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RUBRIC FOR ASSESSING LAB REPORTS
0
Missing
1
Beginning or incomplete
2
Developing
3
Accomplished
Objective/
Background
Very little background
information provided or
information is incorrect
Some introductory information,
but still missing some major
points
Introduction is nearly complete,
missing some minor points
Experimental
procedure
Missing several important
experimental details or not
written in paragraph format
Written in paragraph format, still
missing some important
experimental details
Data, figures,
graphs, tables,
etc.
Calculations are missing or
mostly incorrect. Figures, graphs,
tables contain errors or are poorly
constructed, have missing titles,
captions or numbers, units
missing or incorrect, etc.
Uncertainty is not included.
Very incomplete or incorrect
interpretation of trends and
comparison of data indicating a
lack of understanding of results
There are multiple mistakes with
the calculations. Most figures,
graphs, tables are OK, some still
missing some important or
required features. Uncertainty
calculations have many mistakes
or omissions.
Some of the results have been
correctly interpreted and
discussed; partial but incomplete
understanding of results is still
evident
Conclusions regarding major
points are drawn, but many are
misstated, indicating a lack of
understanding
Sections in order, contains the
minimum allowable amount of
handwritten copy, formatting is
rough but readable
More than 2 calculations,
questions, or data are missing.
But reasonable effort is apparent.
Written in paragraph format,
important experimental details
are covered, some minor details
missing
Most calculation are correct. All
figures, graphs, tables are
correctly drawn, but some have
minor problems or could still be
improved. Uncertainty is
included but may have one or
two errors or omissions.
Almost all of the results have
been correctly interpreted and
discussed, only minor
improvements are needed
Discussion of
Results
Conclusions
Conclusions missing or missing
the important points
Appearance and
formatting
Sections out of order, too much
handwritten copy, sloppy
formatting
Appednix
Only a few calculations or
questions re answered, missing
raw data, etc. Clearly not
complete work.
All important conclusions have
been drawn, could be better
stated
4
Exemplary
Total
Score x
Weight
Introduction complete and wellwritten; provides all necessary
background principles for the
experiment
Well-written in paragraph format,
all experimental details are
covered
___ x 2.5
___ x 2.5
All calculations and results are
correct. All figures, graphs, tables
are correctly drawn, are
numbered and contain
___ x 7.5
titles/captions. Uncertainty
calculations are correct and
indicated in figures/tables.
All important trends and data
comparisons have been
interpreted correctly and
___ x 2.5
discussed, good understanding of
results is conveyed
All important conclusions have
been clearly made, student shows
___ x 2.5
good understanding
All sections in order, formatting
generally good but could still be
improved
All sections in order, wellformatted, very readable
Only 1 or 2 calculations,
questions, or data are missing,
but otherwise is complete.
Entire worksheet is complete;
including calculations, tables,
figures, and discussion
___ x 2.5
___ x 5
Total: ______
Technical Report Writing
Note: This document has been modified from the ME 360 technical writing handout. Major
differences between ME 360 and ME 460 presented in italics.
This article provides some general guidelines and "tips" for writing technical reports.
Throughout the Mechanical Engineering curriculum you will be required to write formal reportslab reports in ME 360 and ME 460; design project reports in ME 372 and ME 415; a capstone
design project report in ME 490; and similar reports in other courses. Each of these reports has
particular requirements established by the course instructor. However, the following rules for
references, figures, tables, tense and voice, equations, etc., apply to all mechanical engineering
writing. Specific instructions for ME 460 are spelled out at the end of this section.
How to Write a Report
All engineers must report their work, usually in writing. Skilled writers impress their readers
favorably. Clear writing helps in preparing oral presentations. Follow the three rules given
below for all reports, oral and written.
1. Imagine your audience. In ME 460, imagine you are on your first job and your boss has
assigned you to do this experiment. Your boss has an engineering background similar to
yours, but does not know the details of the experiment (has not read the ME 460 handout).
Your reader (your boss) relies on you for clear explanations.
2. Be thorough and brief. Include all the required sections (discussed below) and informative
tables, equations, etc. Write a first draft, then edit it carefully for redundancy, wordiness,
clutter, etc.
3. Organize for readability. The question "Is the reader ready for this material?" guides the
structure of the report. Overly detailed material, such as calculations, belong in the appendix.
Sections of the Lab Report
1. Title Page. Include the title of the lab, the author’s name, the names of all lab partners, and
the date.
2. Objective. Describe in one or two sentences the purpose of the laboratory exercise: the
“why.” Be specific. Possible objectives are “to evaluate,” “to verify,” “to measure,” “to
compare,” etc. Avoid non-engineering objectives, such as “to teach us” or “to show the
student.” In general, you will write a technical report where experimental results are
compared to theory. The Objective section is written in the present tense.
3. Background. This section gives the reader information necessary to understand or appreciate
the balance of the report. It puts things in focus by providing background and perspective. It
should answer such questions as: Why was this done? How does this effort fit into the
overall scope of things? The Background section is also used to relate your efforts to
previous work done by yourself or others. For example, if your report covers electrical
filters, then you should discuss a few (three to four) applications of filters. Applications that
ME 460 Technical Report Writing
1
relate to mechanical engineering are preferred over generic engineering, technical, or
consumer applications.
In a lab report, the Background section should also briefly describe the engineering theory
used in the experiment and the analysis of its results. Any theoretically predicted results of
your experiment would also be included. Commonly used engineering equations (such as
Newton's 2nd law, F = ma) can be presented without attributing a source. However,
equations taken directly from a textbook must be given proper reference. The Background
section is written in the present tense.
You may use the ME 460 Lab Manual (handouts) to find equations provided that you provide
a proper reference. You will be given the MS Word file of the lab handout so that you can
cut and paste equations and figures.
4. Experiment. Write what was done in the lab and how it was accomplished in chronological
order. Imagine your group performing the experiment and describe what you did and what
happened. Describe the experimental apparatus (including manufacturer and capacity or
range of equipment used) and include a diagram, sketch, or scanned photograph with any
relevant dimensions. This section should be complete enough for someone to duplicate the
results of your efforts. Write the Experiment section in the past tense, since the experiment
has already been done. Note that “raw” data does not belong in the Experiment section – it
belongs in the Appendix.
5. Results. Present the results in words, tables, and figures. Be sure that tables and figures are
mentioned in the text before the actual table or figure is presented. Include a comparison of
actual results to theory, if appropriate, and an analysis of sources of error in your
experimental technique. All formal reports require an uncertainty analysis. Discuss the
results from the uncertainty analysis and use it to guide your discussion. Think carefully: Do
the sources of error you have defined adequately explain your experimental results? Cite
"human error" only if you discuss exactly what is meant. Remember that you never really
know the exact source of error. Always address any specific questions asked in your lab
handout. Write the Results section in the present tense.
6. Conclusions. Restate and interpret the major results using numerical values when possible.
Were the objectives of the lab or design project met? What can you conclude from the lab?
Write the Conclusions section in the present tense.
7. References. Any material taken directly from another author other than you, including the
ME 460 Lab Manual, must be referenced. See the section on References in the Writing Style
and Format Requirements section. No minimum number of references is required for ME 460
formal lab reports.
8. Appendix. All portions of the appendix should be specifically mentioned somewhere in the
main part of the lab report. The appendix should include
♦ an outline of your appendix (continue page numbering from the main report),
♦ a clear listing of your assumptions about uncertainty values,
♦ an example / sample of each calculation required to generate your results - all necessary
unit conversions required,
ME 460 Technical Report Writing
2
♦ an uncertainty analysis for all results computed from a formula (including both
experimental values and theoretical values that use measured values in a formula), ♦
raw data sheets.
Writing Style and Format Requirements
Reports written for ME 460 will generally follow the style requirements of the APA (American
Psychological Association) unless specifically contradicted in this handout. See the ME 360
website for a list of references to the APA style.
Appearance
1. Word process the body of the report, from the title page through the conclusions. The
appendix material may be neatly handwritten in either ink or pencil.
2. Figures should be embedded in the report, typically scanned or cut from another source, and
then inserted.
3. Use the 12 point Times or Times New Roman fonts for your text, figure captions, and table
headings. Use a 12 point Arial or Calibri font for text in figures.
4. Use a one-inch margin on all four sides. Do not right justify the text.
5. Double-space all of the text.
6. Put page numbers on all pages, starting with 1 on the title page. Page numbers are placed
one-half inch from the top edge and one inch from the right edge. Use the Header feature of
Word to automatically place your page numbers.
7. A header identifying the lab report immediately precedes the page number on all pages: ME
460 Lab Report 0. Leave five spaces between this header and the page number.
Tense and Voice
1. Write in the passive voice: "Strain gages were used with a Wheatstone bridge to determine
the bending stress in the cantilever beam."
2. Avoid -ing verbs with the passive voice (especially avoid the words “using” and “utilizing”):
RIGHT: With a Wheatstone bridge, . . .
or
A Wheatstone bridge was used to . .
WRONG: Using a Wheatstone bridge, . . .
3. Use present tense for the Objective, Background, Results and Conclusions section and any
time you state general rules or truths: "The relationship between uniaxial stress and strain is
σ =E."
4. Use past tense for the Experiment section. Tell what was done and what happened in your
particular case.
Spelling, Punctuation, and Word Selection
1. Use a colon only where a period would fit.
2. Put a comma before the conjunction (and, or, but) in lists of three or more.
ME 460 Technical Report Writing
3
Set off the words “therefore,” “however,” with (a) comma(s).
Spell out contractions (cannot, is not, could not, etc.).
Use a plural verb for the word “data”: the data are (were); the datum is (was).
Do not write in first person [I, me, my]. The report should be objective. In the group reports
it will be acceptable to use third person [we].
7. Second person pronouns are unacceptable--do not use the word “you” as in “You will see . .
.”
8. Avoid non-technical language. Avoid the words “thing” and “stuff” as they relate no
information.
9. Avoid the word “there” everywhere in the report. It does not carry any information. Choose
more specific words.
10. Avoid referring to measurements by their units (“The psi in the cylinder was 34.”). Instead,
use the dimension to refer to the measurement (“The pressure in the cylinder was 34 psi.”).
3.
4.
5.
6.
Labeling, Referencing, and Placement of Tables and Figures
Tables present numerical or textual material or information in a regular array. Figures present
sketches, pictures, charts, graphs, etc. Put the independent values in the first column of a table
and on the horizontal axis of plots when possible.
1. Mention each table and figure in the text before it appears in the report. Tables and figures
should appear on the same page or on the next available page after they are mentioned. Do
not leave large gaps at the bottom of a page if a figure or table will not fit. Continue the text
and put the figure or table at the top of the next page.
2. Number and label each table and figure in order, e.g. Table 1, Table 2, etc., not Table 1.1,
Table 1-2, etc. Tables are numbered independently of figures and not consecutively as one
group.
3. Tables and figures are centered on the page within the one inch margins.
4. A modified version of the APA style for table headings and figure captions will be used in
ME 360 & ME 460 as shown below. Note that the table title and the figure number are
italicized as shown below.
Table 1
Force Sensor Specifications
Figure 1. Experimental setup for filter test.
5. Title each figure and table. Note that table titles are placed above the table, while figure titles
(these are called captions) are placed below the figure.
6. Acknowledge all figures taken directly from any source. Failure to do so is PLAGIARISM!
Follow the example below.
Figure 6. Opposed piston engine (Bell & Parker, 1997).
ME 460 Technical Report Writing
4
APA Style Tables (from http://web.indstate.edu/mary/tables.htm)
•
The first part of a table is the table number. Tables are numbered with Arabic numerals in
the order of appearance.
•
The next part is the table title. The table title should be upper and lowercased, centered, and
double spaced below the table number. The title should be italicized as well. Double space
again after the table title before the actual table begins.
•
Next is the first horizontal line of the table, which separates the table title from the column
headings.
•
Use upper and lowercase letters in the column headings. The column heading is the label
which is centered over each column. Column headings are not boldface, italicized, or
underlined.
•
A second horizontal line separates the column headings from the table data. Table data
must be in the same style and size font used for the report’s text. It should also fit within the
boundaries of the page’s margins.
•
The table is ended with a final horizontal line. Any table notes should follow this last line,
being designated by Note. and followed by a period.
•
These three horizontal lines are the only lines which are required for an APA style table. In
some cases additional horizontal lines may be used for clarification (American Psychological
Association, 2001).
•
Strict APA style does not allow the use of vertical lines. Check with your instructor if you
want to use vertical lines in a table.
•
In ME 460 we will single-space the table data. In strict APA style the entire table is double
spaced, just like the rest of the paper.
•
Numbers used in tables should have approximately the correct number of significant digits.
Do not let Excel determine how many significant digits you use!
Correct APA style table (modified slightly for ME 360 and 460):
Table 1
Desired and Actual Frequencies for Low Pass Filter Experiment
Desired
Actual
Desired
Actual
Frequency
Frequency
Frequency
Frequency
(Hz)
(Hz)
(Hz)
(Hz)
10
8
800
800
15
16
1500
1600
ME 460 Technical Report Writing
5
Incorrect APA style table (too many horizontal lines, vertical lines, Arial font):
Table 1.
Desired and actual frequencies for low pass filter experiment
Desired
Actual
Desired
Actual
Frequency
Frequency
Frequency
Frequency
(Hz)
(Hz)
(Hz)
(Hz)
10
8
800
800
15
16
1500
1600
Formatting Figures and Graphs
1. You may use scanned or copied figures taken directly from lab handout or course notes in
your ME 460 lab report, but you must reference the ME 460 Lab Manual.
2. All figures should be neatly drawn, either by hand or by computer. All plots of data must be
computer generated with Excel, Matlab, or an equivalent program.
3. Plot the independent variable along the abscissa ("X axis") and the dependent variable(s)
along the ordinate ("Y axis").
4. Use appropriate scales for each axis: Divisions of 1, 2, 5, 10, or multiples are preferred.
Avoid awkward fractions along labeled divisions (computer programs are particularly bad
about this). Show 0 on the scale unless this would compress the data unnecessarily. Do not
use numbers like “0.0, 1.0, 2.0, …” for labeling axes, but “0.0. 0.5, 1.0, 1.5, …” is OK.
5. Label the horizontal axis across the bottom of the plot, and the vertical axis along the left
hand edge. A “secondary” vertical axis is sometimes provided along the right hand edge.
6. Label each axis with units as well as variable names. If you are plotting two or more
variables along the ordinate, use multiple scales (or log scale) if a single scale would
compress one set of data excessively.
7. Use similar scales for plots of similar data (perhaps the same experiment run with two
different settings).
8. Align each figure so that it reads normally or from the right-hand edge of the page, (i.e., the
page should be bound along the left or top side).
9. Plot theoretical relationships along a smooth line or curve, without individual data points
(since any point along the curve is equally valid).
10. Plot empirical relationships with individual data points and smooth curves of the appropriate
mathematical type. For example, a plot of measured resistance vs. displacement for a
potentiometer would use a "best-fit" straight line, since this is the expected relationship.
11. Draw measured data not supported by theory or empirical formula as distinct data points
without any lines. Make data points large enough to be easily read.
ME 460 Technical Report Writing
6
Some specific comments about graphs in Microsoft Excel
12. Use the X-Y (Scatter) plot option for most of your plots--not Line plot (which equally spaces
X axis data). The only exception to this rule is when no independent variable exists. An
example of this case would be plotting the experimentally measured resistance of several
resistors.
13. The default placement of the X and Y axis can be changed on the Format Axis – Scale option
under “Value (X or Y) axis Crosses at ___”.
14. See the ME 360 website (www.me.ua.edu/me360) for additional comments on using Excel in
your lab reports. This site is old, but still has some good information about report writing.
Equations
1. Provide the reference for all equations taken from another source, including a textbook or a
handout. Embed the reference in the text, do not put the reference on the same line as the
equation:
“Bernoulli's equation for incompressible flow is given by Equation 15.2 of Beckwith, Buck,
& Marangoni (1982) as
P1 − P2
=
V22 − V12 ( Z 2 − Z1 ) g
+
2 gc
gc
(1)
2. Define all symbols immediately after they are first used:
Mechanical output power is calculated from the formula
P =
(1)
where
P is the power (typically horsepower or watts),
is the torque (typically ft-lbf or N-m), and
is the angular velocity in RPM (revolutions per minute).
3. Number each equation sequentially in parentheses as shown. The equation can then be
referenced by number: "Equation (2) was used to compute motor power output."
4. Center equations (using tab that looks like a perpendicular symbol), and number them along
the right margin (using a right align tab), e.g., see Equation 2 above.
5. Refer to a numbered equation with a capital E: Equation 1. If you use the abbreviations
"Eqn" or "Eq." and "Eqns." or "Eqs.," do so consistently.
6. Place each equation on a separate line. Unless the equation is universally well known or very
short, division should be shown on two separate lines. Note the ambiguity in the first two
examples below and the clarity of the third.
Not acceptable:
ME 460 Technical Report Writing
Ymax=3*Pa^4/16*E*t^3*(1-v^2)
(4)
7
Not acceptable:
(
Ymax = 3Pa4 /16 Et 3 1 − 2
Acceptable:
Ymax =
3Pa4
(
16 Et 3 1 − 2
)
)
(5)
(6)
7. Equations should be generated using the Equation Editor that is included with Microsoft
Word of (preferred) the MathType 6.0 upgrade.
References
All references must be specifically mentioned in the text of your report. References are cited in
two different places: in text as part of the information within a sentence; OR in text
parenthetically not as part of the sentence’s direct information [in which case they are put into
parentheses]; AND in the references section. If a reference is cited by authors’ names in the text,
the date should immediately follow in parentheses. The date only has to be stated the first time it
is mentioned within a paragraph. When it is mentioned again in the next paragraph, the date
must be restated. The names are separated by “and.” If a reference is cited parenthetically, the
names and date are put in parentheses together. The names are separated by an ampersand (&).
In the references section, the names are also separated by an ampersand.
Here are the two ways reference citations can appear in text: 1) “… Wheeler and Ganji (1996)
give the equation for gain as …” or 2) “Gain is the ratio of output amplitude to input amplitude
(Wheeler & Ganji, 1996).” Note that both authors and dates are given in each style. Spell out the
names for one or two authors. For three or more authors, name all of the authors the first time (
“Cuttino, Woodbury, and Parker (1996) described a process for group writing of reports.”), but
use “et al.” for all subsequent references (“Cuttino et al. (1996) also described …”).
Several examples of references using the APA style are listed below. References number 5
(Degelman & Harris, 2000) and number 6 (A guide for writing research papers, APA style, n.d.)
listed below can be consulted for additional examples. The APA style for reference listings
requires that references be listed alphabetically with a hanging indent format as shown below and
in the ME 360 “Good Lab Report.” Note that strict APA style requires the reference list to be
double-spaced, but single-spacing the entries with a double-space between entries is used in ME
360/460.
1. Book
Franklin, G. F., Powell, J. D., & Emani-Naeini, A. (2002). Feedback control of dynamic systems
(4th ed.). Upper Saddle River, NJ: Prentice Hall.
2. Article or chapter in an edited book
Norton, H. N. (1997). Transducers and sensors. In D. Christiansen (Ed.), Electronic engineers’
handbook (pp. 13.1-13.50). New York: McGraw-Hill.
ME 460 Technical Report Writing
8
3. Magazine article
Viterna, L. A. (1998, July). Hybrid electric bus. Power Conversion and Intelligent
Motion, 24, 38-47.
4. Journal article
Parker, J. K., Bell, S. R. & Davis, D.M. (1992). An opposed piston engine. Journal of
Engineering for Gas Turbines and Power, 115, 734-741.
5. Web document on university program or department Web site (with copyright)
Degelman, D., & Harris, M. L. (2000). APA style essentials. Retrieved May 18, 2000, from
Vanguard University, Department of Psychology Website: http://www.vanguard.edu/
psychology/index.cfm?doc_id=796 
6. Stand-alone Web document (no author, no date)
A guide for writing research papers, APA style. (n.d.). Retrieved October 13, 2008, from
http://webster.commnet.edu/apa/
Note that web addresses can be and should be divided so that the type continues to the right
margin. They can be forcefully split after a period or a slash only. The “shift-Enter” option in
Word (instead of the “hard” Enter) often works well to force a split in a desired spot without
causing other formatting problems.
ME 460 Technical Report Writing
9
Specific Requirements for ME 460 Formal and Informal Lab Reports
All of the laboratory work conducted in ME 460 will be done in teams. During the course of the
semester, there will be two formal lab reports. These reports will be composed, edited, and
graded on an individual basis both for technical content and writing. Reports for the remaining
labs require less writing and are called “informal reports.” Unless stated otherwise in class, all
lab reports are due in class on the last day of class of the week following the lab.
Formal Lab Requirements
Generally, each formal lab will have emphasized portions that will be the subject of the formal
report. The formal report is written as if only the emphasized portions of the lab were performed.
An uncertainty analysis is required for all results in the emphasized portion(s) of formal labs
reports. The calculations, figures and data sheets for the remaining portion(s) of the lab are
attached as separate appendices to the formal report following the rules for an informal report,
described below. You will be told before the lab meeting which sections of each lab are to be
emphasized in the formal report. Two copies of a formal report should be submitted. One
complete physical (“hard-copy”) report (with appendices) for technical grading will be handed in
to your lab instructor. One electronic copy must be submitted through Turnitin on Blackboard
(appendices may be omitted) for English grading.
Formal reports are to be written in accordance with the rules described in the previous technical
writing section. You may work with your lab partners in data reduction calculations, answering
questions, performing the uncertainty analyses, and preparing tables and figures. Each lab team
may share/use the same figures and tables. However, the writing presented in formal lab
reports is to be only that of the student turning in the report. Do not “share” in writing the
reports.
MEMO Report Requirements
Essential elements are
1. A brief statement of the purpose of the experiment. It can be assumed that the person to
whom the report is written is familiar with the problem or purpose, but s/he should be
reminded in the opening paragraph.
2. A summary of the most important results, with references to supporting tables or plots.
This section should be the bulk of the report. Trivial details and descriptions of the
procedures are not necessary. Tell the recipient only what s/he needs to know.
3. A short statement of recommendations or conclusions. Conclusions must be firmly
supported by the results of the experiment. Opinions or speculations should be clearly
labeled as such.
4. Supporting documents to include original data, sample calculations, equipment list, plots,
tables etc.
It is important that the report be neat and orderly. Give all figures and tables numbers and titles.
ME 460 Technical Report Writing
10
MEMORANDUM
To: Ralph Smartguy, Chief Engineer
From: Billy Students
Date: August 31, 2011
Subject: Calibration of entropy meters
The seven thermal-induction entropy meters (list attached) were calibrated August 28, 2011, in
the Energy Affairs Laboratory as requested. Standard entropy values used for the calibration
were provided by the Model V Van Wylen entropy generator.
Six of the meters were found to have an average percent error of less than 0.5% based on 10 data
points per meter, distributed in regular increments throughout the instrument range. The
Calibration curves for these six meters are attached. As seen from the curves, none of these
meters exhibits significant hysteresis. It should be noted that the only errors were at the lower
and upper ends of the range.
The seventh meter (ID No. 12345) showed an average percent error greater than 10%. The
calibration curve for this meter shows significant hysteresis, particularly in the upper range.
During the testing period it appeared that small globules of entropy were becoming jammed in
the meter. This could explain the inaccuracies, but the results are inconclusive in this regard.
Calibration of the six meters indicates they are in sound condition and can be used with
confidence. There were no signs of entropy jamming in them. Meter number 12345 should not
be put back into use. It is recommended that further testing be done to pinpoint the cause if its
inaccuracies. If the cause is jamming, it can be corrected by careful adjustment of the Carnot
valve.
I hope these tests and this report meet your needs. If further information is needed, feel free to
call or email me.
ME 460 Technical Report Writing
11
Heat Exchangers
Descriptions of Test Heat Exchangers
A heat exchanger is a device that facilitates the transfer of heat from one fluid stream
to another. Heat exchangers of many types are widely used in industrial, HVAC, commercial, residential and transportation applications. A tube-in-tube heat exchanger is studied in
this lab.
The tube-in-tube heat exchanger is perhaps the simplest heat exchanger design other
than a bare pipe exposed to external convection. As its name implies, this heat exchanger is
constructed by passing a smaller tube through a larger tube. One fluid flows through the inside of the small tube and the other fluid flows in the annular space (washer-shaped cross
section) between the inner wall of the larger tube and outer wall of the smaller tube. If the
two fluids both enter at one end and exit at the other end, the heat exchanger is said to be in
parallel flow, as shown in Figure 1.
annulus flow
tube flow
parallel flow
Th,i
Th,o
ΔT1
ΔT2
Tc,o
Tc,i
Figure 1. Tube-in-tube heat exchanger in parallel flow.
ME 460
1
Heat Exchangers
If the two fluids enter at opposite ends and flow past each other in opposite directions, the
heat exchanger is said to be in counterflow, as shown in Figure 2.
annulus flow
tube flow
counterflow
Th,i
ΔT1
Tc,o
Th,o
ΔT2
Tc,i
Figure 2. Tube-in-tube heat exchanger in counterflow.
All else equal, counterflow allows a more complete exchange of heat (higher effectiveness
Heat Exchanger Analysis
Two methods commonly used to calculate heat exchanger performance are the
LMTD method and the effectiveness-NTU method. Both can be used to calculate the capacity of the heat exchanger, q. The heat rate to the cold fluid, qc, and heat rate from the hot
fluid, qh, can be measured as
𝑞𝑐 = 𝑚̇𝑐 𝑐𝑐 ∆𝑇𝑐 = 𝜌𝑐 𝑄𝑐 𝑐𝑐 ∆𝑇𝑐
𝑞ℎ = 𝑚̇ℎ 𝑐ℎ ∆𝑇ℎ = 𝜌ℎ 𝑄ℎ 𝑐ℎ ∆𝑇ℎ
(1)
Theoretically, q = qc = qh; however, the measured values will likely be different because of
𝑞 +𝑞
inaccuracies in the experiments. In that case the best estimate of q is the average, 𝑞 = ℎ 2 𝑐.
The log mean temperature difference (LMTD) method also allows (UA)meas to be determined
as:
𝑞 = (𝑈𝐴)𝑚𝑒𝑎𝑠 𝐿𝑀𝑇𝐷
(𝑈𝐴)𝑚𝑒𝑎𝑠 =
(2)
𝑞
𝐿𝑀𝑇𝐷
Recall, the LMTD is defined as:
ME 460
2
Heat Exchangers
LMTD =
T2 − T1
ln (T2 T1 )
(3)
where T1 = Th,in – Tc,out and T2 = Th,out – Tc,in in for counterflow exchangers, and T1 =
Th,in – Tc,in and T2 = Th,out – Tc,out for parallel flow exchangers. See Figures 1 and 2.
The second method of analysis is the effectiveness, number of transfer units (NTU)
method. The NTU method allows the heat exchanger effectiveness, , to be calculated. The
effectiveness is ratio of the heat transfer actually accomplished to the maximum heat transfer
that could be accomplished for the same two flows and same entering temperatures in a
counterflow heat exchanger of infinite UA. The maximum possible heat transfer, qmax, depends on the total heat capacities, C, of the two flows. C is defined as:
𝐶𝑖 = 𝑚̇𝑖 𝑐𝑖
(7)
Then Cc is the total heat capacity of the cold flow, Ch is the total heat capacity of the hot
flow, Cmin is the minimum of Cc and Ch, and Cmax is the maximum of Cc and Ch. The maximum heat that could possibly be transferred is that required to heat or cool the flow having C
= Cmin from its entering temperature to the entering temperature of the other flow. Thus,
qmax = Cmin(Th,in – Tc,in)
(8)
The measured heat transfer rates are:
qc = Cc(Tc,out – Tc,in)
qh= Ch(Th,in – Th,out)
(9)
Therefore, the effectiveness is:
meas =
q
q max
q + qh
q= c
2
(10)
The number of transfer units is defined as:
NTU =
UA meas
C min
(11)
Equations and charts are available that present in the functional form of (NTU, Cmin/Cmax)
for a variety of heat exchanger types. Charts and equations are presented in the Appendix for
parallel flow and counter flow HXs. The predicted effectiveness can be calculated from the
appropriate formula.
𝜀𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑 = 𝑓(𝑁𝑇𝑈, 𝐶𝑚𝑖𝑛 , 𝐶𝑚𝑎𝑥 )
(12)
ME 460
3
Heat Exchangers
Other types of heat exchangers
Tube-in-tube exchangers are very simple and are easily analyzed using heat exchanger theory
and therefore are the main focus of this lab. However, these heat exchangers are bulky and
impractical for routine use. Two common liquid/liquid heat exchanger geometries are the
coiled (or helical) tube-in-tube, and the plate frame exchanger.
Helical Exchanger
By taking a tube-in-tube exchanger and bending it into a
coiled or helical shape, a much more compact exchanger results. Additionally, the continuous curvature
of the passage induces a secondary flow in
the fluid, which enhances mixing and increases the heat transfer coefficient. Other
types of heat transfer enhancement are possible, notably use of flow tubes with spiraled
cross sections, which both enhance heat
transfer and increase the area for heat transfer.
Plate Heat Exchanger
Another type of heat exchanger that makes use of the same
basic principles as the tube-in-tube exchanger it the plate
heat exchanger. This exchanger has a number of flow passages that allow hot and cold fluids to flow in alternating
passages in either a parallel- or counter-flow arrangement.
These heat exchangers are very compact and are widely
used in industry. An added advantage is that the plates can
be stacked into a frame and bolted together (rather than permanently brazed or bonded) so that the exchanger can be
disassembled and cleaned periodically to remove scale or
organic build-up.
ME 460
4
Heat Exchangers
Objective
The objective of this experiment is to experimentally test the correlations for the Effectiveness-NTU relationships for parallel and counter flow heat exchangers, and to measure
the effectiveness of other types of heat exchangers.
Procedure
Make sure to record measurements in worksheet.
Testing Activities- Tube-in-Tube Exchanger
1. Connect hot and cold water supplies for full double length counterflow, in the tube-intube heat exchanger as detailed by lab instructor. Make sure that rotameters are placed at
each of the appropriate two outlets. Make sure that rotameters are vertical at all times.
Cold water should flow in the annulus and hot in the inner tube.
2. Set the flow rates as close as possible to those indicated in Table 2. For the first three
cases, adjust the flows so that cold and hot are as close to equal as you can. For the last
two, adjust the flows so that the hot is as close to twice the cold as possible. It is important that the heat transfer be steady state. Monitor the exit temperatures; after both
have stabilized, wait and additional minute. To get good results, temperatures
must be stable, not rising or falling! For each case, record the actual flow rates
as indicated by the rotameters and the four temperatures in a table like Table 1.
3. Shut off water to both sides of the exchanger. Reverse the supply and discharge connections for the cold flow so that the heat exchanger is now in parallel flow.
4. Repeat the cases in Table 2 following the procedure outlined in Step 2.
5. Repeat “Case 1” using the plate heat exchanger. Test in both parallel and counterflow.
6. Clean up any water spilled during the testing activities, and assist the lab instructor in any
other manner he/she requests.
Documentation Activities
Record model, manufacturer, range and accuracy of all rotameters used. Record model,
manufacturer and accuracy of thermocouple reader. Estimate the accuracy of the type-K
thermocouples
Calculations and Data Presentation
1. Set up an Excel spreadsheet to take the measurements in Table 2 and calculate the
values as shown in Table 3, one table each for parallel and counter flow. Values for ρ
and Cp will be taken from property data for water at the appropriate average temperature. Add any additional rows, if needed, to complete your calculations.
ME 460
5
Heat Exchangers
2. For the tube-in-tube exchanger, compare εmeas (data points) and εpredicted (curve) for
both flow arrangements by plotting the ε’s versus NTU based on UAmeas. Include error bars for εmeas. Use Cmin/Cmax = 1 and 0.5 for the predicted curves.
3. For the plate exchanger and the coiled exchanger, create a table comparing the measured effectiveness and NTU to that of the tube-in-tube exchanger for the same flow
rates.
4. Compare the effectiveness of parallel flow HX and counter flow HX and discuss the
comparison of the experimental values with the predicted values.
5. Compare the effectiveness and NTU of the plate and coiled exchangers with those
from the tube-in-tube exchanger.
Uncertainty Analysis
The dominant sources of uncertainty in εmeas are the inaccuracies in the measurement
of flow rates using the rotameters and the inaccuracies in the temperature measurements using the thermocouples. Combining the equations from the discussion of analysis
𝜀𝑚𝑒𝑎𝑠 =
𝜌𝑐 𝑄𝑐 𝐶𝑝,𝑐 (𝑇𝑐,𝑜 −𝑇𝑐,𝑖 )+𝜌ℎ 𝑄ℎ 𝐶𝑝,ℎ (𝑇ℎ,𝑖 −𝑇ℎ,𝑜 )
(13)
2𝜌𝑚𝑖𝑛 𝑄𝑚𝑖𝑛 𝐶𝑝,𝑚𝑖𝑛 (𝑇ℎ,𝑖 −𝑇𝑐,𝑖 )
For each case, estimate uncertainties for the Q’s and T’s. Don’t just guess; accuracies should
be given in the online catalogs by the manufacturers. Use these estimates to determine and
estimated uncertainty in εmeas. Treat the ρ’s and Cp’s as constants.
The math will be much easier if you treat the above equation as 𝜀𝑚𝑒𝑎𝑠 =
𝑞𝑎𝑣𝑔
𝑞𝑚𝑎𝑥
. You can solve
for the uncertainty in qavg and qmax separately.
References
Hodge, B. K., and Taylor, R. P., 1999, Analysis and Design of Energy Systems, 3rd ed, Prentice-Hall,
Upper Saddle River, N.J.
ME 460
6
Heat Exchangers
Appendix—Charts and formulae for effectiveness NTU
Counter Flow
A
x
i
s
T
i
t
l
e
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Parallel Flow
A
x
i
s
Cmin/Cmax =1
Cmin/Cmax
=0.5
0
1
2
3
4
5
T
i
t
l
e
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Cmin/Cmax =1
Cmin/Cmax
=0.5
0
1
2
3
4
5
NTU
NTU
Figure A-1. Chart for determination of heat exchanger effectiveness,
Equations for parallel and counter flow HX’s can be found in Hodge and Taylor (1999). For
parallel flow,
𝜀=
𝐶
1−exp[−𝑁𝑇𝑈(1+ 𝑚𝑖𝑛 )]
𝐶
1+ 𝑚𝑖𝑛
𝐶𝑚𝑎𝑥
𝐶𝑚𝑎𝑥
(A-1)
For counter flow,
𝜀=
𝐶
1−exp[−𝑁𝑇𝑈∗(1− 𝑚𝑖𝑛 )]
𝐶𝑚𝑎𝑥
𝐶𝑚𝑖𝑛
𝐶
1−
exp[−𝑁𝑇𝑈∗(1− 𝑚𝑖𝑛 )]
𝐶𝑚𝑎𝑥
𝐶𝑚𝑎𝑥
(A-2)
When Cmin/Cmax = 1 Equation A-2 is indeterminate as 0/0. In that case, l’Hopital’s rule from
calculus must be used to evaluate the limiting formula as Cmin/Cmax approaches 1. The result
is
𝑁𝑇𝑈
𝜀 = 𝑁𝑇𝑈+1
ME 460
7
(A-3)
Heat Exchangers
ME 360/460 Formal Lab Grading Rubric (Writing Grade)
In evaluating the writing quality for the formal labs submitted in ME 360/460, grades will be
assigned based on the following criteria.
Correct grammar, tense, spelling, etc., are all critical to good writing. Compiled from previous
semesters of 360/460 lab reports, the following list represents the most common mistakes
students typically make—and thus the types of mistakes that will be assessed.
Critical common mistakes:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Comma-splices and run-on sentences
Sentence fragments
Capitalization errors
APA formatting issues
Misuse of commas, semi-colons, and colons
Spelling
Subject-verb agreement
Not following tense requirements for specific sections
Formatting of units of measure
Any single manifestation of mistakes 1-9 will result in a two-point deduction, with a maximum
of four points within that particular category. After finding two occurrences of a mistake, the
grader will stop looking for this specific variety. Thus, a maximum overall deduction of 36
points is possible within these nine common mistakes.
Beyond these types of mistakes, which are easy to evaluate, the overall quality of writing will be
evaluated subjectively. What your writing sounds like matters a great deal, and your ability to
construct sentences and entire paragraphs that flow well and effectively convey the message is
critical.
The writing grader will deduct up to 15 points in assessing your overall writing quality. A
deduction of 0 points indicates an overall high quality of writing, a 5-point deduction indicates
general competency with only minor lapses, a 10-point deduction indicates overall deficiency,
and a 15-point deduction indicates clear lack of effort or proofreading.
Summary:
Up to 36 points of deduction for common editing/proofreading/presentation mistakes.
Up to 15 points deduction for overall writing quality.
Please review the attached “What to Keep in Mind” document for further details and reference
you can review regarding the common mistakes and subjective evaluation.
What to Keep in Mind
Lab Reports for ME 360/460
1. In formal writing, avoid comma-splices (use of a comma to join two independent
clauses) and run-on sentences (two independent clauses joined without punctuation) at
all costs.
○ comma-splice example: “Jillian left for Tennessee, she won’t be back until
Friday.”
○ example of a run-on sentence: “We haven’t eaten yet we’re getting dinner later.”
2. Sentence fragments aren’t acceptable in lab reports. Use complete sentences.
○ This is a sentence fragment: “Leaving campus at 9 PM.”
○ Here’s another: “Which is why I can’t meet you there.”
○ And another: “Because my car broke down.”
3. Capitalization mistakes are very common in 360/460 lab reports. Consult the rules.
Don’t capitalize words to indicate emphasis or particularity. In the sentences forming the
body of your report, for example, terms such as “operational amplifier” and the “second
law of thermodynamics” call for lowercase letters.
4. Formatting: I’ll show no mercy here. Adhere strictly to the APA template provided for
your lab reports (including citations).
5. Misuse of commas, semi-colons, and colons: Review the accepted conventions. Make
an appointment at the UA Writing Center if you need help navigating the many rules.
6. Spelling mistakes: When you’re drafting a document on a computer, there’s no excuse
for making spelling mistakes. Misspellings will make you appear slovenly and
uneducated.
7. Subject-verb agreement: Singular subjects take singular verbs; plural subjects take
plural verbs.
8. Follow the tense requirements for each section to a T.
9. Units of measure: Insert a space between numbers and any associated units of measure.
Refer here for more information.
10. Rhythm: What your writing sounds like matters a great deal. Modulate the lengths and
structures of your sentences.
○ Here’s an example of excellent writing by Nicola Twilley:
“Just over a billion years ago, many millions of galaxies from here, a pair of black
holes collided. They had been circling each other for aeons in a sort of mating
dance, gathering pace with each orbit, hurtling closer and closer. By the time they
were a few hundred miles apart, they were whipping around at nearly the speed of
light, releasing great shudders of gravitational energy. Space and time became
distorted, like water at a rolling boil. In the fraction of a second that it took for the
black holes to finally merge, they radiated a hundred times more energy than all
the stars in the universe combined. They formed a new black hole, sixty-two
times as heavy as our sun and almost as wide across as the state of Maine. As it
smoothed itself out, assuming the shape of a slightly flattened sphere, a few last
quivers of energy escaped. Then space and time became silent again.”
○ The following writing isn’t atrocious, but it’s far from good. Notice the monotony
of its rhythm—the sentences are all long and of similar lengths. And be precise
when choosing your words. Avoid the lack of specificity (“the theoretical
formula,” “decrease significantly,” “very similar to the experimental ones”)
exhibited here.
“Sinusoidal input signals of different frequencies were applied to an electrical
low-pass filter. At frequencies below the break frequency the input and output
signals had the same amplitude. As the input frequency was increased above the
break frequency, the output signal amplitude began to decrease significantly. The
theoretical formula that predicts the magnitude response gave results very similar
to the experimental ones. This experiment was successful in demonstrating the
validity of the theoretical formula for a first-order, low-pass filter constructed
from a single resistor and capacitor. Therefore, the objectives of the lab were
met.”
○ This passage is plain awful:
“Op amps are used to amplify a signal so that it can be more easily measured.
Ideally electronic amplifiers have no offset voltage so they should be perfectly
accurate when amplifying a signal. However real operational amplifiers have an
offset voltage that can change the measured voltage in a circuit. This offset
voltage must either be accounted for or preferably removed using the circuits
described in the later sections of the lab. Using one operational amplifier to
provide the gain necessary for the experiment and a potentiometer along with
resistors can help to remove this offset voltage. Potentiometers are adjustable
instruments that can be used to measure electromotive force by balancing it
against the potential difference by passing it through a circuit of known
resistance. Using these with a voltage follower and summing amplifier allows for
the removal of the offset voltage using a complex circuit that will be constructed
in this lab.”
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