a speaker should practice the talk.
If possible, some friends or colleagues should be asked to listen to trial runs. Such
practice is needed, first of all to ensure that the talk will not be too long but also to check
the quality of the visual aids, to practice speaking on one's feet, and to test the planned
wording of the introduction and the conclusion.
Presentation
Giving a speech in front of an audience is always stressful, even for the most
accomplished speakers. You can reduce the stress by following the guidelines given by
Pfeiffer (2001).

ChE 324 Lab Manual
When the time comes for the actual presentation, there are a few other issues to
keep in mind. Think about the many bad talks (or lectures) that you have attended and
think of all of the mistakes that the speaker made. These are mistakes that you wish to
avoid.
With respect to delivery, remember to speak at a sufficiently audible level that
those in the back of the room can easily hear what you say. The graphics should be
designed so that the same people can easily read them. Look at your own projected
graphics from the same distance to see how they work. Be careful to speak at a
comfortable pace, neither too rapidly nor too slowly, and inject some dynamics into your
delivery. Maintain eye contact with your audience to sense whether they are following
you. If you see a puzzled face, you might ask whether there is a question.
When displaying projected graphics, use a pointer to help keep the audience with
you. Use the hand closer to the screen to avoid blocking the view or turning your back to
the audience. Leave the graphics up on the screen long enough for the audience to absorb
the content. Although it is not desirable to read one's entire talk from the screen, some
reading is helpful for the audience. That is, one should not be expecting the audience to
be reading an outline or a statement on the screen and at the same time listening to the
speaker make a separate point.
Speak naturally, not too stiffly, but avoid also being too informal. That is, use
proper English and avoid slang and clichés. Also, try to eliminate nervous gestures and
hemming and hawing that will distract or annoy the audience.
Finally, try to make the planned logical structure of the talk transparent to the
audience. Orally and with visual aids, emphasize clear transitions as you step through the
presentation. Also, it is very helpful to the audience when the speaker repeats the key
points of the talk. One old recommendation, “The Preacher’s Maxim” is:
First tell them what you are going to tell them, then tell them, and finally tell them
what you told them.
People are generally not very good listeners. They remember only a portion of
what they hear and a bit more of what they read. They do remember the most when they
both hear and see the information. It is the speaker’s obligation to help the audience to
absorb and to remember the most important information from a talk. This can be done
through planning, preparation, and practice of the presentation.
References
Beer, David, and David McMurrey, A Guide to Writing as an Engineer, John Wiley &
Sons, Inc., New York, 1997, Chapter 8.
Pfeiffer, William S., Pocket Guide to Technical Writing, 2nd
Edition, Prentice Hall, Upper
Saddle River, New Jersey (2001), Chapter 3.

ChE 324 Lab Manual
Experimental Design and Statistical Analysis of Data
Page I-23
VI. Experimental Design and Statistical Analysis of Data
As discussed in Section I, the successful application of chemical engineering
methods to practical problems requires experimentation. Although we have a sound
theoretical framework for structuring our treatment of processes or chemical materials, the
underlying theories almost always involve specific parameters that must be determined
with experimental tests.
The textbook Transport Phenomena (Bird et al. 2002) develops a systematic
approach for analyzing a wide variety of processes and systems, but applications require
values of thermodynamic and transport properties. For example, flow problems require
information about fluid viscosity as well as fluid densities. Heat transfer processes involve
thermal conductivity as well as enthalpy and heat capacity of the materials involved.
Separation processes and chemical reactors cannot be treated quantitatively unless one
knows material properties such as vapor pressures, activity coefficients, solubility,
equilibrium constants, reaction-rate constants, etc. All of these quantities must be
determined experimentally for any given material as functions of the state variables such as
temperature, pressure, and chemical composition.
Furthermore, although conservation laws yield the differential equations of change
for predicting profiles of velocity, pressure, temperature, and concentrations within a fluid,
as well as the associated fluxes of momentum, energy, and mass, either mathematical
complications associated with complex geometries and boundary conditions or the
inherently random nature of turbulent flow make rigorous computations and a priori
predictions impractical in most cases. For that reason, one uses phenomenological
relations to define transport coefficients such as the friction factor, drag coefficients, heat-
transfer coefficients, and mass-transfer coefficients, which are useful quantities, but they
must be determined experimentally for a given situation.
There are generally two types of quantities that must be measured. There are the
material properties, and there are macroscopic characteristics of a certain type of system or
process. The unknown quantity may be a single constant, or it may be an unknown
function that varies with changes in local conditions. In the case of basic materials
properties, thermodynamics usually reveals a set of independent variables upon which a
quantity should depend. In the more general case, dimensional analysis often helps one to
identify an appropriate set of independent variables to be considered. Based on theoretical
analysis, one may know the functional form that the unknown quantity should follow.
When a theoretical form is known, the task of the experimenter is to find the specific
parameter values that enable the function to fit the behavior of the particular material or
process of interest. When there is no theoretical guidance or experience that provides a
functional form for the expected dependence of the measured quantity on its independent
variables, the experiment has to seek an empirical functional form that represents the

ChE 324 Lab Manual
Page I-24
system behavior. One must also determine the associated parameter values that provide a
quantitative description of the phenomenon.
Thus, in the conduct of practical chemical engineering there are two related
activities that are crucial to the effectiveness of an experimental program. First, one must
consider the matter of experimental design. The other issue is statistical analysis of the
data.
When one has available a deterministic model for a system that is based on a
rigorous theoretical analysis, the purpose of experimentation might be simply to confirm
the validity of the theory. In this case one might use statistical analysis, combined with
replicated measures, to discrimiate experimental error from shortcomings in the theoretical
model. More often, the chemical engineer is working with a deterministic process model
that contains some unknown parameters. These unknown parameters may be
thermodynamic or transport properties of the material or they may be parameters such as
transport coefficients that depend on the detailed geometry or flow conditions in the
equipment. In this case, the objective is to estimate the value of the unknown parameter or
parameters from the experimental tests.
Estimation of model parameters from data is often referred to as "curve fitting" or
regression analysis. A brief summary of curve fitting and parameter estimation is given in
Appendix 13 of this manual. The statistical approach to parameter estimation not only
provides a quantitative result from the experiment but also indicates the chance that the
estimated value is accurate. Statistical analysis considers different kinds of experimental
errors and provides a criterion for omitting data points that are clearly inconsistent with the
bulk of the data set. (Of course, one should be alert to possible messages from the data
that there is some effect occurring in the system that is not accounted for in the basic
model.)
In the case where one does not know initially what functional form should
represent the magnitude and variation of a quantity of interest, it is appropriate to adopt a
strategy of experimental design. That is, one has to decide which independent variables
might have an effect on the outcome of an experiment. Then one must choose values of
those variables to use in setting up the experiment. A number of experiments must be
conducted at different settings of the suspected independent variables to see what effect
each actually has. Because experiments are usually costly and time-consuming, one hopes
to answer this question with a minimum number of tests.
For example, suppose one were interested in maximizing the yield of a particular
reaction in a certain type of reactor. The independent variables that might be relevant
could include temperature, pressure, reactant concentrations, residence time in the reactor,
as well as mixing characteristics. Another variable might be the concentration of a
possible catalyst. To find out under what conditions the amount of product produced from
the reactants is maximized, one could do many experiments at different settings of the
various variables, but an exhaustive study might be prohibitively expensive.

ChE 324 Lab Manual
Page I-25
To make the experimental study of a problem like this most efficient, statisticians
have developed techniques known as factorial design. The first objective of statistical
design is to determine which variables have a large effect and which have little or no effect
on the outcome of the experimental system. More advanced analysis considers whether the
effects of variables are independent or whether there are interactions among the variables.
Then there is the question of how the dependence on the variables can be represented by
quantitative formula.
Box, Hunter, and Hunter (1978) provide a good treatment of experimental design
and factorial analysis. Many of their examples are taken from the field of chemistry. The
fourth and last part of this book deals with model building, that is, identification of
quantitative functions that can successfully describe observed experimental behavior.
Although models based on statistics and empiricism, rather than a rigorous underlying
theory, are limited in their predictive capacity to the actual range of variables studied, they
are nevertheless quite useful for practical purposes.
Reference
Box, G.E.P., W.G. Hunter, and J.S. Hunter, Statistics for Experimenters, An Introduction
to Design, Data Analysis, and Model Building, John Wiley & Sons, New York (1978

ChE 324 Lab Manual
Syllabus Page I-26

ChE 324 Lab Manual
Part A
Measurement of Transport Properties

ChE 324 Lab Manual
Experiment A.1
Viscosity of Newtonian Fluids Page A.1-1
Experiment A.1
VISCOSITY OF NEWTONIAN LIQUIDS
Viscosity is a fundamental property of fluids that indicates a material's capacity to
transport momentum by molecular mechanisms. The magnitude of liquid viscosity,
which depends on temperature and chemical composition, determines not only the
quantitative but also the qualitative nature of fluid flow (Bird et al., 2002). Numerous
experimental methods have been devised for the measurement of the viscosity of a
Newtonian fluid. An accurate determination of absolute viscosity, which is denoted by µ,
demands a careful analysis of the experimental technique that is used. As an example of
some of the problems involved in practical viscometry, this experiment employs a simple
capillary-tube viscometer to measure the viscosities of several Newtonian liquids.
Theory
Application of Newton’s law of viscosity and conservation of momentum to the
steady flow of a constant-density fluid through a straight tube of uniform circular cross
section of length L leads to the Hagen-Poiseuille relationship (Bird et al., 2002)
Q
( )R
4
8 L
=
−π
µ
∆℘
(A.1-1)
where (-∆℘) is the net driving force for the flow, Q is the volumetric flow rate of fluid,
and R is the tube radius. The quantity ℘ is defined as (p+ρgh) where p is static, or
thermodynamic, pressure, ρ is fluid density, g is the acceleration of gravity, and h is
vertical elevation above a datum plane. Thus, ℘ represents the combined effects of
pressure and gravity in causing the fluid motion. (The notation in this manual follows
that used in Transport Phenomena by Bird et al., 2002, which presents a summary table
on pp. 757-764. For example, ∆x ≡ x2-x1 where the subscript 1 indicates the value of a
quantity x at the fluid entrance and 2 the value at the exit.)
There are a number of assumptions involved in the development of the Hagen-
Poiseuille law. Among other conditions, the flow must be laminar and free from end
effects. If the construction and operation of an experimental apparatus can conform
accurately to the key assumptions, it is possible to use Equation A.1.1 to measure the
viscosity of Newtonian fluids.
A simple experimental arrangement which could yield a viscosity determination
based on Equation A.1.1 is the steady flow Q of a fluid in a long, straight tube that is
maintained at a constant temperature and is equipped with a device to measure the
pressure gradient ∆p/L at some distance from the ends of the tube; a capillary manometer,
for example. In most instances the control of the operating conditions over the entire
length of the tube, the cleaning difficulties, and the need for a large sample of liquid to
fill the length of the tube prohibit or make very difficult the use of such a device. Other
more convenient and compact types of viscometers to which the Hagen-Poiseuille

ChE 324 Lab Manual
Experiment A.1
equation may be applied have been developed. The Cannon-Fenske viscometer and other
modifications of the Ostwald pipette are examples (ASTM, 1955).
When the total change in the driving force ℘ associated with a flow rate Q
through a tube is due to hydrostatic head alone, Equation A.1.1 may be written as
ν
π
=
−g h R
8Q L
( )∆
4
(A.1-2)
where (-∆h) is upstream elevation minus downstream elevation, called the hydrostatic
head difference, and the quantity ν is defined as
ν = µ / ρ (A.1-3)
and is called the kinematic viscosity. The kinematic viscosity is often expressed in units
of cm2
/sec, which is called stoke.
Consider steady fluid flow through a straight capillary tube of fixed length L for
which the hydrostatic head differential ∆h is constant. If one measures the time for a
fixed volume of fluid V to pass through a particular tube, the kinematic viscosity should
be related to the observed efflux time te as follows:
ν = C te (A.1-4)
where C is called the viscometer constant. If C is evaluated by observing te with a liquid
of known viscosity, C may be calculated for the apparatus. Then measurements of te for
the same V in the same cell with other fluids allows the kinematic viscosities of the latter
to be calculated from Equation A.1.4. Dynamic viscosity value is then obtained by
multiplication with the density of the liquid.
Equation A.1.4 is derived by substituting the relation
Q = V/te (A.1-5)
into Equation A.1.2 and combining all constant factors into one term. The viscometer
constant C is thus identified to be
C
g h R
VL
=
−π ( )∆ 4
8
(A.1-6)
Although the preceding equations are derived for constant ∆h and constant Q,
they may be applied with reasonable success to a pipette-type viscometer in which a
liquid drains under a slowly varying hydrostatic head. In that case, one may use average
values of Q and ∆h in Equations A.1.2 and 6, and the constant C should still be a property
of only the viscometer geometry and not depend on the properties of the fluid.
Apparatus

ChE 324 Lab Manual
Experiment A.1
The capillary-tube viscometer apparatus consists of the following items:
1. A commercial Number 200 Cannon-Fenske pipette type viscometer, which is designed
for a 20-to-80 centistoke range in kinematic viscosity
2. A stopwatch
3. Several constant temperature baths (plain, cylindrical Pyrex jar; 12-inch outside-
diameter by 12-inch height; 4.5 gallon capacity), set at various temperatures
4. Automatic temperature controls
a. Temperature sensing element (mercury-contact, wide-range, quick setting,
0.01°C thermoregulator)
b. Electric heating-elements (200 watt, hairpin, immersion heaters)
5. A 10 ml. graduated pipette
6. Cleaning solution
7. Acetone
8. Distilled water
9. Source of dry filtered air
10. A mounting device for holding the viscometer in the water baths
11. A stock of 60-weight-percent aqueous sucrose solution
12. A stock of approximately 85-weight-percent aqueous glycerol solution
13. A glass pycnometer (25 ml)
14. An analytical balance
The design and construction details of the Cannon-Fenske pipette-type
viscometer, including the dimensions for size No. 200, are shown in Figure A.1-1.
The viscometer may be filled with liquid such that there is an initial elevation
difference, or static head (-∆h), between the liquid surface in the tube on the right side
and that in the spherical bulb at the bottom of the cell. Both surfaces are at atmospheric
pressure. Liquid is allowed to drain through the capillary tube, and the efflux time te is
measured as the time for the liquid level on the right side to drop through the lower bulb.
The volume V is the fixed volume contained between the two marks above and below
that small reservoir. The elevation difference in Equation A.1.2 or 6 is taken to be the
average difference between the liquid level in the larger bulb on the left side, which
changes only slightly, and that in the lower bulb on the right as the liquid level drops
from the upper mark to the lower one.
The cell constant C is determined from Equation A.1.4 by measuring the
efflux time for a liquid of known kinematic viscosity. Then Equation A.1.4 may be used
to calculate the kinematic viscosity of an unknown liquid from its efflux time in the same
apparatus.

ChE 324 Lab Manual
Experiment A.1
Working capillary
Figure A.1-1. The Cannon-Fenske Pipette-Type Viscometer For Transparent
Liquids. Dimensions are given for size Number 200.
Procedure
1. Ensure that the thermostat baths have attained the predetermined temperatures at
which the viscosity measurements are to be made, 30, 45, and 60o
C.
2. Clean the viscometer thoroughly before using. In the case where aqueous solutions of
organic materials are involved, clean with cleaning solution, rinse with distilled water
followed by acetone, and dry with filtered air. NOTE: In order for the viscometer to
operate properly, it must be absolutely clean.

ChE 324 Lab Manual
Experiment A.1
3. Calibrate the viscometer using the 60-weight-percent aqueous sucrose solution that is
provided. Measurements are to be taken at three temperatures, 30, 45, and 60o
C.
4. With the viscometer in a vertical position, use the 10-ml graduated pipette to
introduce exactly 6.5 ml of the sucrose solution into the wider leg of the viscometer.
NOTE: All liquids are to be introduced into the viscometer at room temperature.
5. Place the viscometer in a constant temperature bath. It should be submerged such
that the bath-water is at least one centimeter above the upper of the two small
reservoirs. Allow at least ten minutes for the viscometer and its contents to reach
thermal equilibrium with the bath, particularly at the higher temperatures. The filled
viscometer will be moved from bath to bath to obtain data at various temperatures.
6. Before measuring any efflux times, align the viscometer vertically in the constant
temperature bath, in the orientation shown in Figure A.1-1.
7. Apply suction to the narrow leg of the viscometer until the liquid level is about 0.5
cm above the etched mark between the two small reservoirs.
8. Place a thumb over open end of narrow leg to maintain the liquid level. At this point
an unbroken column of liquid should extend from the large bulb at the bottom to a
level near the bottom of the upper small reservoir.
9. Remove thumb and measure with the stopwatch the time required for the liquid
meniscus to pass from the upper etched mark to the lower etched mark.
10. Repeat Steps 7. through 9 to obtain replicate data points. The runs go faster at the
higher temperatures so it is more convenient to take replicates in the warmer baths.
11. Clean the viscometer thoroughly and dry it, as described in Step 2, both when a new
liquid is to be introduced into the cell and when no further measurements are to be
made.
12. Repeat Steps 4 through 11, replacing the sucrose solution first with the 85-weight-
percent aqueous glycerol solution, then with distilled water. For glycerol use the
same temperatures as in the calibration process. With pure water, it is sufficient to
make a measurement only at 30o
C; this measurement will be used to test the
applicability of the method to less viscous fluids.
13. Collect the following data needed for the determination of the density of the sucrose
and glycerol solutions, using water as a standard:
a) Weight of the empty, dry pycnometer
b) Weight of the pycnometer plus distilled water
c) Weight of pycnometer plus sucrose solution
d) Weight of pycnometer plus glycerol solution
e) Temperatures of all solutions weighed
These measurements may be done at room temperature or in the 30o
C bath. Calculate
densities in order to determine the actual solution concentrations from the density
tables given in Appendix 4.
14. Note also approximate values of the quantities appearing in Equation A.1.6. These can
be used to estimate the expected value of C.

ChE 324 Lab Manual
Experiment A.1
15. Always pour the solutions slowly. Otherwise, they will entrain air bubbles that are
very slow to escape and can affect the experimental results.
16. Be especially careful while cleaning and drying your viscometer. Return test solutions
to their containers, and wipe up any spills. Rinse out the glassware as thoroughly as
possible with distilled water and with Alconox if necessary. Rinse with a minimal
amount of acetone, disposing of the waste acetone in the waste-solvent container
provided, and dry very gingerly with compressed air. The greatest risk of breaking the
glass occurs during the drying.
Data Analysis
1. For the 60-weight-percent aqueous sucrose solution plot:
a. density vs. temperature
b. absolute viscosity vs. temperature
c. kinematic viscosity vs. temperature
These properties are given in Appendix 4 and 4a.
2. Use these sucrose-solution data with measured efflux times to determine the
viscometer constant C. Consider whether the data indicate any dependence of C on
temperature.
3. Determine the experimental kinematic viscosity of the glycerol solution as a function
of temperature. Plot the results, and for comparison include in the plot a literature
value for the kinematic viscosity of an 85-weight-percent aqueous glycerol solution at
20°C. Properties of glycerol solutions are given in Appendix 4.
4. Compare the experimentally determined viscosity of water with published values.
Properties of water are given in Appendix 5.
5. As a check on the validity of the viscometer calibration, estimate the geometrical
parameters of the cell, and calculate the expected value of C from Equation A.1.6.
6. For laminar-flow conditions, the entrance length Le , i.e., the distance in the tube
required for the flow patterns to become fully developed, has been found to be a
function of the Reynolds number:
Le ≅ (0.05)(2R)(Re) (A.1-7)
where Re ≡ (2R<vz>ρ)/µ is the Reynolds number , and <vz> is the average velocity
in the tube. Estimate the volume V and the mean velocity <vz> in order to estimate
Re and the entrance length for both the glycerol solution and the water at 45o
C.
Compare the estimated entrance-length values with the actual capillary length to
check the validity of neglecting end effects in the data analysis.
References
Bird, R.B., W.E. Stewart and E.N. Lightfoot, Transport Phenomena, 2nd
Edition, John
Wiley and Sons, Inc., New York (2002).

ChE 324 Lab Manual
Experiment A.1
American Society for Testing Materials, Book of ASTM Standards, Part 5, Fuels,
Petroleum, Aromatic Hydrocarbons, Engines Antifreezes. Philadelphia (1955). Tentative
Method of Test for Kinematic Viscosity, ASTM Designation. D 445-53T, pp. 197, 200-
224.
Viscometers, Bulletin 19, Cannon Instrument Company, Box 812, State College,
Pennsylvania.
Prandtl, L. and O.G. Tietjens, Applied Hydro- and Aeromechanics, Dover Publications,
Inc., New York (1934), pp. 26-27.
Cannon, M.R., R.E. Manning, and J.D. Bell, Anal. Chem., 32, 355-358 (1960).
Cannon, M.R., and M.R. Fenske, Ind. Eng. Chem. (Anal. Ed.), 10, 297-301 (1938).

Experiment A.2
THERMAL CONDUCTIVITY OF SOLIDS
Thermal conductivity, like viscosity, is an important transport property of matter.
The rates of heat flow, particularly in solids, are determined by the magnitude of thermal
conductivity, which reflects the capacity of the material to transmit energy by molecular
mechanisms. Like density or heat capacity, thermal conductivity is a state property, and
its value is generally a function of local temperature, pressure, and chemical composition
of a material.
Thermal conductivity, denoted by k, is defined by Fourier's law as the
proportionality factor between the heat flux q and a temperature gradient, which is the
driving force for heat flow:
q k T= − ∇ (A.2-1)
The minus sign in Fourier's law indicates that heat always flows from regions of high
temperature to regions of lower temperature.
The thermal conductivity of solids can exhibit values that range over many orders
of magnitude. Good conductors such as metals have high conductivity, while good
insulators, like wool, have much smaller values. It is necessary to measure the
conductivity of a material experimentally in order to ascertain the correct value of k to use
in quantitative heat-transfer calculations. This experiment demonstrates one method for
measuring the thermal conductivity of solids.
This experiment is based on measurement of transient temperature changes in a
sample of an initially cool solid material after it is immersed in a hot fluid bath. The
experiment is modeled by use of Fourier's law, combined with the principle of
conservation of energy, in order to obtain a theoretical relation for temperature as a
function of time in the unsteady-state heating process. Comparison between experimental
data for temperature as a function of time and the theoretical prediction allows calculation
of the thermal conductivity.
Unfortunately, there is some uncertainty concerning the effect of the fluid mixing
in the bath on the rate of heating in the solid. Therefore the apparatus must be calibrated
with solids of known conductivities in order to determine the efficiency of heat transfer
from the stirred fluid to the outer surface of the solid samples.
Theory
A microscopic energy balance in a homogeneous solid, where the physical
properties are assumed to be constant yields

ChE 324 Lab Manual
Experiment A.2
Thermal Conductivity of Solids Page A.2-2
ρ
∂
∂
~
C
T
t
k Tp = ∇2
(A.2-2)
In solids of simple geometry, Equation A.2-2 can be used along with appropriate boundary
conditions to solve for the temperature T within the solid body as a function of time t as
well as position. Spatial derivatives ∇ and ∇2
are given for various coordinate systems in
Bird et al. (2002, §A.7).
As an example consider a thin, wide slab of solid material with thickness 2b that is
initially at a uniform temperature To. At time t=0 the slab is exposed on its surfaces to a
fluid held at a different temperature T∞. The temperature profiles in the solid can be
calculated from Equation 2 if the heat conduction from the edges of the slab is neglected
and the temperature profile is taken to be a function only of time and distance y. The
position coordinate y is measured from the center plane of the slab, and Equation A.2-2
becomes,
2
2
~
y
T
k
t
T
Cp
∂
∂
=
∂
∂
ρ (A.2-3)
It is convenient to express Equation A.2-3 in dimensionless form. Let a
dimensionless temperature be defined as
Θ=
−
−
∞
∞
T T y t
T To
( , )
, (A.2-4)
where T∞ is the surrounding fluid temperature and To is the solid’s initial temperature. A
dimensionless position η is defined as
η=
y
b
, (A.2-5)
where b is the distance from the center to the surface of the slab. The dimensionless time,
τ, is defined as
τ
α
=
t
b2
, (A.2-6)
where the thermal diffusivity, α, is
α
ρ
=
k
Cp
~ . (A.2-7)
Observe that the magnitude of the thermal diffusivity is proportional to the value of the
thermal conductivity, k. Equation A.2-3 becomes
2
2
η∂τ
∂
∂
Θ∂
=
Θ
(A.2-8)

ChE 324 Lab Manual
Experiment A.2
Two boundary conditions and an initial conditions are needed to solve the problem.
At t=0, T=To, which in dimensionless from becomes,
1=Θ at τ = 0 (A.2-9)
In general, heat transfer from a stirred fluid to a solid surface is not perfectly efficient. In
that case T1 is not equal to T∞ at all times, and the boundary condition for solving Equation
2 must be established accordingly. Although the flow patterns and convective heat transfer
in the fluid phase surrounding the solid may be quite complex, it is common to represent
the heat-transfer efficiency by use of Newton's "law" of cooling:
q h T T1 1= − ∞( ) (A.2-10)
where q1 is the flux of heat crossing the solid-fluid interface into the fluid. Equation A.2-
10 is not a fundamental law; it is merely a convenient approximation used to describe the
efficiency of the fluid-side heat-transfer process. It defines the proportionality factor h, the
fluid-film heat transfer coefficient, the value of which depends on the flow conditions and
geometry as well as the properties of the fluid. Better mixing and more efficient heat
transfer give larger values of h.
Assuming that in a given situation, one can estimate the value of h, Equation A.2-
10 can be used as a more realistic boundary condition on the solid surface instead of the
condition of a constant temperature. That is, the appropriate boundary condition for
solving Equation A.2-2 for a slab becomes
q k
T
y
h T T1 = − = − ∞
∂
∂
( ) at y = ±b (A.2-11)
where the first relation expresses Fourier's law for the heat flux on the solid side of the
interface and the second gives the flux on the fluid side.
In dimensionless form, Equation A.2-11 becomes
∂
∂ η
Θ
Θ+ =Bi 0 at η=±1 (A.2-12)
where the dimensionless parameter Bi is defined as
Bi
bh
k
= (A.2-13)
and called the Biot number. The magnitude of the Biot number indicates the resistance to
heat flow of the solid body relative to that in the surrounding fluid.
This problem has been solved and is given in many textbooks on heat conduction
(Carslaw and Jaeger, 1959, Jacob, 1949). The result is an infinite series solution of the
form

ChE 324 Lab Manual
Experiment A.2
∑
∞
=
−
++
=Θ
1
2
)(
)1(
)cos()sec(
2
2
n n
nn
BiBi
eBi n
β
ηββ τβ
(A.2-14)
where the βn quantities are called eigenvalues and are identified as the positive roots of the
relation
β βtan( ) − =Bi 0 (A.2-15)
The solution given in Equation A.2-14 converges slowly at short times. On the
other hand, at longer times, as τ gets large, the exponential factors in each term get smaller,
particularly those of higher order with large values of βn. At sufficiently long times the
first term, with the smallest βn value, dominates, and the approach to the equilibrium
temperature is everywhere in the solid a pure exponential decay.
For example, at times sufficiently long that Θ has fallen below 0.8 everywhere in
the solid, the dimensionless temperature at the center of the slab may be approximated
accurately by
ln ( , ; ) lnΘ τ β τ0 1
2
1Bi A≈ − + (A.2-16)
where A1 is a combination of constants appearing in the first term in Equation A.2-14. At
these longer times a semilog plot of Θ versus τ should become a straight line with a slope
of 2
1β− and an intercept of lnA1.
Similar relations can be derived for unsteady conduction in a cylinder or in a sphere
by solving Equation A.2-2 in cylindrical or spherical coordinates. The results for a
cylinder are
[ ]
Θ =
+
−
=
∞
∑2
2
2 2
1
Bi J e
Bi J
o n
n o nn
n
( )
( )
β η
β β
β τ
(A.2-17)
where Jo(x) is a Bessel function of the first kind and zero order. The eigenvalues in this
case are determined as the roots of
β β βJ Bi Jo1 0( ) ( )− = (A.2-18)
where J1(x) is the Bessel function of the first kind and first order.
The temperature profile in a sphere is given as
[ ]
Θ =
− +
−
=
∞
∑2
2
2 2
1
Bi e
Bi Bi
n
n nn
n
sin( )
sin( )
β η
η β β
β τ
(A.2-19)

ChE 324 Lab Manual
Experiment A.2
with the eigenvalues being given as the roots of
β βcot( ) + − =Bi 1 0 (A.2.20)
For the cylinder and sphere the characteristic distance b used to define the
dimensionless groups in Equations A.2-5, 6, and 13 is the radius of the body, and the
dimensionless distance η is the fractional distance from the center of the body to the
surface. For these two cases as well as the slab, the behavior of the temperature at the
center of the body at longer times takes on the form of Equation A.2-16.
Values of the first (smallest) eigenvalue, β1, calculated from Equations A.2-15, 18,
and 20, are given for the three geometrical cases as functions of Bi in Figure A.2-1.
Tabulated values are given in Appendix 6. These values can be used in Equation A.2-16,
which is valid for all three cases.
0
2
4
6
8
10
12
14
16
18
20
0 0.5 1 1.5 2 2.5 3 3.5
β 1
1/Bi=k/hb
Slab
Cylinder
Sphere
Figure A.2-1. The first eigenvalue β1 for heat conduction in a slab, cylinder, or sphere,
given in relation to the Biot number. At a given value of Bi, the magnitude of the first
eigenvalue is largest for the sphere and smallest for the slab.
For very large values of Bi, it is also possible to derive approximate asymptotic
forms for the β1 factor that appears in Equation A.2-16. The following approximations,
which are accurate within about 1% for the range indicated, may be more convenient that
tabulated values for use in data analysis:

ChE 324 Lab Manual
Experiment A.2
[ ]β
π
ε ε ε ε1
2 3
2
1 01775 0 3= − + − + <. ... .for (A.2-21)
for a slab,
β ε
ε
ε1
2
2 405 1
2
0 2= − +





 + <. ..., .for (A.2-22)
for a cylinder, and
[ ]β π ε ε ε1
3
1 329 0 2= − + + <. ..., .for (A.2-23)
for a sphere, where ε = 1/ Bi.
Plots of the complete forms of Equations A.2-14, 17, and 19 for a slab, cylinder,
and sphere can be found in Perry's handbook or in one of a number of heat-transfer
textbooks. (Kreith, 1958).
Apparatus
The apparatus for this experiment consists of (1) a relatively large constant-
temperature bath with automatic temperature control; (2) a circulation chamber for
contacting a solid specimen with the bath fluid under controlled flow conditions;(3) a
pump to circulate the bath fluid from the thermostat through the circulation chamber; (4) a
mercury thermometer; (5) copper-constantan thermocouples connected to a digital
thermometer; (6) a stop watch; and (7) solid test specimens of various shapes and
materials, each with a copper-constantan thermocouple inserted at its center and mounting
brackets attached for suspending it in the circulation chamber.
The test specimens are shown schematically in Figure A.2-2. Physical properties
and dimensions of the materials used are given in Table A.2-1. A diagram of the apparatus
is given in Figure A.2-3.

ChE 324 Lab Manual
Experiment A.2
Figure A.2-2. Geometry of the test specimens.
Table A.2-1. Physical properties and dimensions of the specimens used in Experiment A.2
Material of
Construction
Density, ρ
(lbm/in3
)
Heat
Capacity, CP
(Btu/°F·lbm)
Thermal
Conductivity, k
(Btu/hr·ft·°F)
Specimen Shape
and size
Aluminum Bronze 0.274 0.170 41 Sphere: D = 3.0 in.
Chrome Steel 0.283 0.113 26 Sphere: D = 3.0 in.
Carbon Steel 0.256 0.112 31 Cylinder: D = 2.0 in
Slab: 2b = 2.0 in.
Brass 0.307 0.136 58 Cylinder: D = 2.0 in.
Slab: 2b = 2.0 in.
Nylon 0.040 0.4 -- Cylinder D = 2.0 in.
Slab: 2b = 2.0 in.
Sphere: D = 3.0 in.

ChE 324 Lab Manual
Experiment A.2
Figure A.2-3. Diagram of the experimental apparatus.
Procedure
1. Turn on the thermostat, if it has not been done, and set the bath temperature at 60o
C.
2. Turn on the circulation pump, and check that there is flow through the test chamber.
3. Ensure that the bath has reached the pre-determined temperature and that it is holding
constant.
4. Inspect the digital thermometers and make sure that they are all reading room
temperature properly. Note any offset observed with a particular thermocouple.
5. Choose a particular geometry for your experiment, slab, cylinder, or sphere. Check the
dimensions, and note the materials of the solid test specimens that will be used. See
Appendix 7.
6. Just prior to placing a test specimen in the circulation chamber, measure the bath
temperature with the mercury thermometer, and record the temperature at the center of the
test specimen.
7. Place the test specimen in the circulation chamber and record the temperature history at
the center of the specimen by recording both time and temperature as the solid heats up.

ChE 324 Lab Manual
Experiment A.2
This may be done most conveniently by choosing a temperature, using the stopwatch to
record when that temperature is reached, and then selecting the next temperature to be
recorded. Be careful not to turn off the stopwatch when interval readings are taken. Take
as many readings as possible at the beginning of a run while the temperature is changing
most rapidly. Later the data may be taken in a more leisurely manner. Take data until the
solid centerline temperature reaches at least 95% of its ultimate change, that is, until Θ ≤
0.05 at η=0.
8. Just after the measurement of the temperature history at the center of the test specimen
has been completed, once again measure the bath temperature with the mercury
thermometer.
9. Repeat this procedure with two known materials (iron or steel and copper or brass) and
with the unknown (nylon), all of the same shape and size.
Note: Initial filling and any make-up of water lost from the bath should be done with hot
tap water to minimize bath-temperature recovery time.
Data Analysis
The logic of this experiment is that the thermal conductivity of nylon, presumably
unknown, can be determined in an apparatus in which the rate of heating of a nylon object
can be observed. We have a theoretical model for the rate of heating of simple solid shapes
that relates the changing temperature of the solid body to the thermal conductivity of the
solid. There is a complication, however, in that the rate of heating also depends on the
efficiency of the fluid in transferring heat to the surface of the solid. This efficiency
depends on the properties of the bath fluid, the intensity of fluid mixing, and the geometry.
These factors are characterized by the parameter h.
In order to calibrate the apparatus, that is, to determine the value of h for the bath
being used here, one observes heating rates with one or two materials of the same shape
and size but with known thermal properties.
Calculations:
1. For each of the known materials tested, plot the temperature-time data in
dimensionless form on a semi-log graph, according to Equation A.2-16. Obtain the value
of β1 from the slope of the linear region and calculate the Biot number, hL/k, from the
appropriate equation (A.2-15,18, or 20) depending on the shape. Calculate the value of h.
The fluid-film heat-transfer coefficient, h, is characteristic of the water bath, its flow rate,
and of the shape of the solid body, but it is independent of the thermal properties of the
solid. Therefore, the solid specimens should yield similar values of h.
2. After you have fit the semi-log plots of your temperature data for the two known
materials and estimated the corresponding values of β1 (and Bi) from the slopes of the
linear regions, estimate the values of the intercept ln A1 in Equation A.2-16 calculated
from β1 and the truncated theoretical model. This theoretical intercept may be compared

ChE 324 Lab Manual
Experiment A.2
with the intercepts of your linear fit of the data for each known material in order to check
for consistency.
The theoretical values of A1 are the following:
A
Bi
Bi Bi
1
1
1
2
2
1
=
+ +
sec
( )
β
β
(A.2-24)
for the slab,
[ ] ( )
A
Bi
Bi J
1
1
2 2
0 1
2
=
+β β
(A.2-25)
for a cylinder, and
( )
A
Bi
Bi Bi
1
1
1
2 2
1
2
=
+ −
β
β β( ) sin
(A.2-26)
for a sphere. Values of the Bessel function Jo(β1) are tabulated in Appendix 6.
3. From the temperature measurements on the nylon object, make an initial estimate of k
by comparing the temperature-versus-time data with the theoretical form. Again, use only
the data falling in the linear region of the semi-log plot. Because we can guess that the
thermal conductivity of this polymer is relatively small, we can get an initial estimate of k
by assuming that the Biot number is very large, that is, k/hb ≅ 0, and use the corresponding
theoretical value of β1. (If this approximation turns out to be a good assumption, we would
not need to determine the actual value of h from measurements with known materials.)
4. Refine your estimate of k of nylon by accounting for the effect of a finite Bi on β1, that
is, the effect of the finite resistance to heat transfer in the water. This could be done by
iterative calculations, starting with the initial estimate of k obtained in the previous step
and successively revising the values of β1, α, and k until a good fit of the data is obtained.
More conveniently, you may solve for k directly by noting that you have two independent
expressions that may be solved simultaneously for β1 and k with nylon. The procedure is
the following.
First, you have in Appendix 6 or Figure A.2-1 a relation between β1 and Bi into
which you can substitute the definition of Bi from Equation A.2-13 and the known value of
h to obtain β1 as a function of k. Also, you can plot the dimensionless temperature
calculated from the experimental data with nylon versus real time. According to Equation
A.2-16 and the definition of τ in Equation A.2-6, the slope of the linear region of such a
plot, called m, will be
m b= − β α1
2 2
( / ) (A.2-27)
Substituting the definition of α into Equation A.2-27 yields a second relation between β1
and k. Simultaneous solution of the two relations gives the values of k and β1 for the nylon.

ChE 324 Lab Manual
Experiment A.2
The two relations may be solved graphically by plotting them both as curves of β1 versus k
and determining the location of their intersection.
References
Bird, R.B., W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, Second Edition, John
Wiley and Sons, Inc., New York (2002).
Carslaw, H.S., and J.C. Jaeger, Conduction of Heat in Solids, 2nd edition, Oxford
University Press, London (1959), pp. 121-124
Jacob, M., Heat Transfer, Volume 1, John Wiley and Sons, Inc., New York (1949), pp.
270-287
Kreith, F., Principles of Heat Transfer, International Textbook Company, Scranton (1958),
pp. 137-145

ChE 324 Lab Manual
Part B
Measurement of Profiles of Velocity, Temperature, and Concentration

ChE 324 Lab Manual
Experiment B.1
Velocity Profiles in Steady Turbulent Flow Page B.1-1
Experiment B.1
VELOCITY PROFILES IN STEADY TURBULENT FLOW
For fluids in steady laminar flow in simple geometries, it is often possible to
predict theoretically the exact velocity distribution of the fluid. This is the case in
straight tubes with cross sections that are either circular, concentric annular, rectangular,
or elliptical (Bird et al., 2002, pp. 48-56). In order to calculate such velocity distributions
from the differential equations of motion that are based on conservation of mass and
momentum in the fluid, one must express the flux of momentum by molecular
mechanisms, called τ, in terms of the velocity gradient ∇v. Such expressions are given
by Newton’s law of viscosity, for Newtonian fluids, and by a number of empirical models
for non-Newtonian fluids (Bird et al., 2002, pp. 231-257).
In the case of steady turbulent flow, it is not possible to predict exactly the
time-smoothed velocity distribution of a fluid because of the complex nature of the
“turbulent momentum flux”, that is, the average rate of momentum transport by random
turbulent eddies. A number of empirical and semi-empirical relationships have been used
to describe this additional momentum flux and the resulting time-smoothed velocity
distributions in certain types of turbulent flows. In this experiment the nature of turbulent
flow is examined by measuring velocity distributions for water flowing through a smooth
tube, under turbulent conditions, at various flow rates. The results will be analyzed in
terms of standard models of the structure of turbulent boundary layers and of the
turbulent transport of momentum.
Theory
When the velocity is fast relative to the fluid viscosity, fluid flow becomes
unstable with respect to various disturbances, and the streamlines experience
instantaneous fluctuations in both magnitude and direction called turbulent eddies. For
pipe flow this usually occurs when the Reynolds number, Re = D<vz>ρ/µ, exceeds 2100.
The fluctuations in velocity provide an additional mechanism for momentum transport
across the time-averaged streamlines, with the result that the rate of momentum transport
to a solid wall is increased. Also, the enhancement of the momentum flux by turbulent
eddies modifies the time-smoothed velocity profile of the fluid; in regions of effective
turbulent transport steep velocity gradients are not needed to drive momentum transport
by viscous forces. Thus, the time-smoothed velocity profile can be flatter than the
corresponding laminar flow field. On the other hand, near a solid wall, where the
velocity fluctuations are blocked or damped out, viscous forces must carry the
momentum flux into the wall. A laminar sublayer exists near the wall in which the
velocity gradient becomes steep according to Newton's law of viscosity.
The principle of conservation of momentum and the associated equations of
motion, are still valid in the case of turbulent flow. When the equations are averaged

ChE 324 Lab Manual
Experiment B.1
over a time period that is long compared with the frequency of the turbulent fluctuations
one obtains equations for the time-smoothed velocity profiles. As shown by Bird et al.
(2002, §5.2),
Time-smoothed
equation of
continuity
0)( =•∇ v (B.1-1)
Time-smoothed
equation of motion gττ
v
ρρ +•∇−•∇−−∇= ][][ )()( tv
p
Dt
D (B.1.2)
These equations contain, in addition to the usual viscous transport and inertial
terms, extra terms that arise from the mixing effects of the eddies. The over bars indicate
time-smoothed quantities. The extra terms are identified as the turbulent momentum flux,
)(t
τ , and called the Reynolds stresses. If one could identify a general relation between
the turbulent momentum flux and the time-smoothed velocity gradient for turbulent
flows, in a form analogous to Newton's law of viscosity, then one could solve the time-
smoothed equations of motion to obtain the averaged velocity profile and the shear stress
on the walls.
A number of empirical relationships have been proposed to describe the turbulent
momentum flux; Bird et al. (2002, §5.4) summarizes some of them. The empirical
relations of Prandtl and Diessler were combined with the time-smoothed equation of
motion and experimental data to yield the so-called Universal Velocity Profile, which
agrees closely with experimental data for the time-smoothed velocity distributions in
pipes at Reynolds numbers greater than 20,000. The profile has three identifiable regions:
the laminar sublayer, the buffer layer, and the turbulent core. The three following semi-
empirical expressions and ranges given by McCabe et al.(2001) describe the profile very
closely:
Laminar sublayer:
+
= yv+
for 50 ≤≤ +
y (B.1-3)
Buffer layer: 05.3ln.05 −= ++
yv for 305 ≤≤ +
y (B.1-4)
Turbulent core: ( ) 5.5+ln2.5= ++
yv for 30≥+
y
(B.1-5)
The dimensionless velocity v+
is defined as
*v
v
v
z
=+
(B.1-6)

ChE 324 Lab Manual
Experiment B.1
where ρτo=*v and 0τ is the normal shear stress (or momentum flux) at the wall.
Also,
µ
ρ*vy
y =+
(B.1-7)
where y is the distance from the wall.
The Universal velocity profile is plotted, along with numerous experimental data
for turbulent flow in pipes, in Figure 5.5-3 of Bird et al. (2002). Although these
equations and the corresponding plot fit data on the turbulent velocity profile in pipes at
high Reynolds numbers, an awkward aspect of this approach is that Equation B.1-5 (and
the corresponding graph) do not recognize the existence of the centerline of the pipe,
where the velocity profile should be flat. The pipe radius R does not appear in these
correlations because they focus on the effect of the wall, namely the shear stress τ0, on
the structure of the turbulent boundary layer.
The average shear stress at the wall can be determined from a macroscopic force
balance on the pipe. For steady flow in a horizontal pipe the shear stress on the wall
balances the net pressure force acting axially on the fluid. That is,
( )2 0
2
0π τ πRL R p pL= − (B.1-8)
Therefore, the wall shear stress is given by
( )τ 0
0
2
=
−p p R
L
L
(B.1-9)
As an alternative to fitting the turbulent momentum flux in order to derive the
time-smoothed velocity profile in turbulent flow, one may simply correlate experimental
data on the velocity profile in a particular geometry. For pipe flow at Reynolds numbers
between 104
and 105
, Prengle and Rothfus (1955) reported that
71
max,
1
v
v






−=
R
r
z
z
(B.1-10)
Schlichting (1951) has broadened the applicability of Equation B.1-10 by letting the
exponent be an empirical function of Reynolds number. That is, he proposed the
following empirical equation to describe the velocity distribution for steady flow in round
tubes:
n/1
maxz,
R
r
1v=v 





−z (B.1-11)

ChE 324 Lab Manual
Experiment B.1
where the constant n reported by Schlichting depends on the Reynolds number as
summarized in Table B.1-1. Although extremely simple and in certain respects
unsatisfactory, Equation B.1-11 is convenient. For example, it allows one to relate the
maximum velocity in a pipe to the average velocity (See Problem 5B.1 in Bird et al.,
2002), but it cannot be used to calculate shear stress at the wall nor pressure drop.
Table B.1-1. The Constant n of Equation B.1-11 as a Function of Reynolds Numbers
Re 4 x 103
7.3 x 104
1.1 x 105
1.1 x 106
2.0 x 106
3.2 x 106
n 6.0 6.6 7.0 8.8 10 10
One of the simplest methods of measuring point velocities within a flowing fluid
is with an impact tube, also called a pitot tube, which is described by McCabe et al.
(2001). By conversion of kinetic energy head to static pressure head at the mouth of a
tubular probe, the undisturbed velocity in an impinging streamline can be related to the
rise in pressure within the impact tube above the static pressure in the fluid at the point of
impact. When this pressure difference is measured by a manometer, the local velocity of
the fluid impacting the mouth of the tube vn is related to the manometer reading by the
relation
( )
OH
c
OH
ba
n
pg
22
2
sinhg2=v
2/1
ρρ
ρρ
θ
∆
=







 −
∆ (B.1-12)
where vn is fluid velocity normal to the mouth of the tube, ∆h is the differential length
reading on the manometer scale, θ is the angle of the manometer relative to the horizon,
and the subscripts in the density-difference term refer to the heavier manometer fluid (a)
and to the lighter fluid (b) above it. The second expression can be used when the
pressure drop is measured directly using an electronic transducer.
When the manometer is damped, as it is in this experiment, and the impact tube is
aligned with the pipe axis, Equation B.1.12 may be used to relate the time-averaged value
of the differential reading of the manometer, ∆ h , to the time-averaged axial point
velocity, )(v rz . Be careful that the calculated velocities are dimensionally correct.
Apparatus
The apparatus for this experiment is illustrated in Figures B1-1 and 2. The
equipment consists of
1. A test section of cylindrical pipe that is equipped with two piezometer rings for
measuring the local static pressure and a traversing impact tube with a static pressure
tap. (Inside diameter of test section = 1-1/16 inches; distance between piezometer
rings = 3 ft; length of test section before impact tube = 5 ft; length of test section

ChE 324 Lab Manual
Experiment B.1
after impact tube = 1 ft.) The configuration of the impact tube is shown in Figure
B.1-1. A scale on the probe-positioning mechanism is graduated in tenths of an inch.
2. Two manometers (24-inch air-over-water, and 15-inch water-over-mercury). The
manometer board can be oriented at several angles relative to the horizontal in order
to amplify the ∆h reading.
3. A source of clean water and a 55-gallon galvanized steel drum supply reservoir.
4. A scale, collection container, and stopwatch for measuring the mass flow rate of
water.
5. A thermometer
6. Auxiliary piping (1.5 inch, Schedule 40, galvanized iron pipe) as shown in Figure
B.1-2. Valve V-10 controls the flow rate through the pipe.
7. A centrifugal pump driven by a 1.5 horsepower, 60 cycle, 220 volt, 3-phase electric
motor at 1800 rpm. The pump is rated to deliver 45 gal/min under 25 ft of liquid
head at 1750 rpm.
Figure B.1-1. Diagram of the test section and traversing impact tube.

ChE 324 Lab Manual
Experiment B.1
Figure B.1-2. Diagram of the piping configuration for Experiment B.1.
Procedure
Measure the time-smoothed velocity profile in the pipe at three Reynolds numbers
according to the following procedure.
1. Locate all the valves and become familiar with the operation of the equipment,
particularly that concerning functions of the manometers and the pressure taps on the
test section. Check and record dimensions of the apparatus, and measure the water
temperature.
2. Purge the manometer lines of air as follows:
a) Start with all valves closed except V-10, which is to be fully opened. Let
water flow through the test section.
b) Turn valves V-1 and V-2 to the “piezometer” position.
c) Open valves V-3, V-4, and V-5. When no more air bubbles are visible in the
manometer, close V-3, V-4, and V-5.

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