Department of Chemical
Engineering
Ch.E. 333.2
Laboratory Manual
W2011_T2
Course Outline
I.
PURPOSE OF THIS COURSE
This course is intended to develop skills, which will be of use to you as a practicing
chemical engineer. You will be expected to use typical items of equipment and to conduct
simple measurements and tests. You will be expected to communicate the results in a clear
and effective manner.
II.
ORGANIZATION OF THE COURSE
1. Data Recording*
Each student in the course must have a hard-cover laboratory notebook. Experimental
investigations will be conducted in groups of two or three students. One student from
each group will be designated to be responsible for planning the investigation (this
task is described more fully below). All students are responsible for:
a) Visits to the laboratory to view the apparatus and discussions with the instructors.
b) Producing a notebook record of what was done in the laboratory. This will be
signed by the Demonstrator, who will certify that all students were present.
c) Experimental observations both quantitatively and qualitatively.
d) Preparation of a suitable apparatus diagram.
e) Sample calculations, showing how the data were used. If a technical memo is to be
submitted then the sample calculations must be in the log book.
f) Preparation of graphs and/or tables showing the salient conclusions from the
experiment as clearly as possible.
g) Preparation of formal, brief or technical report.
*refer to section VI for rules for laboratory notebooks.
2. Planning.
The designated student leader is responsible for planning the experiment and for
ensuring that sufficient data of an appropriate quality are obtained. This will require
background reading, visits to the laboratory to view the apparatus and discussion with
the instructors. All partners will be assessed for their contribution to the experiment by
the Demonstrator.
3. Reporting.
1
Each student is required to hand in one full formal report, one brief formal report and
two technical memos. When one partner submits a formal report, the other partner
must submit a technical memo. Reports and memos are due two weeks from the
completion of the experiment, unless a time extension has been granted. Student will
get 7 “free” late hand–in days for the whole course. Indicate on your report when you
use it. Reports and tech memo‟s are to be handed in to Dale Claude in Room 1D43
(office inside 1D25), and marks will be deducted for tardiness (read EVALUATION
below).
III. EXPERIMENTS
1.
2.
3.
4.
5.
6.
Ion Exchange in Water Softening
Viscosity
Centrifugal Pump
Fluid Metering
Expansion Processes in a Perfect Gas
Heat Exchange: Double Pipe, water-water
Visit http://www.engr.usask.ca/classes/CHE/333/ to download LABORATORY MANUAL.
Only 4 experiments will be performed.
IV. GUIDES FOR PREPARING REPORTS
Full Formal Reports:
All formal reports must be done on a word processor. The following sections of the report
should be included:
1. Title: Course number
Name of the experiment
Students participating (group members present)
Date of Experiment
Due Date
2.
3.
4.
5.
(The template file for the title page of formal, brief and technical reports can be
downloaded under the heading of Title Pages at
http://www.engr.usask.ca/classes/CHE/333/)
Abstract: This is written after the Discussion has been completed. It may be prepared
with a word processor and pasted into the notebook. It is intended to be read by
persons who will not read the rest of the report.
Table of Content: Give titles of sections with their page numbers. This should include
the Appendix with titles of each section of the Appendix.
Introduction. This is a brief statement of the purpose of the experiment. It serves as an
introduction to the rest of the report.
Theory. A brief summary, giving the equations to be used, is required.
2
6. Apparatus and Procedure. The apparatus diagram can be prepared with a drawing
program or drawn by hand. Chemical Engineering symbols for the unit operations
should be used wherever possible so that a proper Process Flow diagram (PFD) is
prepared. The procedure should record what was done. It must not be written as
instructions.
7. Presentation and Discussion of Results: In this section, indicate where the data and
results are presented. Any significant observations should be reported here and what
effect that had on the outcome of the experiment. Data and result are probably
presented most effectively in tabular form in an Appendix. Graphs can be presented in
this section or in an Appendix. Your results should then be fully discussed in this
section. All conclusions and recommendations must be defended. Error analyses may
or may not be useful in this regard. Figures or Graphs can be included in the body
(insert as the page following the first mention of the graph in the body of the report) of
the report or presented in an Appendix. If there are several graphs that are similar, a
representative graph can be included in the body of the report.
8. Conclusions: Give your conclusions in numbered statements, each one concise and
precise. No discussion is given here. All conclusions must be fully discussed and
supported in the Discussion Section.
9. Nomenclature: List all symbols used in alphabetical order. Greek symbols should be
kept in a separate list.
10. Recommendations: A similar format to that of the Conclusions should be followed
here.
11. Reference: A list of references must be included here. Use a standard format (list in
alphabetical order and in the body of the report refer to the last name of the first author
followed by the year of publication in brackets).
12. Appendix: Identify them by A, B, C … and in the following order: data, results,
sample calculation. All tables and Figures should have headings (e.g., Table B1, Figure
A1, etc.) and full titles. In your sample calculation, indicate the run number used and
which table(s) the information can be found.
13. Constrain the length of the formal report within 20 pages.
Brief Technical Reports:
A brief technical report should include the following: title page, summary, results and
discussion, conclusions, data, results and sample calculation. It is equivalent to the formal
report but with the abstract replaced by a summary and the absence of the introduction,
theory/literature review, and materials and methods sections. The summary should include:
a brief introduction stating the nature and purpose of the investigation, a brief explanation of
the procedures used and a summary of the important results. The data, results, samples
calculations and any derived theoretical equations, etc., should be put in an Appendix (A, B,
C, etc.) A no-more-than 15 pages of brief technical report is sufficient.
Technical Memos:
A technical memo is a brief memorandum to the supervisor. It should state concisely the
experimental conditions, results, discussion, conclusions and recommendations. A brief
3
table of results or a graph should be included to support the conclusions. Limit your
technical memo within a 2-page length.
V. EVALUATION
Careful measurements, correct calculations, logical deductions and clear conclusions are
necessary to a good report. However, even if all these are present but the report is not well
written, some of the positive effects of the investigation will be lost. Although proper
spelling, grammar and general use of the English language are somewhat less important than
clarity, conciseness and technical contents, they will also have an effect on the marking.
Both formal reports, brief technical reports and technical memos will be marked out of 10
grade points. However, for the final mark, each formal report will be worth 35 marks, the
brief technical report, 25, and the technical memo, 10 marks. The lab demonstrator will be
reviewing your performance and your lab notebook while you are in the lab and will assign a
mark (out of 5) at the end of each lab period. A summary of the marking scheme is given
Table 1 below.
Reports and technical memos must be completed and submitted within two weeks i.e. while
the experiment is still fresh in the student's mind. Therefore, the deadline for receiving
reports and technical memos without any penalty will be two weeks after the experiment was
performed. A penalty of 10% per week will be deducted from late reports or memos.
Submissions will not be accepted after the last day of classes and will be given a mark of
zero. Visit http://www.engr.usask.ca/classes/CHE/333/; click on Class Info; scroll down to
Grading Sheets; choose an appropriate marking sheet to view what will be evaluated in the
submitted report and memo.
Table 1. Distribution of Marks
Item
Full Report
Brief Tech Report
Technical Memo
Lab Performance
& Notebook
Total Mark
Number Individual
Mark
1
35
1
25
2
10
4
5
Final
Mark
35
25
20
20
Penalty (10%)
3.5
2.5
1.0
100
VI. RULES FOR LABORATORY NOTEBOOKS
1.
2.
3.
4.
Use a hard-covered and numbered record book (purchase from University Bookstore)
Label research ideas/proposal to differentiate them from experiments that are performed
Explain all abbreviations or terms that you use that are not universally known
Make all entries in ink
4
5. Do not erase any entry. Instead draw a line neatly through the error and then initial and date
the
correction in the margin
6. Record data and observations when they are made. Date each entry
7. Stick to the facts (positive and negative). Your notebook is not the place for your opinion
8. Leave no blank space between entries. Cancel all blank spaces (including blank pages) with
diagonal lines drawn across the space. Initial and date the cancellation in the margin
9. Have each page of your notebook witnesses by someone who is not an inventor but who
understands the experiment and its objectives (ask your Lab Demonstrator as the witness)
10. Make no changes or insertions on a page after it has been signed and witnessed
11. Attach support records to the notebook where practical. If not practical, then, cross-reference
the notebook with the material and witness as above
12. Maintain safe custody of your notebook
5
Sample of evaluation sheets
6
ChE 333 – FORMAL REPORT GRADE SHEET
Student: _____________________ Experiment: __________________
Date Due: ___/___/___ Date Rec‟d: ___/___/___ Late Penalty: _____%
REPORT SECTION
Title Page
CLARITY OF
PRESENTATION
Max. Mark
TECHNICAL
CONTENT
Max. Mark
2
Abstract
3
Table of Contents
Nomenclature
Introduction
Theory
Apparatus
Procedure
Pres. & Disc. Results
6
3
Conclusions
Recommendations
References
8
10
6
20
3
10
3
6
2
Appendices
Experimental Data
Calculated Results
Sample Calculation
6
4
4
4
Totals
36
64
Report Mark = (Total Mark) * 0.35 = ____________ (MAX = 35)
* GRADE POINT (G.P.) DESCRIPTOR *
10
9.5
Exceptional Excellent
8-9
Very
Good
7 – 7.5
Good
6 - 6.5
Satisfactory
7
5 – 5.5
Passable
0 – 4.5
Fail
ChE 333 – BRIEF REPORT GRADE SHEET
Student: _________________________________________
Experiment: _________________________________________
Due Date: ___/___/___ Date Rec‟d: ___/___/___ Late Penalty: ____%
REPORT
SECTION
CLARITY OF
PRESENTATION
Max.
Mark
TECHNICAL
CONTENT
Max.
Mark
Title Page
2
Summary
5
15
Pres. & Disc. Results
10
20
Conclusions
5
10
Recommendations
5
10
Reference
2
Appendices
6
Experimental Data
5
Sample Calculation
5
Totals
35
65
Report Mark = (Total Mark) / 4 = ____________ (MAX = 25)
* GRADE POINT (G.P.) DESCRIPTOR *
10
9.5
Exceptional Excellent
8-9
Very
Good
7 – 7.5
Good
6 - 6.5
Satisfactory
SEE OTHER SIDE FOR COMMENTS
8
5 – 5.5
Passable
0 – 4.5
Fail
ChE 333 – TECH MEMO GRADE SHEET
Student: ______________________________________
Experiment: ______________________________________
Date Performed: ___/___/___
Due Date: ___/___/___ Date Rec‟d: ___/___/___ Free Late Days: ___
Late Penalty: ___ %
MAX
PRESENTATION
Title page……………………………...
5
Purpose clearly stated…………………
5
Experimental conditions & constants
clearly stated…………………………..
5
Apparatus, procedure, conclusions, &
recommendations content…………......
15
READABILITY
Spelling & grammar…………………..
10
Sentence & paragraph structure/ clarity
10
Logical sequence & cohesiveness of
writing…………………………………
10
TECHNICAL CONTENT (RESULTS)
Presentation & correctness……………
20
Discussion & interpretation…………...
20
Total
100
9
MARK
EXPERIMENTS
1. Ion Exchange In Water Softening
Objective: Determine the exchange capacity of a cationic resin in water softening.
Introduction:
Water softening is a process to reduce hardness in water and prevent the
build-up of lime scale and calcium deposits in pipes and equipment. Hardness is normally
measured by the amount of calcium and magnesium that is present in water and is reported as the
concentration of CaCO3. To get an idea of scale, the Saskatoon Water Treatment and Meters
Branch reports the potable water has an average hardness of 126 mg/L as CaCO3. The river
water has an average hardness of 176 mg/L. 120 mg/L as CaCO3 or greater is considered hard.
Ion exchange is an important technique to reduce hardness in water. It is the reversible
interchange of ions between a solid (ion exchange material) and a liquid. The ions in solution
become attached to the solid and the displaced ions will be forced into solution. The process of
exchange continues until both ions reach equilibrium on the surface and in solution. This
process is dynamic and can be reversible depending on the relative concentrations of the ions in
solution.
Ion exchange has been used on an industrial basis since 1910 with the introduction of water
softening. Cation exchange is widely used to soften water. The most usual ion exchange material
employed in water softening is a sulphonated styrene-based resin, supplied by the makers in the
sodium form. In the process, calcium and magnesium ions in water are exchanged for sodium
ions on the resins. Ferrous iron and other metals such as manganese and aluminum, sometimes
present in small quantities, are also exchanged
Figure 1. Ion Exchange Columns
(Picture courtesy to www.stockinterview.com/News/)
10
after calcium and magnesium are removed, but are unimportant in the softening process.
Removal of the hardness, or scale-forming calcium and magnesium ions, produces “soft water”.
Softening can be carried out as a batch process by stirring a suspension of the ion exchange resin
in the water for a period until equilibrium, or an acceptable level of hardness, is reached.
However, it is more convenient to operate a continuous flow process by passing the water
downwards through a column of resin beads.
Theory: The exchange reaction for water softening with a sulphonated styrene-based resin in the
form of sodium can be described below.
2Na+R- + Ca2+(aq)↔Ca2+R-2+ 2Na+(aq)
(1)
where R represents the resin chain and the exchange point on the beads.
The reaction takes place rapidly enough for the upper layers of the bed to approach exhaustion
before the lower layers being able to exchange ions. There is thus, a zone of active exchange
which moves down the column until the resin at all depths becomes exhausted. The position at
an intermediate stage can be illustrated as shown in Figure 2a. Plotting the hardness readings as
CaCO3 (mg/L) in the effluent against the volume of water treated (L) generates the breakthrough
curve as shown in Fig.2b. The breakthrough point can be determined at which the concentration
of CaCO3 in the effluent reaches an acceptable level of hardness or the hardness of the feed. It is
usually the limit of the exhaustion cycle.
Figure 2a. Ion Exchange Zone
Figure 2b. Idealized Breakthrough Point
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When the resin is exhausted, it can be regenerated with a copious amount of sodium salt such as
sodium chloride. The excess salt will shift the equilibrium (Eq.1) to the left and sodium ions will
replace calcium and be present on the solid.
If the hardness is measured by CaCO3, the ion exchange capacity of the resin can be determined
as follows:
Exchange Capacity
Removed Mass of CaCO 3 (mg)
X0.02 (meq/mg)
Vol of Wet Bed (mL)
(2)
where
Volume of Wet Bed (mL)
πD 2
XFinal Depth of Resin Bed (cm)
4
(3)
where D is the diameter of the column (cm), equal to 1.5 cm in this investigation.
The mass of CaCO3 removed from the tap water up to the breakthrough point can be calculated.
Graphically, this is given by the area in the graph of breakthrough curve between the curve
plotted and the horizontal line, representing the original hardness of the water. The mass of
CaCO3 (mg) can be converted to milliequivalent (meq) by multiplying a factor of 0.02.
(DOWEX, Ion Exchange Resins, Water Conditioning Manual, p.74.) Knowing the wet volume
of the resin bed, the exchange capacity of the resin can be calculated as meq/mL. If other
minerals such as magnesium carbonate, calcium oxide and so on are removed, they can be
converted to the equivalent concentration as CaCO3 by certain conversion factors. The
conversion factors of common substances are given in literature (DOWEX, Ion Exchange
Resins, Water Conditioning Manual, p.75).
Once the exchange capacity of the resin bed is determined, it can be used to design a column
packed with the resins for water softening at large scale. The required resin volume can be
determined in the following equation:
Resin Volume (L)
Feed Hardness (meq/L)X Throughput (L)
X10 3 (L/mL)
Exchange Capacity (meq/mL)
(4)
where the throughput refers to the volume treated per exhausted cycle of resin.
Apparatus: Water softening in this investigation is carried by the Armfield Ion Exchange
Apparatus W9. The sketch is shown below in Figure 3. The system consists of a column packed
with a sulphonated styrene-based resin, a pump to supply liquids to the column, four tanks to
store solutions of HCl, NaCl, test and deionized water and a sump tank. A rotameter is used to
measure the flowrate of the feed. A conductivity meter is used to monitor the concentration of
12
sodium in the effluent. An anion exchange column was set up for the experiment of
demineralization but not used in this investigation.
A Mettler Toledo DL28 automatic titrator with an attached DP5 Phototrode is used for
determination of CaCO3 concentration in the effluent. For this purpose, 100 ml plastic sample
cups are provided.
Figure 3. – Diagram of Ion Exchange Apparatus
13
Materials and Methods:
The hardness of the test water passing through the ion exchange column is determined by
titrating the effluent of the W9 Ion Exchange apparatus with a complexometric reaction.
(Appendix A).
The concentration of sodium ions [Na+] in solution is measured by the conductivity of the
collected effluent.
The required chemicals are:
Ammonia buffer ~pH10
Calcium chloride dihydrate
Sodium chloride
pH 4, 7, & 10 buffer solutions
Disodium ethylenediamine-tetraacetic acid dihydrate (EDTA) solution 0.01 M
Calmagite 1% solution – indicator
Procedure:
A.
B.
Adding Cation Resin to the Column
1.
Drain the column by first placing a waste vessel at valve 10, then opening valves
6 and 10
2.
Remove the cation column by undoing the plastic holders on each end of the
column. The column pulls out towards you and has no catches.
3.
Fill the cation column to ~300 mm of cationic resin (golden-brown colored
granules).
4.
Replace the column and close valves 6 and 10
Regenerate the Cationic Resin
This may already be done for you, check with your TA
Regeneration is required at the beginning of the experiment to ensure that the cation
column has the requisite amount of Na+ ions. You are assuming that the column is
depleted.
For apparatus configuration see Data Sheet I, Figure 1c.
14
C.
1.
Select Tank B, open valves 2 and 12 turn on the main switch.
2.
Add 30 g of salt to a beaker. Add RO water.
3.
Set the flow meter to 20 -50 mL/min and add the salt to the column. Continue
until the conductivity reaches 1.1 x 10-2 Siemens for three minutes or all the salt
has been placed in the column. This means that the column has reached the
saturation point and has an excess of Na+ ions.
3.
Select Tank “D” and flush the column for 5 minutes at 70 ml/min.
4.
Close all valves afterwards.
Fluidizing the Resin Bed
The Resin is pre-regenerated with excess sodium. Backwashing ensures that the
remaining regeneration solution and debris from the last experimental run are washed out
of the column. Plus it expands the resin beads so that no air pockets remain in the resin
bed.
For apparatus configuration see Data Sheet I (Page 9 of this manual), Figure 1b.
1.
Make sure all valves are closed.
2.
Open valves 3 and 6.
3.
Select Tank D and turn on the pump, then backwash the cation column at a flow
rate of 50-70 ml/min for 5 minutes.
Large air bubbles can be gotten rid of by closing valve 6 and opening 12 until the water
has reached the top of the column. Then close 12 and re-open 6. Repeat if necessary.
D.
4.
When the air bubbles have been eliminated and the resin has settled, turn off
valves 3 and 6.
5.
Measure the final depth of the resin.
Softening of Water Sample
For apparatus configuration see Data Sheet I, Figure 1d.
1.
Select Tank C containing the test water.
2.
Open valves 2 and 10.
3.
The TA will provide the appropriate flow rate
15
E.
4.
Collect the initial 2 samples at 300-400 ml intervals, the remainder at 100-400 ml
intervals.
5.
Determine the hardness of each sample as per Appendix “A” and continue testing
each sample until hardness rises above 100 mg/L as CaCO3.
Shutdown
1.
Select Tank “D” and flush the column at max flow for 5 minutes
2.
Turn off the pump, open valve 10 and completely drain the resin column.
3.
Rinse the beakers and equipment with RO water.
Data Analysis:
a) Plot the hardness as CaCO3 concentration (mg/L) against effluent volume (L). Identify the
breakthrough point. Determine the total amount of CaCO3 (mg) removed by the column up to the
breakthrough point.
b) Calculate the exchange capacity (meq/mL).
c) Design a column (area and height) to reduce the hardness of 10,000 L of water to 100 mg/L of
CaCO3. The initial hardness of water is the same as your experimental. Keep the height-todiameter ratio of the wet resin bed the same as that of the resin column used in this experiment.
Provide brief discussion on your design results including the feasibility of using one column and
one exhausted cycle to complete the task.
Hint: you need to first determine the required resin volume for this project. A safety factor
should be applied to the exchange capacity figure to compensate for non-ideal operating
conditions and resin aging on a working plant. Typical safety margin is 5% for cation resins.
Column sizing should be adjusted to allow for resin expansion if backwashing is performed (80–
100% of the settled resin bed height) and resin swelling during service, approximately 5-8% for
strong acid cation resin.
Suggestion: Determine the hardness of the untreated test water at the beginning of the
experiment. (5 ml sample)
16
Data Sheet I – Configuration of Ion Exchange Apparatus
17
Appendix “A”
Complexometric Titration for the Determination of Water Hardness
Titration Procedure
Water Hardness Titration
Disodium Ethylenediamine-tetraacetic acid dihydrate (EDTA or Na2H2Y∙2H2O) forms a
chelated soluble complex when added to a solution of certain metal cations. If a small
amount of dye (Calmagite) is added to a solution containing calcium and magnesium ions
at a pH of 10 ± 1, the solution becomes wine red due to the MgIn- formation. If EDTA is
added as a titrant, the calcium and magnesium will become complexed.
The calcium will be complexed out first as it has a larger formation constant with EDTA
than magnesium. When all of the calcium ions have been complexed with EDTA, the
trace amount of magnesium ions in the buffer will react. Once the trace amount of
magnesium is complexed, the solution will change to a blue. The addition of the trace
amount of magnesium is required for the complexometric titration and eliminates the
need for a blank correction titration.
pH is very important in this experiment as having a higher value than 10.5 will precipitate
out CaCO3 or Mg(OH)2 immediately. However, even at a pH of 10 Ca2+ will precipitate
out eventually. Thus, a maximum of 5 minutes from the addition of the buffer solution
should be observed, to prevent interference from Calcium (III) hydroxide precipitation.
Mettler Toledo DL28 with Phototrode DP5
A Mettler Toledo DL28 auto-titrator is used for the titrations. The main switch is in the
back. The Phototrode DP5 allows for an automatic titration based on a colorimetric
endpoint.
Procedure:
1.
Take 10-25 mL of collected sample then add buffer solution until the pH is 10,
2.
Press F3 to reset the display, if needed. Press “100”, “OK”
3.
The end point is a 24 mV or 50 mL max EDTA
4.
Dispose of all solutions in the waste container provided.
Calculation of Hardness: Ideally, 1 mL EDTA used is equivalent to 1 mg CaCO3 titrated.
Volume of EDTA Added (mL) x Correction Factor x 1000 mL/L
Volume of Water Sample (mL)
18
mg/L CaCO 3 as hardness
The correction factor will be provided by the Lab Demonstrator.
Example 1
If 9.5 mL of EDTA is added to 25 mL of sample and there is a correction factor of 0.909:
9.5 mL x 0.909 x 1000 = 345.4 mg/L CaCO3 as hardness
25 mL
References:
Armfield Instruction Manual. 2000. Ion Exchange Apparatus W9. Issue 14. WO014461.
Dowex, 2007. “Water Condition Manual – A Practical Handbook for Engineers and Chemists”.
Dow Liquid Separations. http://www.reskem.com/pages/resin-pdfs.php.
Bailey, S. J., et al. 2003. “Standard Test Method for Hardness in Water, D1126-02”. Annual
Book of ASTM Standards, Vol 11.01. ASTM International, West Conshohocken, PA. Pg
98-101.
Frason, M. 2005. “2340C EDTA Titrimetric Method.” Standard Methods for the Examination
of Water and Wastewater. 21st Ed. American Public Health Association, Washington
D.C. Pg 2-37 – 2-39.
Harris, D. 2003. “EDTA Determination of Total Water Hardness.” Quantitative Chemical
Analysis. 6th Ed. W.H. Freeman, New York. Pg. 259-267, 272-277.
19
2.
Viscometry
Introduction
This experiment involves the use of a cone and plate viscometer. You will be asked to
characterize a fluid which may or may not be Newtonian. Newtonian fluids should be tested at
different shear rates for a range of temperatures. Non-Newtonian fluids should be tested at a
range of shear rates. Discuss the choice of a fluid with the instructor before planning the
experiment.
Procedures
The viscometers are operated empty at first to find deflections at zero load. The viscometers
must be operated according to the procedures in the literature provided in the laboratory.
Because they are sensitive and expensive instruments, please read the procedures carefully
before operating them. If you are unaware about any procedure, ask the demonstrator before
proceeding. When you are placing the fluid in the viscometer, try to avoid entrapping air
bubbles as these may cause significant errors. Also, before changing fluids in a viscometer,
wash it thoroughly since small amounts of contamination may distort the results. Be careful not
to scratch the surfaces of the measuring elements.
Before testing an unknown fluid, a Newtonian standard fluid should be used to verify instrument
performance.
Data
1. Brookfield Viscometers (springs are linear)
(i) LV, full scale deflection = 673.7 dyne-cm
(ii) RV, full scale deflection = 7187 dyne-cm
(iii) Cone Angle,
= 0.8 degrees
(iv) Cone Radius, r = 2.4 cm
(v) Cone and Plate, sample = 0.5 ml
2. Working equations:
i)
Cone and Plate
20
( dyne / cm 2 )
(sec 1 )
where
3T
2 r3
sin
= shear stress ( dynes/cm2)
= shear rate ( sec -1)
T = torque (dyne-cm)
= angular velocity of the spindle (rad/sec)
= cone angle (degrees)
r = cone radius (cm)
Characterizing a Fluid:
For Newtonian fluids, comment on the effect of temperature upon viscosity by
comparing your results with those predicted by the Eyring theory(4) . For nonNewtonian fluids, select a suitable model and evaluate the coefficients in its equation of
state relating shear stress to shear rate.
For non-Newtonian fluids calculate the pressure drop per meter of pipe in horizontal
flow if the velocity is 1.0 m/s and the pipe diameter is just small enough to ensure
laminar flow (i.e., the flow is not turbulent).
References
1.1 Streeter, V.L., “Handbook of Fluid Dynamics”, Chapter 7. McGraw-Hill Book Company
Inc., 1961.
1.2 Middleman, S., “The Flow of High Polymers”, Interscience Publishers, 1968.
1.3 Cheremisinoff, N.P. and Gupta, R., “Handbook of Fluids in Motion”, Ann Arbor Science,
1983.
1.4 Tabor, D., “Gases, Liquids and Solids”, 2nd Ed., Cambridge Univ. Press, 1979.
21
3.
Centrifugal Pump
Objectives:
a)
To determine the characteristics of a centrifugal pump including total head, power,
efficiency and NPSH versus flowrate.
b)
To determine the size of a geometrically similar pump that would be needed to pump
against a total head of 100 feet of water at peak efficiency using the same RPM.
Introduction:
Centrifugal pumps are the most common type of fluid mover in the chemical industry. A
fundamental understanding of the operation and performance of a centrifugal pump is of primary
importance to any engineering student.
A centrifugal pump converts energy of a prime mover (an electric motor or turbine) first
into velocity or kinetic energy and then into pressure energy of a fluid that is being pumped.
The energy changes occur by virtue of two main parts of the pump, the impeller and the volute
or diffuser. The impeller is the rotating part that converts driver energy into the kinetic energy.
The volute or diffuser is the stationary part that converts the kinetic energy into pressure energy.
All of the forms of energy involved in a liquid flow system are expressed in terms of feet of
liquid i.e. head.
The process liquid enters the suction nozzle and then into the eye (center) of an impeller.
When the impeller rotates, it spins the liquid sitting in the cavities between the vanes outward
and provides centrifugal acceleration. As liquid leaves the eye of the impeller, a low-pressure
area is created causing more liquid to flow toward the inlet. Because the impeller blades are
curved, the fluid is pushed in a tangential and radial direction by the centrifugal force. This
force acting inside the pump is the same one that keeps water inside a bucket that is rotating at
the end of a string.
The key idea is that the energy created by the centrifugal force is kinetic energy. The
amount of energy given to the liquid is proportional to the velocity at the edge or vane tip of the
impeller. The faster the impeller revolves or the bigger the impeller is, then the higher will be
the velocity of the liquid at the vane tip and the greater the energy imparted to the liquid. This
kinetic energy of a liquid coming out of an impeller is harnessed by creating a resistance to the
flow. The first resistance is created by the pump volute (casing) that catches the liquid and
slows it down. In the discharge nozzle, the liquid further decelerates and its velocity is
converted to pressure according to Bernoulli‟s principle.
22
Theory:
If we consider the inlet and discharge of the pump under test as the boundaries of a
control volume then we may apply Bernoulli's Theorem of continuity to the fluid within that
boundary (Armfield, 1980).
The head generated by the machine is:
Machine Head = g ΔH
J/kg
(1)
where ΔH is the pump differential head (m) and g is gravitational acceleration 9.807 m/s2.
Hydraulic power:
The hydraulic power of the pump is the product of machine head and flow, thus hydraulic
Power Nh,
Nh = g•Q• ΔH•ρwater
W
(2)
where Q is the flowrate (m3/s) and ρwater is the density of water kg/ m3
Power Input to Pump:
The dynamometer output power (brake horsepower) No is given by:
No=T*n
W
where, T = dynamometer torque
n = dynamometer rotational speed
(3)
N-m
rad/s
60
nm = n * 2
2
n = nm * 60
RPM
(4)
rad/s
(5)
W
(6)
Substituting in equation (3):
2
No=T * nm* 60
The power absorbed by the pump therefore, is the dynamometer output less transmission losses,
thus:
N p = No- NL
W
23
(7)
NL represents the transmission losses between the pump and the dynamometer motor and is the
power absorbed by bearing friction, air drag, etc. The value of the power loss will vary
between rigs and on the same rig will vary with motor speed.
The efficiency of the pump:
Nh
No
(8)
100 %
Pump Differential Head:
The measurement of pump differential head is effected by means of the two Bourdon
type pressure gauges.
It should be noted that the suction and discharge pipes are of different nominal bores thus
generating a velocity head across the pump which must be accounted for when measuring the
differential head.
The differential head can be calculated:
Ps Vd2
[
g
2g
water
Pd
H
Vs2
] Z
2g
m
(9)
where Ps is the pressure at the inlet of the pump; Pd is the pressure at the outlet of the pump; and
Z is the vertical difference between the inlet and outlet (negligible in this case). Vs is the
velocity at the inlet and Vd is the velocity at discharge (m/s).
From a mass balance:
V2
d
Vs2
Ds4
D4
d
m2 / s2
(10)
m
(11)
(m/s)2
(12)
So,
H
Pd
Ps
water g
Vs2 Ds4
[
1]
2 g Dd4
In the case where:
Suction pipe NB, Ds=2.0"
Discharge pipe NB, Dd=1.5"
Since:
Vs2
Q2
As2
where Q is the flowrate (m3/s) and As is the cross section area of the inlet pipe (m2).
then:
24
Q 2 Ds4
[
2 gAs2 Dd4
Pd
Ps
water g
H
1]
m
(13)
Net Positive Suction Head (NPSH):
The net positive suction head is the equivalent total head of liquid at the inlet of the pump
(suction) (Hs) minus the vapour pressure p.
NPSH
Hs
p
g
(14)
Vs2
2g
(15)
Where:
Hs
Ps
water
g
Pump Discharge
1. The basic method of measuring the pump discharge on the test rig is by means of the
volumetric measuring tank. The discharge is directed into the tank for a known period of time
and the rise in water level during that period noted, then:
Q=
A d
t
m3/s
(16)
where A = area of measuring tank, m2
d = change in water level in tank, m
t = time, s
2. Venturi:
The pump discharge may be measured by means of the perspex venturi tube after the tube
has been calibrated. The venturi is being used in conjunction with a Dwyer Differential Pressure
transmitter.
The venturi demonstrates the principle of Bernoulli's continuity equation, thus flowrate Q
is related to the difference in pressure across the Venturi meter,
w
CA2
2
P
1
water
4
Kg/s
(17)
where A2 is the cross-sectional area of the throat of the Venturi, C is the Venturi coefficient, and
β is the ratio of throat diameter to inside pipe diameter (pump outlet pipe diameter for the case
being studied).
In the case of an actual venturi, small losses occur due to viscous shear and friction effects, thus
reducing the theoretical flow through the device into Equation (17). A calibration curve for a
25
particular venturi tube will therefore show curves of theoretical discharge, predicted by the
equation, and actual discharge determined by volumetric measurement.
Nomenclature:
A
As
D
H
Hatm
Hgs
Hgd
Hs
Hvs
ΔH
L
n
N
p
Q
t
T
V
W
d
w
Suffix:p
o
L
h
s
d
1, 2
Constants:
g
water
area of measuring tank m2.
cross section area of the inlet pipe, m2.
diameter of pipe, m
head, m
the barometer reading, m.
the reading of a gauge at the inlet of the pump, m.
the reading of a gauge at the outlet of the pump, m
the equivalent total head of liquid at the inlet of the pump
(suction), m
the velocity head at the inlet, m.
pump differential head, m.
length of dynamometer torque arm, m.
rotational speed rad/s.
power, w
the vapor pressure, mmHg
flowrate m3 /s
time, s.
torque kg-m
velocity. m/s.
weight applied to torque arm, Kg
change in water level in tank, m
flowrate Kg/s
pump input
dynamometer motor output
dynamometer transmission losses
hydraulic output
inlet (suction)
discharge
differential manometer limbs
Gravitational acceleration = 9.807 m/s2
density of water, 103 kg/ m3
26
Apparatus:
The centrifugal pump used in this experiment is the Armfield R2-00. The pump
is of cast iron construction and is provided with an open impeller. On the pump cover plate
tappings are provided at various radii so that the increase in pressure across the impeller may be
determined. These tappings are brought to a manifold with valves for pressure sampling as
required.
The pump is driven by a trunnion mounted variable speed 1.6 kW DC motor. The pump
set is mounted on a substantial bed plate. The equipment includes a combined
transformer/rectifier and speed controller.
The rig includes the tanks necessary for carrying out performance testing. The main
reservoir is approximately 1.36m x 0.66 m x 0.53 m fabricated in G.R P. and fitted with a drain
valve. On this tank is mounted the volumetric measuring tank which incorporate a level indicator
and scale. A quick acting drain valve is provided together with an emergency overflow. A
manually operated diverter is included so that water discharged by the pump can be returned
either directly to the sump or to the measuring tank as required. To carry out flow measurement
it is necessary for a stop watch to be used. This system allows level measurements to be taken in
still water and, hence, increases the accuracy of flow measurement.
The pump suction pipe is fabricated in PVC with pressure tapping. The pump delivery
pipe work incorporates a gate type throttle valve. Pressure and suction electronic indicators are
supplied complete with small bore pipe work and valves to allow multiple pressure readings.
A perspex Venturi uses pressure transmitters and indicators. This Venturi is modeled on
the requirements of B.S. 1042 Part 1- 1964 having a nominal bore of 1.5" and a throat diameter
of 1.28". The Venturi operates in conjunction with a 25 psi Dwyer differential transmitter and
Omega DP32 indicator. This instrument allows pump flows up to 60 GPM (5 L/sec.) to be
determined, after the instrument has been calibrated.
A 50 psi Differential Pressure
transmitter is also available. This instrument allows the differential heads developed by the
pump up to 30 ft to be determined. Tappings are provided on the pump and the supply includes
all necessary fittings and connecting flexible tube.
Specification:
Inlet pipe diameter
Outlet pipe diameter
Venturi throat diameter
Impeller outside diameter
Blade width
Number of blades
Blade type
Impeller type
Radius of strain gauge
2.0"
1.5"
1.28"
127 mm
11.4 mm
6
Backward curving
Open
1144.2 mm
27
Shaft Speed
Rating
Motor type
Electrical Supply
0 - 3000 RPM
1.6 kW at 2900 RPM.
Variable speed
220V/single phase/50-60 Hz
Relationship between Torque and voltage for strain gauge (when using x 10
amplification):
Torque=1.5861*Volts*g*0.1442
Procedure:
Start up Procedure
a) Be sure suction side and discharge side valves are closed.
b) Turn on Main Power.
c) Turn on priming pump and slightly open discharge valve.
d) Adjust pump speed to approximately 15%.
e) Open suction side valve SLOWLY. Repeat as necessary.
f) Open discharge side valve SLOWLY.
g) Turn the Venturi Drain valve until line is drained of air.
h) Turn the Pressure Guage Drain(s) to Vent until the line is drained of air, and then
turn the valve to the right until suction lines are airless. Then turn valve to Suction so
the line is static.
Shut Down Procedure
a)
b)
c)
d)
Close discharge side valve.
Close suction side valve.
Reduce motor speed to 0 RPM using controller.
Switch motor off.
Experimental Procedure
a) Calibrate the venturi meter by making at least 8 runs from a low flowrate to a high
flowrate. The venturi meter is calibrated using the measuring tank and stopwatch.
b) At 8 or more discharge rates collect the data necessary to characterize the pump
including the pressures across the pump, venturi pressure drop, motor rotating speed
and the Torque Gauge Reading.
28
Report:
1) To determine various characteristics and parameters of a centrifugal pump. These
include graphs of total pump differential head, hydraulic power, brake horse power, efficiency
and Net positive suction power versus discharge flowrates.
2) To determine the size of a geometrically similar pump that would be needed to pump
against a total head of 100 feet of water at peak efficiency using the same RPM. What flowrate
is generated by the big pump at this condition? If energy costs 10.2 cents/kw-hr, how much
does it cost to operate the big pump each year?
References:
Armfield Technical Education Co. Ltd., “Instructional Manual for Centrifugal Pump Test Rig
R2-00”, 1980.
Other references related to this lab:
Perry, R. H., Green, D. W. and Maloney J. O., “Perry‟s Chemical Engineering Handbook”,
McGraw-Hill, 1997.
Sulzer Pump Division, Sulzer Brothers Ltd., “Sulzer centrifugal pump handbook”, Elsevier
Applied Sicence, London and New York, 1989.
Lobanoff, V. S. and Robert, R. R., “Centrifugal Pumps – Design & Application”, Gulf
Publishing Company, Houston, 1985.
Karassik, I. J., “Centrifugal Pump Clinic”, Dekker, New York, 1989.
Brown, G. G., “Unit Operation”, Wiley, New York, 1950.
Coulson, J.M. and Richardson, J. F., „Chemical Engineering” Vol. 1. 3rd Edition, p.133-144,
1977, (TP145C45).
.
29
4.
Fluid Metering
Introduction
In this experiment you will be measuring the flow rate of water which is pumped through a loop,
using a variety of flowmeters as listed below:
1. Magnetic Drive
2. Nutating Disc
3. Coriolis
4. Torsion Paddle
5. 3 Beam Ultrasonic
6. Vortex
7. Altometer (Enviromag)
8. Variable Area (Rotameter)
9. Venturi
10. Orifice
11. Doppler Ultrasonic
12. V-notch Weir
You may use the readings from the Coriolis flow meter as the standard value. Compare the
reading of other flow meters with this value and discuss the observed differences, if any. Using
the values of flow rates obtained by the Coriolis Meter, determine the meter coefficients for the
Orifice and Venturi meters as functions of Reynolds number. These can be compared to the
expected values found in the literature.The Magnetic flowmeter readings should be linear with
flow rate. Evaluate the magnetic flowmeter coefficient for converting EMF to flow rate. The
Ultrasonic meter should also give a linear signal with respect to flow rate. Examine your
readings with the ultrasonic meter to see if such linear relationship can be established.
In your reports review the operating principles of each flow meter, compare their advantages and
disadvantages and comment on the practical applications for each device.
Finally,
consider the following situations and suggest a suitable flowmeter for each case. The factors to
be considered are capital cost (including data processing), operating cost (primarily energy
losses), reliability (whether calibration is required or not).
a)
b)
c)
d)
e)
f)
g)
measuring the flow of water into households
measuring the flow of water in a 5 foot diameter pipe
measuring the flow of heavy crude oil in a 3 inch pipe
measuring the flow of coal-water in a 12 inch pipe
measuring the flow of water into a laboratory reactor
measuring the flow of water in a small creek
measuring the flows of petroleum derivatives in an automated refinery
Some background information is given in References 1, 2, 3.
30
Procedure
Determine the direction the water flows and decide how you will adjust the flow rate. Be sure to
start your measurements at a low flow rate and then increase between readings. Determine
where each meter is located and how to make a measurement for it (discuss this with the TA).
Note that for the Orifice and Venturi meters you have to make pressure measurements and this is
accomplished with a pressure transducer. The transducers will need to have the air removed and
the associated demodulators will have to be zeroed. Confirm this procedure with your TA before
adjustments are made. Make at least eight measurements by first increasing the flow rate and
then reducing it to zero.
Calculations
(1) Orifice or Venturi: The flowrate Q is related to the pressure drop, minimum (throat) area and
density by the equation:
Q
CA
2 P
(1
4
)
where C is the coefficient of discharge.
(2) V-Notch Weir:
Q (0.31h02.5 2g ) / tan
Where ho is the height of the liquid above the bottom of the weir and
the side of the notch and the horizontal.
is the angle between
Data
Diameter of pipe
Diameter of orifice
Diameter of venturi
Angle of weir
=
=
=
=
1.049 in.
0.441 in.
0.33 in.
54o
References
1. N. de Nevers, Fluid Mechanics for Chemical Engineers, 3rd Ed. McGraw Hill (2005).
2. J. O. Wilkes, Fluid Mechanics for Chemical Engineers, 2nd Ed. Prentice Hall (2006).
3. Y. A. Cengel, J.M. Cimbala, Fluid Mechanics: Fundamentals and Applications.
McGraw Hill (2006).
31
5.
Expansion Processes of a Perfect Gas
Introduction
The concept of an ideal gas (perfect gas) is introduced early in the study of thermodynamics
because it plays a crucial role in understanding the simplest relationships between pressure,
volume, temperature and other thermodynamic properties. By using these relationships, and
informed by the First Law of Thermodynamics, process path calculations can give heat and work
requirements. As covered in CHE 223 and CHE 323, a very important ratio for calculating these
heat and work requirements is the ratio of
.
Many gases that exist near room temperature and atmospheric pressure exhibit near ideal gas
behavior. Air is one of these gases. This experiment, although simple in concept, will allow you
to utilize your knowledge of ideal gas behavior to determine the important ratio
for
air. Through this experiment you will see first-hand the effects of rapid expansion on pressure,
temperature and volume, and you should be able to demonstrate your understanding of
equilibrium, data collection, uncertainty analysis, and reporting.
Overview
The Armfield TH5 apparatus consists of a base with two rigid acrylic tanks connected by valves
and tappings. Tank One is the Pressurized vessel and Tank Two is the Vacuum vessel. Each
tank has a piezo-resistive sensor and a miniature semiconductor thermistor bead to capture
pressure and temperature.
32
Figure 1 - Screen Capture
The piezo-resistive effect describes the changing resistivity of a semiconductor due to applied
mechanical stress. The piezo-resistive effect differs from the piezoelectric effect. In contrast to
the piezoelectric effect, the piezo-resistive effect only causes a change in electrical resistance; it
does not produce an electric potential.
The miniature semiconductor thermistor bead is a thermistor that exhibits a highly non-linear and
negative characteristic (resistance falls with increasing temperature). The extremely small size of
the thermistor bead and connecting leads means that the thermal capacity of the sensor is small.
Therefore the first-order time constant is extremely small and the response time is fast when the
air temperature rapidly changes. The response of the thermistor can never be as fast as the
pressure sensor because of the small size but it is sufficiently fast enough to indicate the
temperature changes in the exercises.
Experiment A: Determination of Heat Capacity Ratio
Warning: May want to use earplugs for this part of the experiment
Objective
This experiment is a modern version of the original experiment attributed to Clement and
Desormes (or Shoemaker).
33
The heat capacity ratio γ = Cp/Cv can be determined for air near standard temperature and
pressure. The demonstration gives students experience with the properties of an ideal gas,
adiabatic processes, and the first law of thermodynamics. It also illustrates how P-V-T are used
to measure other thermodynamic properties.
Method
The experiment involves a two-step process. The pressurized vessel is depressurized very
quickly by opening a large bore valve. The gas expands from Ps to Pi which is assumed to be
adiabatic and reversible (P/T(γ-1/γ) is constant).
The volume of gas is then allowed to return to thermal equilibrium attaining the final pressure Pf
thus becoming a constant volume process. (P/T is constant).
Theory
For a perfect gas,
Cp = Cv + R
Where
Cp = molar heat capacity at constant pressure, and
Cv = molar heat capacity at constant volume.
For a real gas a relationship may be defined between the heat capacities, which is dependent on
the equation of state, although it is more complex than that for a perfect gas. The heat capacity
ratio may be determined experimentally.
Equipment Set Up
Ensure that software is running and make sure both vessels are at atmospheric pressure. Data
collection should be set for automatic and milliseconds for this exercise
The USB data collection unit has a minimum setting of 10 milliseconds which is sufficient
for this exercise. The automatic setting makes sure that the pressure drop is recorded but
there are a lot of data points to export to Excel.
Procedure
Close all valves.
34
Start the data logger.
Open the proper valve and pressurize the large vessel to 20 – 60 kNm-2. Close valve.
Wait until the pressure stabilizes.
Open large bore valve, that vents to atmosphere, in a snap action.
Allow pressure to re-stabilize.
Repeat with different pressures and perhaps vacuum.
Results
Record your results under the following headings:
Atmospheric pressure (absolute)
Patm
N/m2
Starting pressure (measured)
P1s
N/m2
Starting pressure (absolute)
P1abss
N/m2 (= Patm+ Ps)
Intermediate pressure (measured)
Pi
N/m2
Intermediate pressure (absolute)
P1absi
N/m2 (= Pi + Patm)
Final pressure (measured)
Pf
N/m2
Final pressure (absolute)
P1absf
N/m2 (= Patm+ Pf)
For each step response calculate the heat capacity ratio γ (Cp/Cv) for air as follows:
Observe the transient changes in the air resistance and temperature following each step change
(note the increasing resistance to the thermistor means decreasing temperature).
Conclusions
Why can the initial expansion process be considered adiabatic?
35
How well does the result obtained compare to the expected result? Give possible reasons for any
difference.
Comment on any difference in transient responses of the pressure and temperature sensors.
Nomenclature of the TH5: Expansion Process of a Perfect Gas
Name
Measured
pressure in large
vessel
Measured
vacuum in small
vessel
Measured
resistance in
large vessel
Measured
resistance in
small vessel
Volume of large
vessel
Volume of small
vessel
Temperature in
large vessel
Temperature in
small vessel
Barometric
Pressure
Absolute
pressure in large
vessel
Absolute
pressure in small
vessel
Subscript
Subscript
Subscript
Symbol Unit
Type
P
N/m2
Recorded
V
N/m2
Recorded
T(R)1
Ohms
Ω
Recorded
Definition
Instantaneous pressure (gauge) inside
large vessel. Sign convention: +ve
when above atmospheric pressure
Instantaneous pressure (gauge) inside
small vessel. Sign convention: +ve
when below atmospheric pressure
Instantaneous temperature of thermistor
sensor inside large vessel
T(R)1
Ohms
Ω
Recorded
Instantaneous temperature of thermistor
sensor inside small vessel
Vol1
m3
Given
Vol2
m3
Given
T1
°C
Calculated
T2
°C
Calculated
Patm
N/m2
Measured
P1abs
N/m2
Calculated
P2abs
N/m2
Calculated
s
i
f
36
Nominal value = 0.0224 m3
Nominal value = 0.0091 m3
Derived from resistance T(R)1 using
Data Sheet 3
Derived from resistance T(R)2 using
Data Sheet 3
Barometer on center pillar
Applied pressure relative to the
pressure of total vacuum
=P + Patm
Applied pressure relative to the
pressure of total vacuum
=Patm - V
Denotes start condition
Denotes intermediate condition
Denotes final condition
Data Sheet 1: Relative and Absolute Pressure
In any experiment the measurement of a physical property is compared against a fixed precise
reference point. In the TH5 experiment, the obvious fixed reference point is the ambient
pressure of laboratory. The pressure are scaled
Gauge
Pressure 1
(+ve)
P1
Gauge
Pressure 2
(-ve)
P2
Absolute
Pressure 2
Barometric
Pressure
Absolute
Pressure 1
Pressure
Atmospheric Reference
0
Data Sheet 2: Technical Data
Nominal height of large and small vessels
0.590 m
Nominal cross-sectional area of large vessel
0.037 m2
Nominal cross-sectional area of small vessel
0.0154 m2
Approximate volume of large vessel
0.0224 m3
Approximate volume of small vessel
0.0091 m3
37
6.
HEAT EXCHANGE – Double Pipe (W/W)
Purpose
To determine the heat transfer rates and coefficients for a
exchanger
Double Pipe - (water-water) heat
Each evaluation should consist of a check on the enthalpy balance and a comparison of
experimental and literature values of heat transfer coefficients. Some discussion of pressure drop
may also be appropriate.
Reading
Fairly extensive (but not very difficult) reading will be necessary before you do the experiment
so that you will be able to do a good job and understand what is involved. Read (if you have not
already done so) the following sections in the book by Incropera et al.: 1.2.2, 6.1, 7.1, 8.5, 11.1,
11.2, 11.3.
Background
Cross-flow heat exchangers involve fairly complex flow patterns. Of course the flow pattern
affects the rate of heat transfer. A common approach is to calculate transfer coefficients from
empirical correlations, combine resistances in series at steady state, calculate a logarithmic mean
T for counter-current flow, find a correction factor for the complex flow pattern, and to
combine factors to give the heat transfer rate. This is the LMTD-correction factor method.
The equations for the counter-flow heat exchanger are 11.14, 11.15 and 11.17 with Fig. 11.8.
The mean T for the complex flow pattern is given by:
Tm = F( T)lm,CF
where F is given by Figures 11.10 to 11.13. The subscript lm indicates logarithmic mean and CF
denotes a hypothetical counterflow exchanger.
Theory
Generally speaking, three types of heat transfer mechanisms are thought to exist:
Conduction - occurs by molecular transport in the presence of a temperature gradient
Convection - occurs by molecular or bulk motion of a fluid in the presence of a
temperature gradient
38
Radiation -
occurs by energy transmission from matter in the presence of a
temperature difference.
In these experiments, students will be investigating primarily convective heat transfer
mechanisms. This mechanism is the most commonly found in the chemical industry.
The object of the experiments will be to measure the overall resistance to heat transfer at
different operating conditions and compare these measurements to those predicted by equations
in the literature.
When a fluid flows over a surface which is at a different temperature than the fluid, then the
local heat transfer flux is:
dq
dA
hx Ts
Where q
A
hx
TS
TF
TF
=
=
=
=
=
heat transfer rate
surface area
local heat transfer coefficient
surface temperature
fluid temperature
Because the flow conditions may change with position, the local heat transfer coefficient is not
constant in the above process. Also, as the fluid and/or solid changes temperature, TS – TF will
not be constant. Thus the precise determination of the overall heat transfer rate would require an
integration of the form:
OUT
q
OUT
dq
hx TS
IN
TF dA
IN
Because this would be a difficult (if not impossible) equation to solve for practical heat
exchanger situations, engineers have simplified it to an algebraic equation.
q = h A T1m
… where T1m = log mean temperature difference
h
= individual heat transfer coefficient
The individual heat transfer coefficient is not a constant but depends on velocity and
temperatures. Ranges of h can be found in Bennett & Myers (Table 21-1). The log mean
temperature difference between the surface and fluid is computed by an equation of the type:
TB1IN
TB2OUT
TSI
TS2
39
TS1
T1m
TB1IN
ln TS1
TB1IN
TS 2
TS 2
TB2OUT
TB1OUT
In real heat exchange processes, heat is often transferred from one fluid to another through a
solid medium. Often this solid medium is corroded or contains a layer of solid deposits. Thus
the heat transfer rate is now given by an equation of the form:
q = Uo Ao T1m
And:
Uo
Ao
Ai hi
where: Uo
hi
hdi
kw
xw
ho
hdo
Ao
AI
A1m
=
=
=
=
=
=
=
=
=
=
Ao
Ai hdi
1
Ao x w
A1m k w
1
ho
1
hdo
overall heat transfer coefficient
inside fluid heat transfer coefficient
inside fouling heat transfer coefficient
thermal conductivity of wall
thickness of wall
outside fluid heat transfer coefficient
outside fouling heat transfer coefficient
outside heat transfer area
inside heat transfer area
log mean heat transfer area
Empirical equations exist for hI and ho and depend on dimensionless parameters such as
Reynolds number and Prandtl number. Correlations can be found in the references listed at the
end of this preamble.
In this case, the evaluation of the log mean temperature difference depends on the direction of
flow of the fluids. For countercurrent flow it is given by:
TB1, OUT
TB1, IN
TB2, IN
TB2, OUT
40
T1m
TB 2, IN
TB1, OUT
ln
TB 2, IN
TB 2, OUT
TB 2, OUT
TB1, IN
TB1, OUT
TB1, IN
Finally, we have another complication for real heat exchangers. If the fluids are not in parallel
flow but there is some cross-flow or combination of concurrent flow and countercurrent flow,
(multipass heat exchangers) then a correction factor must be put in the above equation:
q = UoAY T1m
Where Y = correction factor
Y values are dependent on the type of heat exchanger and temperature driving forces. They are
available in graphs in the references listed at the end of this preamble.
In your heat exchange experiments, you measure the temperatures of the fluids, and their flow
rates. The heat transfer rate can then be calculated by:
q2 = MCP2 (TB2, IN - TB2, OUT)
where M = mass flowrate of fluid 2
CP2 = heat capacity of fluid 2
Procedures
1. The flow rates of the fluids can be controlled by adjustment of appropriate valves.
2. Sufficient time must be allowed for the system to come to steady state before measurements
are made. In your report, indicate how you knew that steady state has been achieved. How
much time was required?
3. Measurements are made of temperatures using thermistors and flow rates using calibrated
meters.
4. Several different operating conditions (flow rates, etc.) should be studied in order to obtain as
much information as possible to characterize the system. Discuss choice of operating
conditions with your demonstrator.
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5. Heat transfer rates, heat transfer coefficients, pressure losses and energy losses should all be
evaluated if possible and compared to values and/or trends reported in the literature.
6. When heat balances are of interest, be sure that the temperature differences for the streams
can be determined reasonably accurately.
Report: In your write-up, report the heat transfer rates and coefficients for the exchanger that
you studied and discuss the problem of scaling up your heat exchanger to allow for a one
hundred fold increase in flowrate of the cold fluid but still maintain the same temperature rise.
References:
1. Bennett, C.O. and J.E. Myers, “Momentum, Heat, and Mass Transfer”, McGraw Hill Book
Co., 1982.
2. Incropera, F.P. and D.P. Dewitt, “Fundamentals of Heat Transfer”, John Wiley & Sons,
1981.
3. Perry, R.H., “Perry‟s Chemical Engineers‟ Handbook, McGraw-Hill Book Co., 1985.
Equipment Data
Tube 1: OT Cu – IT Cu
Tube 2: OT Cu – IT Cu
Tube 3: OT Cu – IT SS
Tube 4: OT Cu – IT Cu
Tube 5: OT Cu – IT Cu
Tube 6: Air – not used
OT: 1” Cu Pipe, OD = 1.134”
ID = 0.994”
IT: ½” Cu Pipe, OD = 0.63”
ID = 0.534”
IT: ½” SS Pipe, OD = 0.63”
ID = 0.546”
IT: ¾” Cu Pipe, OD = 0.881”
ID = 0.772”
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