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MECHANICAL ENGINEERING DEPARTMENT. ME 4621 - Thermal Science Laboratory. Semester II 2006-2007. LABORATORY MANUAL & NOTES. January  ...
LOUISIANA STATE UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT ME 4621 - Thermal Science Laboratory Semester II 2006-2007

LABORATORY MANUAL & NOTES January 2006

Dr. Dimitris E. NIKITOPOULOS

ME4621: Semester II 2006-2007

2 TABLE OF CONTENTS

TABLE OF CONTENTS ............................................................................................................................................2 COURSE STAFF.........................................................................................................................................................3 SUPERVISOR ...............................................................................................................................................................3 LABORATORY INSTRUCTORS ......................................................................................................................................3 TECHNICAL STAFF .....................................................................................................................................................3 LABORATORY MEETING TIMES AND LOCATION ........................................................................................4 COURSE CONTENT AND PURPOSE.....................................................................................................................4 TEXT BOOKS .............................................................................................................................................................4 COURSE WORK-LOAD............................................................................................................................................4 COURSE STRUCTURE.............................................................................................................................................4 GRADING SYSTEM ..................................................................................................................................................5 COURSE WEB-PAGE................................................................................................................................................6 STRUCTURE OF EXPERIMENTAL SESSIONS...................................................................................................6 PART I: PLANNING (FIRST WEEK OF THE EXPERIMENT).............................................................................................6 PART II: EXECUTION AND REPORTING (SECOND WEEK OF THE EXPERIMENT)...........................................................7 THE REPORTS...........................................................................................................................................................9 LABORATORY SESSIONS' SCHEDULE.............................................................................................................11 EXPERIMENT #1 .....................................................................................................................................................12 EXPERIMENT #2 .....................................................................................................................................................20 EXPERIMENT #3 .....................................................................................................................................................22 EXPERIMENT #4 .....................................................................................................................................................41 EXPERIMENT #5 .....................................................................................................................................................44 EXPERIMENT #6 .....................................................................................................................................................47 APPENDIX I..............................................................................................................................................................50 LABORATORY PLANNING FORM ..............................................................................................................50 APPENDIX II ............................................................................................................................................................53 FULL-FORMAT GROUP REPORT (1100 POINTS TOTAL) .........................................................................53 BRIEF FORMAT INDIVIDUAL REPORT ....................................................................................................55 TITLE PAGE EXAMPLE ..................................................................................................................................56 APPENDIX III...........................................................................................................................................................57 SAMPLE PLANNING FORM...........................................................................................................................57 APPENDIX IV ...........................................................................................................................................................59 EXAMPLE FIGURE ...........................................................................................................................................59 APPENDIX V.............................................................................................................................................................60 LABORATORY REPORT COVER PAGE.....................................................................................................60

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COURSE STAFF

Supervisor Name: Office: Office Hours: Office Phone: Home Phone: e-mail:

Dimitris E. NIKITOPOULOS CEBA 1419E Tuesdays, 15:30-17:30 & Thursdays, 15:30-17:30 578 - 5903 925 - 3115 (emergencies only) [email protected]

Name: Office: Office Hours: Office Phone: Cell Phone: e-mail:

Jin ZHANG CEBA 2208B Wednesdays, 13:30-15:30 N/A 266-1831 [email protected]

Name: Office: Office Hours: Office Phone: Home Phone: e-mail:

Raghu MUTUKULLA CEBA 2201 Fridays, 13:30-15:30 578-5796

Name: Office: Office Phone:

Glenn EHRETT CEBA 1212A 578 - 6471 [email protected]

Laboratory Instructors Section 1 Section 2

Section 3

[email protected]

Section 4

Technical Staff

e-mail:

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LABORATORY MEETING TIMES AND LOCATION Section 1: Section 2: Section 2: Section 3: Section 5:

07:40 - 10:30 10:40 - 13:30 13:40 - 16:30 16:40 - 19:30 19:40 - 22:30

Mondays Mondays Mondays Mondays Mondays

Room: CEBA 1216 Room: CEBA 1216 Room: CEBA 1216 Room: CEBA 1216 Room: CEBA 1216

COURSE CONTENT AND PURPOSE The course is intended to provide the student with a laboratory experience in the areas of fluid mechanics and heat transfer. This includes usage of standard instrumentation, both manual and computer assisted data acquisition, observation of physical phenomena and reporting of results in a professional manner. The students are trained in designing and executing experimental procedures by utilizing existing resources for the achievement of specific experimental goals. The available instrumentation is used to acquire data necessary for an adequate interpretation of the physical nature of various flows. During the course of the semester, six laboratory experiments will be performed - three in heat transfer and three in fluid mechanics. The objectives of these experiments are provided along with relevant theory, but the experimental methods and the instrumentation to be used are determined by the students. TEXT BOOKS R. W. Fox and A. T. McDonald, Introduction to Fluid Mechanics, Fifth Edition, John Wiley & Sons Inc., 1998, ISBN 0-471-12464-8, TA357.F69 1998 M. C. Potter and D. C. Wiggert: Mechanics of Fluids, Third Edition, Brooks/Cole, 2001. ISBN 0534-37996-6; TA357.P725 2001 F. P., Incropera, and D. P., DeWitt, Introduction to Heat Transfer, Third Edition, John Wiley & Sons Inc., 1996, ISBN 0-471-30458-1, QC320.I46 1996 COURSE WORK-LOAD During this course you will perform six experiments (three in Heat Transfer and three in Fluid Mechanics) with specified experimental objectives. Each section will be divided into groups of three or four students. You will be called to submit written reports on all of these experiments. Namely, you will submit a Full-Format Group Report and a Brief-Format Individual Report for each experiment. At the end of the semester there will be a Final Examination.

COURSE STRUCTURE During the course, You will participate in two types of sessions; namely Experimental and Demonstration. Experimental sessions involve the design/planning and performance of an experiment followed by a laboratory report, and carry the most weight in this course. Demonstration sessions involve simple pre-setup experiments or viewing of films illustrating fundamental fluid mechanics and heat transfer phenomena. Each section has typically 10-12 students separated into 3-4 groups at most. You will carry out the majority of the laboratory work together with your fellow group members and you will report your findings through written group and individual reports, as described earlier. Although you will

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work in a group, your personal performance will be taken under account from your group member evaluations and specified contributions in the experimental and reporting process.

List of Experiments Exp.

Experiment Title

1

Lift and Drag properties of NACA 0015 Airfoil

2

Free Convection from Horizontal and Vertical Surfaces

3

Unsteady Compressible Flow: Shock Wave Propagation in Shock Tube

4

Pump Characteristics

5

Double Pipe (Concentric) Heat Exchanger

6

Unsteady Multi-Dimensional Conduction Experiment

GRADING SYSTEM Your final letter grade will be determined on the basis of your performance in all components of the course. The weighing will be as follows. Each Experiment: Individual Report Group Report Subtotal for all experiments

100 Points 10 Points 90 Points 600 Points

Final Examination

100 Points

Total

700 points

Grading Scale: A (90-100); B (80-89); C (70-79); D (60-69); F (Below 60) The grading of the GROUP AND INDIVIDUAL reports will be based on two major components: a.

Language and Form (10% of report grade): This part of the grade includes spelling, grammar, expression of ideas and conformity with required report format. Grading on expression will necessarily be subjective. However, grading in the other areas will be objective (e.g., a two-point deduction for each misspelled word).

b.

Technical Content (90% of report grade): This part of the grade will be determined by evaluation of your awareness of physical principals involved, historical perspective of the test, experimental equipment and procedures, interpretation and presentation of results and the appropriateness of the conclusions and recommendations which are presented.

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Each group is responsible for its own work and should not collaborate with other groups. Each group member must do his own individual report writing and should not collaborate with others. In the case of Group Reports each person will be graded separately for his/her specified contribution (see task assignment TABLE 1). The tasks of each group member will be clearly specified beforehand. This grade will represent 70% of the individual grade for that report. The other 30% of the individual grade for the report is based on the overall laboratory report grade. THIS MEANS THAT EACH MEMBER OF THE GROUP SHOULD REVIEW THE FINAL REPORT BEFORE IT IS SUBMITTED, TO ENSURE THAT THE OVERALL REPORT IS OF HIGH QUALITY. COURSE WEB-PAGE The course web-page can be reached by doing the following: • On your favorite web browser type the URL: http://me.lsu.edu/~meniki/me4621/me4621.html and you are in. What is available on the web-page? • All official documents associated with the course; e.g. the present document. • Lab schedule • Description of the experiments • Reporting requirements and guidelines • Task assignments for the group reports • Sample (example) forms filled out according to requirements • Student Performance Record (your grades per assignment, quiz, etc.)

STRUCTURE OF EXPERIMENTAL SESSIONS Each experiment will be carried out during two consecutive class sessions covering two main parts; each part involves two or three types of activity.

Part I: Planning (First Week of the Experiment) A full three-hour session will be devoted to this type of activity. 1.

Technical briefing of students by the Instructor During the technical briefing, you will review the experimental objectives and the basic background information regarding the experiment provided in the Manual. The instructor will briefly go through the fundamental physical and mathematical concepts pertinent to the experimental objectives and discuss principles of operation of available instruments.

2.

Design and planning of the experiment by the students Before you begin you will receive from the instructor a parametric data sheet that indicates the basic parameters for the experiment. The results you obtain during the experiment will be assessed on the basis of these parameters. If you fail to use the parameters the instructors provide, you will fail the experiment. Given the information,

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the instrumentation and the other available experimental facilities, you will have to design and plan the experimental procedure. First, select the instrumentation and identify the appropriate reduction procedure of the collected data in order to satisfy the required experimental objectives. Secondly, make some preliminary measurements to get familiar with the instrumentation. This will give you a feel for the measured quantities and also provide you the awareness regarding the possible problems that may arise during the experiment. Thirdly, you will have to do an uncertainty analysis on all quantities that you anticipate to calculating from your raw measurements. You will be expected to run the experiment, evaluate the results, and write the report with minimal instructor support. 3.

Video presentations of thermal-fluid phenomena (Demo sessions) On occasion a 20-minute video movie will be shown regarding some interesting fluid mechanics or heat transfer phenomena. The instructor will provide some explanations during the video.

At the end of the planning part of the session you will have to submit to the instructor a concise yet brief description of your planned course of action. To that effect, and for convenience, you will be asked to fill out a standard Planning Form, which you may find in Appendix I. You should fill out this form in a manner that will allow a future reader, who has not been briefed on the experimental objectives and methods, to assemble and execute the experiment successfully and achieve the experimental objectives. An example of a completed planning form can be found in Appendix III. The instructor will initial this form to certify that the planning has been completed during the regular meeting of the class. The instructor will point out procedural errors and make you aware of possible pitfalls. This will not mean that your experimental plan and methods are foolproof. You will have the chance to find that out during the second part of the experimental session.

Part II: Execution and Reporting (Second Week of the Experiment) 1.

Setting up of experiment and data acquisition You will assemble and connect all components and instruments necessary for the performance of the experiment and acquire the data according to your experimental plan outlined on the Planning Form. You will record the acquired data manually by completing a standard Raw Data Sheet, which will be given to you by the instructor, or electronically when applicable. The instructor will make sure that the experiment is performed in a safe and orderly fashion. If you run into problems during the experiment or have doubts about the integrity of your data you may consult with the instructor without expecting him/her to tell you what to do.

2.

Data reduction and reporting Upon finishing the data acquisition process you will restore all lab equipment to their original state and withdraw to a place designated by the lab instructor. Then you will proceed to the reduction of the experimental data according to your reduction plan outlined on the Planning Form. To that effect you may use your calculators, one of the several computers available in the Thermal Sciences Laboratory, or the CAD lab computers.

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If your experimental data do not seem reasonable enough you will consult with the instructor, identify your error and decide whether you need to repeat any of the measurements. If there is no sufficient time left, you may petition to the supervisor of the course to repeat part of the experiment at another time. The supervisor will usually not grant such petitions unless there is good reason to believe that the group's performance was compromised by faulty equipment or other extenuating factors. Any remaining time will be devoted to the preliminary preparation of a written laboratory report according to the general guidelines provided. The Raw Data Sheet must be signed by all group members and initialized by the instructor before leaving the lab. The group member signatures certify that the data taken by the group during the laboratory session are those required for the experiment. The instructor's initials merely indicate that the data were presented by the group as complete and accurate. Order and Safety of Laboratory The order and cleanliness of the laboratory are very important to the department. At the conclusion of the laboratory period, everything must be left in the same condition and order in which it was found. This means that all instruments will be put in their proper storage locations, all equipment must be cleaned and secured, all chairs must be returned to their places and aligned and all trash must be thrown away. The students are expected to conduct themselves in a professional and responsible manner. Permission from the instructor must be asked before anyone leaves the room. Although it is not required by law, the presence of the students during the lab meeting sessions is deemed to be necessary. Absence without a valid and properly documented reason will be noted and will affect negatively the final grading decisions. No eating and/or drinking is allowed in the laboratory. Safety is also very important. For this reason: All safety regulations are to be observed. Personnel will wear safety glasses or goggles during all tests. Personnel will wear ear protection when necessary. Personnel will report equipment malfunctions and observed safety hazards to the instructor immediately. Absolutely no horseplay or other frivolous activity will be tolerated in the laboratory.

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THE REPORTS All lab reports are to be typewritten with double-spaced text except for the ABSTRACT, which will be single-spaced. Equations may be hand lettered in black ink. Computer generated text tables and graphs are required. To that effect you may use the Thermal Science Laboratory or CAD lab computers equipped with word processing, graphics, spread-sheet software and/or FORTRAN. You will have to submit two types of reports: Full-Format Group Report and Brief-Format Individual Report. The Brief-Format Individual Report, describing the experiment in your own words, is due the Friday of the week during which the experiment was performed. This individual report can be two pages indicating the introduction, background, and experimental procedure. Make it as brief as possible. Also, include in your individual report, an assessment of your fellow group members' contributions to the experiment using a scale of 1 to 10. A rank of 10 indicates that the group member was most beneficial to the success of the effort. Instructions regarding the Brief-Format Individual Report can be found at the end of Appendix II. The Full-Format Group Report is due at the beginning of the second week of the next experiment. That means you have two weeks to submit your group report. Instructions regarding the Full-Format Group Report can be found in Appendix II. Full-Format Group Reports will be prepared by the group as a whole. In order to evaluate the personal contribution of each group member the following task assignment should be adhered to depending on group size. TABLE 1: GROUP MEMBER RESPONSIBILITY Tasks\# of Students in Group

2-Student

3-Student

4-Student

COORDINATION

1

1

1

1. Cover Page

1

1

1

2. Title Page

1

1

1

3. Introduction

1

1

1

4. Theory

2

2

3

5. Apparatus and Instrumentation

1

2

2

6. Exp. Procedure

1

2

2

7. Uncertainty Analysis

1

2

2

8. Raw Data Reduction & Result Presentatation

2

3

4

9. Analysis and Discussion of Results

2

1

3

10. Conclusions and Recommendations

1

1

4

11. References

1

1

3

12. Appendices

2

3

4

The numbers listed under the group-size column are Task Numbers and will be assigned to every group member and for every experiment by the course supervisor.

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Graphical and tabular work is the responsibility of the individual who refers to that work in his section of the report. As mentioned previously, details of the required report formats can be found in Appendix II. THESE FORMATS MUST BE FOLLOWED EXACTLY otherwise there will be loss of credit.

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LABORATORY SESSIONS' SCHEDULE Experiment # 1 2 3 4 5 6 Date 01-23 01-30 02-06 02-10 02-13 02-20 02-20 02-24 03-06 03-13 03-13 03-17 03-20 03-27 03-27 03-30 04-03 04-07 04-17 04-17 04-21 04-24 04-24 05-01

Experiment Title Lift and Drag properties of NACA 0015 Airfoil Free Convection from Horizontal and Vertical Surfaces Unsteady Compressible Flow: Shock Wave Propagation in Shock Tube Pump Characteristics Double Pipe (Concentric) Heat Exchanger Unsteady Multi-Dimensional Conduction Experiment

Activity Introduction Planning Execution Indiv. Rep. Due Planning Group Rep. Due Execution Indiv. Rep. Due Planning Execution Group Rep. Due Indiv. Rep. Due Planning Execution Group Rep. Due Indiv. Rep. Due Planning and Execution Indiv. Rep. Due Group Rep. Due Planning and Execution Indiv. Rep. Due Group Rep. Due Group Rep. Due

Exp. #1

Exp. #2

Exp. #3

Group 1 Group 1 Group 1 Group 2 Group 1 Group 2 Group 2 Group 3 Group 3 Group 2 Group 3 Group 4 Group 4 Group 3 Group 4 Bye

Group 2 Group 2 Group 2 Group 1 Group 2 Group 1 Group 1 Group 4 Group 4 Group 1 Group 4 Group 3 Group 3 Group 4 Group 3 Bye

Exp. #4 All Groups Group 3 Bye Group 3 Bye Group 3 Group 4 Bye Group 3 Group 4 Bye Group 4 Group 2 Bye Group 2 Bye Group 4 Group 2 Group 1 Bye Group 1 Bye Group 2 Group 1 Bye Groups 1&3*

Group 4 Bye

Group 3 Bye

Group 1 Bye

Exp. #5

Exp. #6

Group 4 Group 4 Group 4 Group 3 Group 4 Group 3 Group 3 Group 1 Group 1 Group 3 Group 1 Group 2 Group 2 Group 1 Group 2 Bye

Bye Bye

Groups 1&3 Groups 2&4*

Groups 2&4 Groups 1&3 Final Exam - All Groups Groups 2&4

* Execution of the experiment will be performed concurrently

Bye Bye Bye Bye

Bye Bye

Groups 2&4* Groups 2&4

Group 2 Bye

Groups 1&3* Groups 1&3 Groups 2&4 Groups 1&3

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EXPERIMENT #1 To:

All Groups

Subject:

Lift and Drag properties of NACA 0015 Airfoil

Prepared by:

D. E. Nikitopoulos

Experimental objectives 1.

Experimentally determine the lift force per unit width of the provided NACA 0015 airfoil as well as the lift coefficient.

2.

Experimentally determine the pressure induced drag force per unit width of the NACA 0015 airfoil and the relevant drag coefficient.

3.

Compare your results with theory and comment on their validity.

These tasks should be carried out for different angles of attack, α, and different Reynolds numbers, Rec, based on the chord-length of the airfoil. Consequently, each group must carry out these tasks according to the requirements given by the instructor at the beginning of the class. Report Type: Full Format Group Report. Keywords The following keywords should give you a hint on what to consider while planning your experiment. Momentum Balance Pressure Distribution Drag Lift Available Equipment Subsonic Wind Tunnel NACA 0015 Airfoil Model with pressure taps Electronic Manometer Multi-tube manometer Pitot-static probes Hot-Film probes Hot-Film Bridge and accessories Three degree of freedom traversing system Digital Multimeter with power supply Thermometers Barometer

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Useful Information and Definitions Pressure Coefficient It is traditional to present the pressure distribution on the surface of a body which is immersed into a flowing fluid by introducing a dimensionless quantity called the Pressure Coefficient. That is: Cp

Pressure Coefficient

=

(P − P0 ) 1 ρV02 2

where P Po Vo

Static Pressure on body surface Static Pressure in free stream Free-Stream Velocity

Lift and Drag The total force exerted on a body immersed in a flowing fluid, by the fluid itself is traditionally broken into two components. Namely: L

Lift Force acting in the direction perpendicular to the free-stream fluid motion

D

Drag Force acting in the direction of the free-stream fluid motion

and

The Drag itself can be broken into two components: Pressure Drag and Friction Drag. Form Drag is due to the pressure distribution on the surface of the body alone and it is influenced greatly by the geometry (shape) of the body. Friction Drag owes its existence to the viscous shear stresses on the surface of the body (skin friction) and in most cases is very much weaker than the Pressure Drag. The Friction Drag is the dominant one only when the Reynolds number of the flow around the body is very small (Re = O(1) ). Lift and Drag forces are conveniently presented in the form of dimensionless coefficients: Cl

Cd

Lift Coefficient

=

Drag Coefficient

=

L 1 ρV02 A 2 D 1 ρV02 A 2

where ρ A

Density of Fluid Frontal Area of the body seen by the flow (area of body projection on a plane perpendicular to the free-stream flow direction)

The Drag Coefficient can be split into a Pressure Drag Coefficient, Cdp, and a Friction Drag Coefficient, Cdf. Their definitions are directly analogous to that of the Drag Coefficient.

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For additional general information you should read Part B of Chapter 9 from reference [1] or Chapter 8 of reference [5]. Lift and Drag Coefficients for Wing Sections The Lift and Drag coefficients are presented somewhat differently for wing sections. They are defined with respect to Lift and Drag forces per unit width of the wing. Namely: Cl

Lift Coefficient of wing section

L

Lift Force per unit width of the wing

Cd

Drag Coefficient of wing section

D

Drag Force per unit width of the wing

c

Airfoil Chord.

=

=

L 1 ρV02c 2 D 1 ρV02c 2

with,

The Airfoil Chord is the straight line connecting the foremost point of the airfoil facing the flow (Leading Edge), and the rear end-point of the airfoil (Trailing Edge). Some other important airfoil related terms are: t Rt α

Airfoil Maximum Thickness Leading Edge Radius Angle of Attack. This is the angle formed between the Airfoil Chord and the velocity vector of the incident fluid-flow.

Rec

Reynolds Number

=

ρV0c µ

In the case of subsonic flow both Lift and Drag coefficients are functions of the angle of attack and the Reynolds number. For a given Reynolds number the Lift Coefficient increases as the angle of attack increases until a special value of the angle of attack, αs, is reached. For angles of attack greater than αs (stall angle) the Lift Coefficient decreases and the airfoil is said to be "Stalled". Stalling is a result of separation of the boundary layer on the upper surface of the wing section. For information on the phenomenon of boundary layer separation you are referred to Chapter 8 of reference [5] or Chapters 2 and 9(Part A) of reference [1], while Stalling is discussed in Chapter 9 of the latter source. Theoretical Pressure Coefficient Calculation When the immersed body is a symmetrical airfoil the Pressure Coefficient can be calculated theoretically for a specific Lift Coefficient, Cl, by using the following formula:

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2 ⎡ ⎡ v δv δv ⎤ ⎤ a Cp (theoretical) = ⎢1 − ⎢ ± ± .C1 ⎥ ⎥ ⎢⎣ ⎣V0 V0 V0 ⎦ ⎥⎦

Where:

v V0

δv V0

is the local, dimensionless velocity over the surface of the airfoil (wing section) corresponding to conditions rendering a lift force equal to zero. *

δva V0

is the local, dimensionless velocity increment over the surface of the airfoil (wing section) associated with camber. is the local, dimensionless velocity increment over the surface of the airfoil (wing section) associated with the angle of attack

*

This term is zero for symmetrical airfoils.

Additional useful information can be found in reference [4]. The NACA 0015 Airfoil This simple airfoil is a symmetrical one (no camber) therefore the angle of attack corresponding to a zero Lift Force (L=0) is α=0°. In Table I you are given the basic thickness form of this airfoil in both analytical and tabular forms. Table I also includes the information necessary for the calculation of theoretical Pressure Coefficients. Table II provides the locations of the pressure taps existing on the surface of the NACA 0015 airfoil model that is available in our laboratory (see also Figure 1 for a graphical representation). Table II also includes the calculated distribution of the Pressure Coefficient for α=0°, and the distribution of Cp for an angle of attack corresponding to a Lift Coefficient, Cl, equal to unity. The result for the latter case is shown graphically in Figure 2. The actual Lift Coefficient for this airfoil is given as a function of angle of attack by the following formula: Cl = 0.097×α, where α is in degrees. The maximum Lift Coefficient is obtained at αs = 15.4° (stall angle) and is equal to 1.66. References Fox, R. W., and McDonald, A. T., Introduction to Fluid Mechanics, 3d Edition, J. Wiley, 1985. Goldstein, R. J., Fluid Mechanics Measurements, Hemisphere Pub. Co., 1983. Rae, W. H. Jr, and Pope, A., Low-Speed Wind Tunnel Testing, 2nd Edition, J. Wiley, 1984. Abbott, I. H., and Von Doenhoff, A. E., Theory of Wing Sections, Dover Pubs., New York, 1959. 5. M. C. Potter and D. C. Wiggert: Mechanics of Fluids, 3d Edition, Brooks/Cole, 2001. ISBN 0534-37996-6; TA357.P725 2001

1. 2. 3. 4.

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TABLE I Basic NACA 0015 Thickness Form Subsonic Symmetrical Airfoil X (% of c) Y (% of c) v/Vo (v/Vo)2 δva/Vo 0.00 0.0000 0.000 0.0000 1.600 0.50 1.5266 0.739 0.5461 1.312 1.25 2.3674 0.966 0.9332 1.112 2.50 3.2684 1.112 1.2365 0.900 5.00 4.4434 1.204 1.4496 0.675 7.50 5.2499 1.224 1.4982 0.557 10 5.8535 1.233 1.5203 0.479 15 6.6815 1.233 1.5203 0.381 20 7.1719 1.229 1.5104 0.320 25 7.4266 1.218 1.4835 0.274 30 7.5022 1.204 1.4496 0.239 40 7.2538 1.170 1.3689 0.185 50 6.6175 1.131 1.2792 0.146 60 5.7042 1.098 1.2056 0.115 70 4.5799 1.064 1.1321 0.090 80 3.2789 1.024 1.0486 0.065 y = ±t / 200000(29690 x + x(−1260 + x(−35.16 + x(0.2843 − 0.001015 x)))) Leading Edge Radius (in %c): Rt=0.011019t2

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TABLE II NACA 0015 Subsonic Symmetrical Airfoil Basic Thickness Form X (%c) 0.00 0.18 0.50 1.25 2.40 2.50 5.00 5.61 7.50 9.62 10.00 15.00 20.00 20.03 25.00 30.00 30.45 40.00 40.87 50.00 51.28 60.00 61.70 70.00 72.12 80.00 82.53 90.00 95.00 100.0

Y (%c) 0.0000 0.9276 1.5266 2.3674 3.2080 3.2684 4.4434 4.6647 5.2499 5.7717 5.8535 6.6815 7.1719 7.1741 7.4266 7.5022 7.5015 7.2538 7.2118 6.6175 6.5143 5.7042 5.5267 4.5799 4.3182 3.2789 2.9233 1.8096 1.0082 0.1575

Max. Thickness (t) in % of c L. E. Radius (Rt) in % of c Cp Cp (α for Cl=1.) (α = 0o) Upper Lower Upper/Lower 1.000000 -1.56 -1.560 -3.207 -3.318

0.672 0.979

15 2.47927 P-taps (model) Y (%c) 0.0000

0.453879 0.066844 3.2080

-3.048 -2.531

0.955 0.72

-0.236544 -0.449616 4.6647

-2.172

0.555

-0.498176 5.7717

-1.931 -1.605 -1.399

0.431 0.274 0.174

-0.520289 -0.520289 -0.510441 7.1741

-1.226 -1.082

0.109 0.069

-0.483524 -0.449616 7.5015

-0.836

0.03

-0.3689 7.2118

-0.631

0.03

-0.279161 6.5143

-0.471

0.034

-0.205604 5.5267

-0.332

0.051

-0.132096 4.3182

-0.186

0.08

-0.048576

-0.026 0.076 1.000

0.133 0.177 1.000

0.055216 0.127644 1.000000

2.9233

y = ±t / 200000(29690 x + x(−1260 + x(−35.16 + x(0.2843 − 0.001015 x)))) Leading Edge Radius (in %c): Rt=0.011019t2 NACA 0015: Thickness, Pressure Coefficient and laboratory model Pressure-Tap locations.

16 14 12 10 8 6 4 2 0 -2 -4 -6 -8 -10 -12 -14 -16

0

20

30

40

x/c %

50

60

70

80

90

Pressure Taps

Figure 1: Thickness and Pressure Tap Location of NACA 0015 Airfoil Model.

10

Thickness Form and Pressure Taps NACA 0015, c=3.9 in.

100

ME4621: Semester II 2006-2007 18

y/c %

Cp (Pressure Coefficient)

0

10

20

30

40

x/c %

50

60

70

80

90

Top Surface Bottom Surface

Figure 2: Pressure Distribution for NACA 0015 Airfoil (Theoretical)

-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

NACA 0015 Pressure Coefficient Angle of Attack rendering Cl=1.

100

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EXPERIMENT #2 To:

All Groups

Subject:

Free Convection from Horizontal and Vertical Surfaces

Prepared by:

S. V. Ekkad

Experimental objectives Natural or free convection is caused by density variations, resulting from temperature distributions due to heat transfer, that are acted on by local gravitational and centrifugal forces. Velocities are usually small since the forces are usually small. In this experiment, you will be required to determine the natural convective heat transfer coefficient for both horizontal and vertical heated plane surfaces and to compare your results with parametric correlations. You will use the experimental setup that includes an aluminum plate that can be heated and placed in either a horizontal (heated surface up) or a vertical position. The plate is also instrumented with thermocouples mounted at the center and at the edge of the plate. The plate should be heated to a particular high temperature and then the heating should be shut off and the plate moved to the position you wish to make measurements for. Keywords Natural convection Heat transfer coefficient Heat flux Temperature gradient Available Equipment Hot Plate Thermocouples Heater Enclosure Temperature Measurement System Reading Assignment Read all of Chapter 9 / Sections 9.1, 9.2, 9.3, 9.4 and 9.6 from Chapter 12 of reference [1]. Useful Information and Definitions The heated plate is cooled by natural convection in a transient mode. The plate thermal characteristics will depend on the orientation of the plate. Two orientations are to be tested: horizontal and vertical.

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A thermal balance of the cooling plate (both horizontal and vertical) can be written as follows:

ρVc

∂ Ts = ht As (Ts − T∞ ) ∂t

where ρ, V, c = density, volume, and specific heat of the plate Ts, T∞, As = the plate and ambient temperatures and plate surface area ht = total heat transfer coefficient The total heat transfer coefficient combines both the convective (h) and radiative(hr) part. It is defined as

ht = h + hr where

(

)

h r = σε Ts2 + T∞2 (Ts + T∞ ) where σ and ε are the Boltzmann's constant and emissivity of the surface. Standard correlations are available in Ref. [1] regarding the empirical values for the orientations tested. The experimental values should be compared to the values obtained from the standard correlations. Define the Grashof number for the conditions observed in the experiment ( GrL =

gβ (Ts − T∞ )L3

υ

2

). The characteristic length is given as L ≡

As . P

Procedure 1. Turn on the computer, connect the thermocouples to the A/D unit and set up the software to monitor the thermocouples. 2. Place the propane burner underneath the hot plate with the Aluminum side facing downward. 3. Connect the burner line to the cylinder using the quick connector. 4. Turn the propane regulator to allow for fuel flow into the burner. 5. Light the burner by placing the lighter at all the orifices. 6. Monitor the thermocouples till the plate is heated to about 250 F. 7. Turn the propane flow off and remove the heater from underneath the hot plate. (Make sure you are always wearing gloves) 8. Disconnect the burner and placing it outside the cabinet. 9. Now turn the plate to the right orientation and then initiate the computer to take transient cooling data. Take data for about 1500 seconds. 10. Repeat steps 1-9 for the next orientation. References [1] Incropera, F. P, and DeWitt, D. P., Introduction to Heat Transfer, 3rd Ed., Wiley & Sons, New York.

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EXPERIMENT #3 To:

All Groups

Subject: Unsteady Compressible Flow: Compression (Shock) Wave Propagating in Shock Tube. Prepared by:

D. E. Nikitopoulos

Experimental objectives The study of moving shock waves is an important aspect of compressible fluid flow. The shock tube is an apparatus in which shock waves of specified strength can be generated and forced to propagate down the length of the tube. In this experiment you will conduct a shock study. You are required to set up a shock tube experiment in which a known initial pressure ratio is established across the diaphragm of the tube. Based on this initial condition you can calculate all the theoretical shock tube states and shock wave properties. You will use the shock tube and the available instrumentation to gather experimental data for two distinct values of the pressure ratio. You will collect several samples for the same pressure ratio. Each group must set a different pressure ratio in the tube. Everybody will use all the data collected by all groups in preparing a final report. The data of all groups will be posted by the Instructors of the laboratory. You have the choice of running the experiment with the low pressure end of the shock tube (this is the longest part of the tube bearing the pressure transducers) either closed or open. If you decide to make any runs with an open-ended shock tube make sure to wear ear protection and stay clear of the open end of the tube. The noise generated by the shock wave "blowing out" of the open end may damage your hearing. Keywords Unsteady, One-Dimensional, Compressible Flow Compression Wave Expansion or Rarefaction wave Isentropic Flow Speed of sound Mach Number Shock Wave Shock Tube Available Equipment Shock Tube High Response Pressure Transducers Charge Amplifiers. Pressure and Vacuum Gages of Bourdon-Tube type Oscilloscope with Memory Computer Interface and A/D Converter Data Acquisition Software High-Pressure Air Supply Vacuum Pump

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Reading Assignment Read all of Chapter 11 and Sections 12.1, 12.2, 12.3 and 12.6 from Chapter 12 of reference [1] or Chapter 9 of reference [4], depending on which one was your fluid mechanics test book. When reading, ignore all references to the Rayleigh and Fanno lines, and concentrate on the normal shock theory. A more comprehensive presentation of the subjects can be found in references [2] and [3]. Useful Information and Definitions Formulas for Isentropic Flow of an Ideal Gas The following relations have been derived from the basic conservation equations (Mass, Momentum, Energy) formulated for steady, one-dimensional, compressible flow, the Ideal Gas equation and the isentropic process relation (see [1]/[4] and [3].)

a = kRT p ⎡ k −1 2 ⎤ M ⎥ = 1+ p0 ⎢⎣ 2 ⎦ T ⎡ k −1 2 ⎤ M ⎥ = 1+ T0 ⎢⎣ 2 ⎦

k / (1− k )

−1

ρ ⎡ k −1 2⎤ M ⎥ = 1+ ρ 0 ⎢⎣ 2 ⎦

1 / (1− k )

⎡ k −1 2 ⎤ M ⎥ 1+ A ⎢ 2 =⎢ ⎥ A* ⎢ 1+ k −1 ⎥ 2 ⎣ ⎦ m = A

( k +1) / 2 (1− k )

k p0 ⎡ k −1 2 ⎤ M ⎢1 + M ⎥ R T0 ⎣ 2 ⎦

( k +1) / 2 (1− k )

Tabulated values of some isentropic, compressible flow variables can be found in Table I. Normal Shock Formulas The following relations have been derived from the basic conservation equations (Mass, Momentum, Energy) and the Second Law of Thermodynamics formulated for the steady, one-dimensional, compressible flow across the shock, and the Ideal Gas equation (see [1]/[4] and [3]).

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k −1 2 Mx M 2 or = x Px M y 1 + k − 1 M 2 y 2 Py 1 + kM x2 = Px 1 + kM y2 1+

Py

k −1 2 Mx 2 = Tx 1 + k − 1 M 2 y 2

Ty

1+

k −1

2 ρ y Vx M x 1 + 2 M y = = ρ x Vy M y 1 + k − 1 M 2

2

M y2 =

M x2 +

x

2 k −1

2k M x2 − 1 k −1

T0 x = T0 y ⎡ k −1 2 ⎤ P0 y Py ⎢1 + 2 M y ⎥ = ⎢ ⎥ P0 x Px ⎢ k − 1 2 ⎥ 1+ Mx 2 ⎣ ⎦

k /( k −1)

Tabulated values of important normal-shock variables can be found in Table II. Shock Tube Applications and Uses The shock tube is used for a variety of studies apart from the shock wave experiment you will conduct. It can be used as a simple wind tunnel because there are locations where the flow is uniform and supersonic for small periods of time (a few milliseconds). It is also employed for the study of the structure of shock fronts, measurement of the speed of sound, study of wave interactions, wave diffraction and refraction, shock loading of structures, relaxation phenomena, flame propagation, chemical reaction kinetics and atomic physics of nonequilibrium states. Shock Tube Theory In very simple terms the Shock Tube is usually a long tube of circular cross-section divided into two sections by a diaphragm (see Figure 1a). Each side of the diaphragm is charged at a different pressure and with a different gas. Let us say that on the right of the diaphragm (4) we have gas B

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at high pressure denoted by p4, while on the left of the diaphragm (1) we have gas A at low pressure denoted by p1. The ratio

P4 P1 is traditionally referred to as the diaphragm pressure ratio. The diaphragm is instantly ruptured generating a shock wave (compression) travelling from right to left into the low pressure section (1) of gas A, and a rarefaction (or expansion) wave travelling from left to right into the high pressure section (4) of gas B. A picture illustrating this at some time instant after the rupture of the diaphragm can be found in Figure 1b. After the rapture of the diaphragm the two gases that come in contact with each other are assumed not to mix. This is a fair assumption since the only physical mechanism that would cause them to mix is molecular diffusion, which evolves much slower than the propagation of waves. So the separating surface between the gases, which used to be the diaphragm before its rupture, is preserved and is referred to as the contact surface. This contact surface will be moving from right to left at a certain speed. We will call (2) the region between the contact surface and the shock wave which is still occupied by gas A, and (3) the region between the contact surface and the front of the expansion wave occupied by gas B (see Figure 1b). We then recognize that the pressures and velocities on either side of the contact surface must be the same while temperatures and densities differ. Thus

P2 = P3 v 2 = v3 The flow may be considered isentropic everywhere except across the shock wave. The theory that applies to normal shocks exactly applies to travelling normal shock waves if the flow is looked at with respect to a frame of reference travelling with the shock itself (imagine yourselves riding the shock). For example, if the low pressure region (1) in the shock tube contains a stationary gas (zero velocity with respect to a stationary observer) and the shock propagation speed is denoted by cs, then the velocity of the fluid in region (1) is seen by the observer riding the shock as u1=cs from left to right. Therefore the Mach number ahead of the shock is defined as:

M1 =

cs a1

where a1 is the speed of sound for the gas and the conditions ahead of the shock in region (1). Hence, making use of the normal shock equations, we find that:

⎡ k − 1 k1 + 1 P2 ⎤ cs = M 1a1 = a1 ⎢ 1 + ⎥ 2k1 P1 ⎦ ⎣ 2k1

1/ 2

Ratios of thermodynamic variables and properties before and after the shock, together with the Mach number after the shock with respect to the moving frame of reference, can also be found directly from normal shock relations. We thus find that the speed of the fluid behind the shock with respect to the moving observer is given by

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k1 + 1 P2 + k1 − 1 P1 u 2 = u1 k1 + 1 P2 +1 k1 − 1 P1 and with respect to a stationary observer

⎤ ⎡ ⎥ ⎢ ⎤ 2k1 a ⎡P ⎥ v2 = cs − u 2 = 1 ⎢ 2 − 1⎥ ⎢ k1 ⎣ P1 ⎦ ⎢ P2 (k + 1) + (k − 1) ⎥ 1 ⎥⎦ ⎢⎣ P1 1

1/ 2

Now from the theory relevant to isentropic expansion waves we have that ( k4 −1) / 2 k4 ⎤ 2a4 ⎡ ⎧ P3 ⎫ ⎢1 − ⎨ ⎬ ⎥ v3 = k 4 − 1 ⎢ ⎩ P4 ⎭ ⎥⎦ ⎣

From these last two relations and the conditions at the contact surface we obtain the following equation often referred to as the shock tube equation

(k 4 − 1)(a1 a4 )(P2 P1 − 1) ⎤ P4 P2 ⎡ = ⎢1 − ⎥ P1 P1 ⎢⎣ 2k1 2k1 + (k1 + 1)(P2 P1 − 1) ⎥⎦

−2 k4 / ( k4 −1)

The ratios

P −P P2 or 2 1 P1 P1 are traditionally referred to as the shock strength, while the ratio

P3 P4 is often referred to as the expansion strength. Schematics depicting the variation of several quantities of interest along the shock tube for a given position of the shock and expansion waves at a frozen instant in time are given in Figure 1. Be advised that when the shock wave reaches the end of the shock tube it will be reflected back into the shock tube as a shock wave, if the end of the tube is closed. If the tube is open-ended the shock wave will be reflected as an expansion wave back into the shock tube. The expansion wave generated upon the rupture of the diaphragm will be reflected off the back of the tube as an expansion wave. What happens in the shock tube after the reflections of the original waves is much too complicated to address at this time. There is a lot to be said about travelling shock waves and rarefaction waves that we could not cover here. We only provide the framework for you to understand what goes on in the shock tube. If you would like to know more about both these types of waves you may look up references [2] and [3].

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Nomenclature P Px Py Po Pox Poy T Tx Ty To Tox Toy ρ ρx ρy ρo A A*

m

k V Vx Vy

Static Pressure Static Pressure Upstream of Normal Shock Static Pressure Downstream of Normal Shock Stagnation Pressure Stagnation Pressure Upstream of Normal Shock Stagnation Pressure Downstream of Normal Shock Static Temperature Static Temperature Upstream of Normal Shock Static Temperature Downstream of Normal Shock Stagnation Temperature Stagnation Temperature Upstream of Normal Shock Stagnation Temperature Downstream of Normal Shock Gas Density Gas Density Upstream of Normal Shock Gas Density Downstream of Normal Shock Gas Density at Stagnation Conditions Local Area of the Duct Throat Area Mass Flow Rate Ratio of Specific Heats of Gas Gas Speed Gas Speed Upstream of Normal Shock Gas Speed Downstream of Normal Shock 1/ 2

a

⎡ ⎡ ∂p ⎤ ⎤ Speed of Sound = ⎢ ⎢ ⎥ ⎥ ⎢⎣ ⎣ ∂ρ ⎦ s ⎥⎦

u v cs

Gas Speed with respect to frame of reference moving with the shock wave. Gas Speed with respect to stationary observer Shock Wave Propagation Speed

M

Mach Number =

Mx My

Mach Number Upstream of Normal Shock Mach Number Downstream of Normal Shock

R

Gas Constant =

Ru W

Universal Gas Constant Gas Molecular Weight

V a Ru W

References [1] Fox, R. W., and McDonald, A. T., Introduction to Fluid Mechanics, 3d Ed., J. Wiley, 1985. [2] Liepman, H. W., and Roshko, A., Elements of Gas Dynamics, J. Wiley, 1957. [3] Shapiro, A. H., The Dynamics and Thermodynamics of Compressible Fluid Flow, Vols. 1 and 2, J. Wiley, 1953. [4] M. C. Potter and D. C. Wiggert: Mechanics of Fluids, 3d Ed., Brooks/Cole, 2001. ISBN 0534-37996-6; TA357.P725 2001

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TABLE I Steady, One-Dimensional, Isentropic, Compressible FLow Table (Perfect Gas with k = 1.4) Ma 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.2 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.3 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.4 0.41

P/Po 1 0.99993 0.99972 0.99937 0.998881 0.998252 0.997484 0.996578 0.995533 0.994351 0.993031 0.991576 0.989985 0.988259 0.9864 0.984408 0.982285 0.98003 0.977647 0.975135 0.972497 0.969733 0.966845 0.963835 0.960703 0.957453 0.954085 0.9506 0.947002 0.943291 0.93947 0.93554 0.931503 0.927362 0.923118 0.918773 0.91433 0.90979 0.905156 0.90043 0.895614 0.890711

T/To 1 0.99998 0.99992 0.99982 0.99968 0.9995 0.999281 0.999021 0.998722 0.998383 0.998004 0.997586 0.997128 0.996631 0.996095 0.99552 0.994906 0.994253 0.993562 0.992832 0.992063 0.991257 0.990413 0.989531 0.988611 0.987654 0.98666 0.98563 0.984562 0.983458 0.982318 0.981142 0.979931 0.978684 0.977402 0.976086 0.974735 0.97335 0.971931 0.970478 0.968992 0.967474

ρ/ρο 1 0.99995 0.9998 0.99955 0.9992 0.998751 0.998202 0.997554 0.996807 0.995961 0.995017 0.993976 0.992836 0.9916 0.990267 0.988838 0.987314 0.985695 0.983982 0.982176 0.980277 0.978286 0.976204 0.974032 0.971771 0.969421 0.966984 0.96446 0.961851 0.959157 0.95638 0.953521 0.95058 0.94756 0.94446 0.941283 0.938029 0.9347 0.931297 0.927821 0.924274 0.920657

A/A* (A/A*)(P/Po) Infinite Infinite 57.87384 57.86979 28.94213 28.93403 19.30054 19.28839 14.48149 14.46528 11.59144 11.57118 9.66591 9.64159 8.29153 8.26315 7.26161 7.22917 6.46134 6.42484 5.82183 5.78126 5.29923 5.25459 4.86432 4.8156 4.49686 4.44406 4.1824 4.12552 3.91034 3.84937 3.67274 3.60767 3.46351 3.39434 3.27793 3.20465 3.11226 3.03487 2.96352 2.88201 2.82929 2.74366 2.7076 2.61783 2.59681 2.5029 2.49556 2.3975 2.40271 2.30048 2.31729 2.21089 2.23847 2.12789 2.16555 2.05078 2.09793 1.97896 2.03507 1.91188 1.97651 1.8491 1.92185 1.79021 1.87074 1.73486 1.82288 1.68273 1.77797 1.63355 1.73578 1.58707 1.69609 1.54308 1.6587 1.50138 1.62343 1.46179 1.59014 1.42415 1.55867 1.38833

ME4621: Semester II 2006-2007 Ma 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.6 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.7 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88

P/Po 0.885722 0.880651 0.875498 0.870267 0.86496 0.85958 0.854128 0.848607 0.843019 0.837367 0.831654 0.825881 0.82005 0.814165 0.808228 0.802241 0.796206 0.790127 0.784004 0.777841 0.771639 0.765402 0.759131 0.752829 0.746498 0.74014 0.733758 0.727353 0.720928 0.714485 0.708025 0.701552 0.695068 0.688573 0.68207 0.675562 0.66905 0.662536 0.656022 0.649509 0.643 0.636496 0.63 0.623512 0.617034 0.610569 0.604117

30 T/To 0.965922 0.964339 0.962723 0.961076 0.959398 0.957689 0.95595 0.95418 0.952381 0.950552 0.948695 0.946808 0.944894 0.942951 0.940982 0.938985 0.936961 0.934911 0.932836 0.930735 0.928609 0.926458 0.924283 0.922084 0.919862 0.917616 0.915349 0.913059 0.910747 0.908414 0.90606 0.903685 0.901291 0.898876 0.896443 0.893991 0.89152 0.889031 0.886525 0.884001 0.881461 0.878905 0.876332 0.873744 0.871141 0.868523 0.865891

ρ/ρο 0.916971 0.913217 0.909398 0.905513 0.901566 0.897556 0.893486 0.889357 0.88517 0.880927 0.876629 0.872278 0.867876 0.863422 0.85892 0.854371 0.849775 0.845135 0.840452 0.835728 0.830963 0.82616 0.821319 0.816443 0.811533 0.80659 0.801616 0.796612 0.791579 0.786519 0.781434 0.776324 0.771191 0.766037 0.760863 0.75567 0.75046 0.745234 0.739992 0.734738 0.729471 0.724193 0.718905 0.713609 0.708306 0.702997 0.697683

A/A* 1.5289 1.50072 1.47401 1.44867 1.42463 1.4018 1.3801 1.35947 1.33984 1.32117 1.30339 1.28645 1.27032 1.25495 1.24029 1.22633 1.21301 1.20031 1.1882 1.17665 1.16565 1.15515 1.14515 1.13562 1.12654 1.11789 1.10965 1.10182 1.09437 1.08729 1.08057 1.07419 1.06814 1.06242 1.057 1.05188 1.04705 1.04251 1.03823 1.03422 1.03046 1.02696 1.0237 1.02067 1.01787 1.0153 1.01294

(A/A*)(P/Po) 1.35419 1.32161 1.29049 1.26073 1.23225 1.20495 1.17878 1.15365 1.12951 1.1063 1.08397 1.06246 1.04173 1.02173 1.00244 0.98381 0.9658 0.9484 0.93155 0.91525 0.89946 0.88416 0.86932 0.85493 0.84096 0.82739 0.81422 0.80141 0.78896 0.77685 0.76507 0.7536 0.74243 0.73155 0.72095 0.71061 0.70053 0.6907 0.6811 0.67173 0.66259 0.65366 0.64493 0.6364 0.62806 0.61991 0.61193

ME4621: Semester II 2006-2007 Ma 0.89 0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35

P/Po 0.59768 0.59126 0.584858 0.578476 0.572114 0.565775 0.55946 0.55317 0.546905 0.540669 0.53446 0.528282 0.522134 0.516018 0.509935 0.503886 0.497872 0.491894 0.485952 0.480047 0.474181 0.468354 0.462567 0.45682 0.451114 0.445451 0.439829 0.434251 0.428716 0.423225 0.417778 0.412377 0.407021 0.401711 0.396446 0.391229 0.386058 0.380934 0.375857 0.370828 0.365847 0.360914 0.356029 0.351192 0.346403 0.341663 0.336971

31 T/To 0.863245 0.860585 0.857913 0.855227 0.852529 0.84982 0.847099 0.844366 0.841623 0.83887 0.836106 0.833333 0.830551 0.82776 0.82496 0.822152 0.819336 0.816513 0.813683 0.810846 0.808002 0.805153 0.802298 0.799437 0.796572 0.793701 0.790826 0.787948 0.785065 0.782179 0.77929 0.776398 0.773503 0.770606 0.767707 0.764807 0.761905 0.759002 0.756098 0.753194 0.750289 0.747384 0.74448 0.741576 0.738672 0.73577 0.732869

ρ/ρο 0.692365 0.687044 0.681722 0.6764 0.671079 0.665759 0.660443 0.65513 0.649822 0.64452 0.639225 0.633938 0.62866 0.623391 0.618133 0.612887 0.607653 0.602432 0.597225 0.592033 0.586856 0.581696 0.576553 0.571427 0.56632 0.561232 0.556164 0.551116 0.54609 0.541085 0.536102 0.531142 0.526205 0.521292 0.516403 0.511539 0.506701 0.501888 0.497102 0.492342 0.487608 0.482903 0.478225 0.473575 0.468953 0.464361 0.459797

A/A* 1.0108 1.00886 1.00713 1.0056 1.00426 1.00311 1.00215 1.00136 1.00076 1.00034 1.00008 1 1.00008 1.00033 1.00074 1.00131 1.00203 1.00291 1.00394 1.00512 1.00645 1.00793 1.00955 1.01131 1.01322 1.01527 1.01745 1.01978 1.02224 1.02484 1.02757 1.03044 1.03344 1.03657 1.03983 1.04323 1.04675 1.05041 1.05419 1.0581 1.06214 1.0663 1.0706 1.07502 1.07957 1.08424 1.08904

(A/A*)(P/Po) 0.60413 0.5965 0.58903 0.58171 0.57455 0.56753 0.56066 0.55392 0.54732 0.54085 0.53451 0.52828 0.52218 0.51619 0.51031 0.50454 0.49888 0.49332 0.48787 0.4825 0.47724 0.47207 0.46698 0.46199 0.45708 0.45225 0.44751 0.44284 0.43825 0.43374 0.4293 0.42493 0.42063 0.4164 0.41224 0.40814 0.40411 0.40014 0.39622 0.39237 0.38858 0.38484 0.38116 0.37754 0.37396 0.37044 0.36697

ME4621: Semester II 2006-2007 Ma 1.36 1.37 1.38 1.39 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57 1.58 1.59 1.6 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.7 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82

P/Po 0.332328 0.327733 0.323187 0.31869 0.314241 0.30984 0.305488 0.301185 0.296929 0.292722 0.288563 0.284452 0.280388 0.276372 0.272403 0.268481 0.264607 0.260779 0.256997 0.253262 0.249573 0.24593 0.242332 0.238779 0.235271 0.231808 0.228389 0.225014 0.221683 0.218395 0.21515 0.211948 0.208788 0.20567 0.202593 0.199558 0.196564 0.193611 0.190697 0.187824 0.18499 0.182195 0.179438 0.17672 0.17404 0.171398 0.168792

32 T/To 0.72997 0.727072 0.724176 0.721282 0.718391 0.715502 0.712616 0.709733 0.706854 0.703977 0.701105 0.698236 0.695372 0.692511 0.689655 0.686804 0.683957 0.681115 0.678279 0.675447 0.672622 0.669801 0.666987 0.664178 0.661376 0.658579 0.655789 0.653006 0.650229 0.647459 0.644695 0.641939 0.63919 0.636448 0.633714 0.630986 0.628267 0.625555 0.622851 0.620155 0.617467 0.614787 0.612115 0.609451 0.606796 0.604149 0.601511

ρ/ρο 0.455263 0.450758 0.446283 0.441838 0.437423 0.433039 0.428686 0.424363 0.420072 0.415812 0.411583 0.407386 0.40322 0.399086 0.394984 0.390914 0.386876 0.38287 0.378897 0.374955 0.371045 0.367168 0.363323 0.35951 0.35573 0.351982 0.348266 0.344582 0.34093 0.337311 0.333723 0.330168 0.326644 0.323152 0.319693 0.316264 0.312868 0.309502 0.306169 0.302866 0.299595 0.296354 0.293145 0.289966 0.286818 0.283701 0.280614

A/A* 1.09396 1.09902 1.10419 1.1095 1.11493 1.12048 1.12616 1.13197 1.1379 1.14396 1.15015 1.15646 1.1629 1.16947 1.17617 1.18299 1.18994 1.19702 1.20423 1.21157 1.21904 1.22664 1.23438 1.24224 1.25024 1.25836 1.26663 1.27502 1.28355 1.29222 1.30102 1.30996 1.31904 1.32825 1.33761 1.3471 1.35674 1.36651 1.37643 1.38649 1.3967 1.40705 1.41755 1.42819 1.43898 1.44992 1.46101

(A/A*)(P/Po) 0.36355 0.36018 0.35686 0.35359 0.35036 0.34717 0.34403 0.34093 0.33788 0.33486 0.33189 0.32896 0.32606 0.32321 0.32039 0.31761 0.31487 0.31216 0.30949 0.30685 0.30424 0.30167 0.29913 0.29662 0.29414 0.2917 0.28928 0.2869 0.28454 0.28221 0.27991 0.27764 0.2754 0.27318 0.27099 0.26883 0.26669 0.26457 0.26248 0.26042 0.25837 0.25636 0.25436 0.25239 0.25044 0.24851 0.24661

ME4621: Semester II 2006-2007 Ma 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2 2.01 2.02 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.2 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29

P/Po 0.166224 0.163691 0.161195 0.158734 0.156309 0.153918 0.151562 0.14924 0.146951 0.144696 0.142473 0.140283 0.138126 0.135999 0.133905 0.131841 0.129808 0.127805 0.125831 0.123888 0.121973 0.120087 0.118229 0.116399 0.114597 0.112823 0.111075 0.109353 0.107658 0.105988 0.104345 0.102726 0.101132 0.099562 0.098017 0.096495 0.094997 0.093522 0.092069 0.09064 0.089232 0.087846 0.086482 0.085139 0.083817 0.082515 0.081234

33 T/To 0.598881 0.59626 0.593648 0.591044 0.58845 0.585864 0.583288 0.58072 0.578162 0.575612 0.573072 0.570542 0.56802 0.565509 0.563006 0.560513 0.558029 0.555556 0.553091 0.550637 0.548192 0.545756 0.543331 0.540915 0.538509 0.536113 0.533726 0.53135 0.528983 0.526626 0.524279 0.521942 0.519615 0.517298 0.514991 0.512694 0.510407 0.50813 0.505863 0.503606 0.501359 0.499122 0.496894 0.494677 0.49247 0.490273 0.488086

ρ/ρο 0.277557 0.27453 0.271533 0.268566 0.265628 0.26272 0.259841 0.256991 0.254169 0.251377 0.248613 0.245877 0.24317 0.24049 0.237839 0.235215 0.232618 0.230048 0.227506 0.22499 0.2225 0.220037 0.217601 0.21519 0.212805 0.210446 0.208112 0.205803 0.203519 0.201259 0.199025 0.196814 0.194628 0.192466 0.190327 0.188212 0.18612 0.184051 0.182005 0.179981 0.17798 0.176001 0.174044 0.17211 0.170196 0.168304 0.166433

A/A* 1.47225 1.48365 1.49519 1.50689 1.51875 1.53076 1.54293 1.55526 1.56774 1.58039 1.5932 1.60617 1.61931 1.63261 1.64608 1.65972 1.67352 1.6875 1.70165 1.71597 1.73047 1.74514 1.75999 1.77502 1.79022 1.80561 1.82119 1.83694 1.85289 1.86902 1.88533 1.90184 1.91854 1.93544 1.95252 1.96981 1.98729 2.00497 2.02286 2.04094 2.05923 2.07773 2.09644 2.11535 2.13447 2.15381 2.17336

(A/A*)(P/Po) 0.24472 0.24286 0.24102 0.2392 0.23739 0.23561 0.23385 0.23211 0.23038 0.22868 0.22699 0.22532 0.22367 0.22203 0.22042 0.21882 0.21724 0.21567 0.21412 0.21259 0.21107 0.20957 0.20808 0.20661 0.20516 0.20371 0.20229 0.20088 0.19948 0.19809 0.19672 0.19537 0.19403 0.1927 0.19138 0.19008 0.18879 0.18751 0.18624 0.18499 0.18375 0.18252 0.1813 0.1801 0.1789 0.17772 0.17655

ME4621: Semester II 2006-2007 Ma 2.3 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.4 2.41 2.42 2.43 2.44 2.45 2.46 2.47 2.48 2.49 2.5 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.6 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.76

P/Po 0.079973 0.078731 0.077509 0.076306 0.075122 0.073957 0.07281 0.071681 0.07057 0.069476 0.068399 0.06734 0.066297 0.065271 0.064261 0.063267 0.062288 0.061326 0.060378 0.059445 0.058528 0.057624 0.056736 0.055861 0.055 0.054153 0.053319 0.052499 0.051692 0.050897 0.050115 0.049346 0.048589 0.047844 0.04711 0.046389 0.045679 0.04498 0.044292 0.043616 0.04295 0.042295 0.04165 0.041016 0.040391 0.039777 0.039172

34 T/To 0.485909 0.483741 0.481584 0.479437 0.4773 0.475172 0.473055 0.470947 0.46885 0.466762 0.464684 0.462616 0.460558 0.458509 0.456471 0.454442 0.452423 0.450414 0.448414 0.446425 0.444444 0.442474 0.440513 0.438562 0.43662 0.434688 0.432766 0.430852 0.428949 0.427055 0.42517 0.423295 0.421429 0.419572 0.417725 0.415887 0.414058 0.412239 0.410428 0.408627 0.406835 0.405052 0.403278 0.401513 0.399757 0.39801 0.396272

ρ/ρο 0.164584 0.162755 0.160946 0.159158 0.15739 0.155642 0.153914 0.152206 0.150516 0.148846 0.147195 0.145563 0.14395 0.142354 0.140777 0.139218 0.137677 0.136154 0.134648 0.133159 0.131687 0.130232 0.128794 0.127373 0.125968 0.124579 0.123206 0.121849 0.120507 0.119182 0.117871 0.116575 0.115295 0.114029 0.112778 0.111542 0.11032 0.109112 0.107918 0.106738 0.105571 0.104418 0.103279 0.102152 0.101039 0.099939 0.098851

A/A* 2.19313 2.21312 2.23332 2.25375 2.2744 2.29528 2.31638 2.33771 2.35928 2.38107 2.4031 2.42537 2.44787 2.47061 2.4936 2.51683 2.54031 2.56403 2.58801 2.61224 2.63672 2.66146 2.68645 2.71171 2.73723 2.76301 2.78906 2.81538 2.84197 2.86884 2.89598 2.92339 2.95109 2.97907 3.00733 3.03588 3.06472 3.09385 3.12327 3.15299 3.18301 3.21333 3.24395 3.27488 3.30611 3.33766 3.36952

(A/A*)(P/Po) 0.17539 0.17424 0.1731 0.17198 0.17086 0.16975 0.16866 0.16757 0.16649 0.16543 0.16437 0.16332 0.16229 0.16126 0.16024 0.15923 0.15823 0.15724 0.15626 0.15529 0.15432 0.15337 0.15242 0.15148 0.15055 0.14963 0.14871 0.1478 0.14691 0.14602 0.14513 0.14426 0.14339 0.14253 0.14168 0.14083 0.13999 0.13916 0.13834 0.13752 0.13671 0.13591 0.13511 0.13432 0.13354 0.13276 0.13199

ME4621: Semester II 2006-2007 Ma 2.77 2.78 2.79 2.8 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.9 2.91 2.92 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3

35

P/Po 0.038577 0.037992 0.037415 0.036848 0.03629 0.035741 0.035201 0.034669 0.034146 0.033631 0.033124 0.032625 0.032134 0.031651 0.031176 0.030708 0.030248 0.029795 0.029349 0.02891 0.028479 0.028054 0.027635 0.027224

T/To 0.394543 0.392822 0.391111 0.389408 0.387714 0.386029 0.384352 0.382684 0.381025 0.379374 0.377732 0.376098 0.374473 0.372856 0.371248 0.369648 0.368056 0.366472 0.364897 0.36333 0.361771 0.36022 0.358677 0.357143

ρ/ρο 0.097777 0.096714 0.095664 0.094626 0.093601 0.092587 0.091585 0.090594 0.089616 0.088648 0.087692 0.086747 0.085813 0.084889 0.083977 0.083075 0.082183 0.081302 0.080431 0.079571 0.07872 0.077879 0.077048 0.076226

A/A* 3.40169 3.43418 3.46699 3.50012 3.53358 3.56737 3.60148 3.63593 3.67072 3.70584 3.74131 3.77711 3.81327 3.84977 3.88662 3.92383 3.96139 3.99932 4.0376 4.07625 4.11527 4.15466 4.19443 4.23457

(A/A*)(P/Po) 0.13123 0.13047 0.12972 0.12897 0.12823 0.1275 0.12678 0.12605 0.12534 0.12463 0.12393 0.12323 0.12254 0.12185 0.12117 0.12049 0.11982 0.11916 0.1185 0.11785 0.1172 0.11655 0.11591 0.11528

TABLE II Steady, One-Dimensional, Compressible FLow Across Normal Shock Table (Perfect Gas with k = 1.4)

Mx 1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11 1.12

My 1 0.990132 0.980519 0.971154 0.962025 0.953125 0.944445 0.935977 0.927713 0.919647 0.91177 0.904078 0.896563

py/px 1 1.02345 1.04713 1.07105 1.0952 1.11958 1.1442 1.16905 1.19413 1.21945 1.245 1.27078 1.2968

Vx/Vy and ρy/ρx 1 1.01669 1.03344 1.05024 1.06709 1.08398 1.10092 1.1179 1.13492 1.15199 1.16908 1.18621 1.20338

Ty/Tx 1 1.00664 1.01325 1.01981 1.02634 1.03284 1.03931 1.04575 1.05217 1.05856 1.06494 1.07129 1.07763

Ax*/Ay* and poy/pox 1 0.999999 0.99999 0.999967 0.999923 0.999853 0.999751 0.999611 0.999431 0.999204 0.998928 0.998599 0.998213

poy/px 1.89293 1.91521 1.9379 1.96097 1.98442 2.00825 2.03245 2.05702 2.08194 2.10722 2.13285 2.15882 2.18513

ME4621: Semester II 2006-2007

Mx 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1.2 1.21 1.22 1.23 1.24 1.25 1.26 1.27 1.28 1.29 1.3 1.31 1.32 1.33 1.34 1.35 1.36 1.37 1.38 1.39 1.4 1.41 1.42 1.43 1.44 1.45 1.46 1.47 1.48 1.49 1.5 1.51 1.52 1.53 1.54 1.55 1.56 1.57

My 0.889219 0.882042 0.875024 0.868162 0.861451 0.854884 0.848459 0.84217 0.836014 0.829986 0.824083 0.818301 0.812636 0.807085 0.801645 0.796312 0.791084 0.785957 0.780929 0.775997 0.771159 0.766412 0.761753 0.757181 0.752692 0.748286 0.743959 0.739709 0.735536 0.731436 0.727408 0.723451 0.719562 0.71574 0.711983 0.70829 0.704659 0.701089 0.697578 0.694125 0.690729 0.687388 0.684101 0.680867 0.677685

36

py/px 1.32305 1.34953 1.37625 1.4032 1.43038 1.4578 1.48545 1.51333 1.54145 1.5698 1.59838 1.6272 1.65625 1.68553 1.71505 1.7448 1.77478 1.805 1.83545 1.86613 1.89705 1.9282 1.95958 1.9912 2.02305 2.05513 2.08745 2.12 2.15278 2.1858 2.21905 2.25253 2.28625 2.3202 2.35438 2.3888 2.42345 2.45833 2.49345 2.5288 2.56438 2.6002 2.63625 2.67253 2.70905

Vx/Vy and ρy/ρx 1.22057 1.23779 1.25504 1.27231 1.28961 1.30693 1.32426 1.34161 1.35898 1.37636 1.39376 1.41116 1.42857 1.44599 1.46341 1.48084 1.49827 1.5157 1.53312 1.55055 1.56797 1.58538 1.60278 1.62018 1.63757 1.65494 1.67231 1.68966 1.70699 1.7243 1.7416 1.75888 1.77614 1.79337 1.81058 1.82777 1.84493 1.86207 1.87918 1.89626 1.91331 1.93033 1.94732 1.96427 1.98119

Ty/Tx 1.08396 1.09027 1.09658 1.10287 1.10916 1.11544 1.12172 1.12799 1.13427 1.14054 1.14682 1.15309 1.15938 1.16566 1.17195 1.17825 1.18456 1.19087 1.1972 1.20353 1.20988 1.21624 1.22261 1.229 1.2354 1.24181 1.24825 1.25469 1.26116 1.26764 1.27414 1.28066 1.2872 1.29377 1.30035 1.30695 1.31357 1.32022 1.32688 1.33357 1.34029 1.34703 1.35379 1.36057 1.36738

Ax*/Ay* and poy/pox 0.997768 0.997261 0.99669 0.996052 0.995345 0.994569 0.99372 0.992798 0.991802 0.990731 0.989583 0.988359 0.987057 0.985677 0.984219 0.982682 0.981067 0.979374 0.977602 0.975752 0.973824 0.971819 0.969737 0.967579 0.965344 0.963035 0.960652 0.958194 0.955665 0.953063 0.95039 0.947648 0.944837 0.941958 0.939012 0.936001 0.932925 0.929787 0.926586 0.923324 0.920003 0.916624 0.913188 0.909697 0.906151

poy/px 2.21178 2.23877 2.26608 2.29372 2.32169 2.34998 2.37858 2.4075 2.43674 2.46628 2.49613 2.52629 2.55676 2.58753 2.6186 2.64996 2.68163 2.71359 2.74585 2.7784 2.81125 2.84438 2.87781 2.91152 2.94552 2.97981 3.01438 3.04924 3.08438 3.1198 3.15551 3.19149 3.22776 3.26431 3.30113 3.33823 3.37562 3.41327 3.45121 3.48942 3.52791 3.56667 3.6057 3.64501 3.68459

ME4621: Semester II 2006-2007

Mx 1.58 1.59 1.6 1.61 1.62 1.63 1.64 1.65 1.66 1.67 1.68 1.69 1.7 1.71 1.72 1.73 1.74 1.75 1.76 1.77 1.78 1.79 1.8 1.81 1.82 1.83 1.84 1.85 1.86 1.87 1.88 1.89 1.9 1.91 1.92 1.93 1.94 1.95 1.96 1.97 1.98 1.99 2 2.01 2.02

My 0.674553 0.671471 0.668437 0.665451 0.662511 0.659616 0.656765 0.653958 0.651194 0.648471 0.645789 0.643147 0.640544 0.637979 0.635452 0.632962 0.630508 0.628089 0.625705 0.623354 0.621037 0.618753 0.616501 0.614281 0.612091 0.609931 0.607802 0.605701 0.603629 0.601585 0.599569 0.597579 0.595616 0.59368 0.591769 0.589883 0.588022 0.586185 0.584372 0.582582 0.580816 0.579072 0.57735 0.57565 0.573972

37

py/px 2.7458 2.78278 2.82 2.85745 2.89513 2.93305 2.9712 3.00958 3.0482 3.08705 3.12613 3.16545 3.205 3.24478 3.2848 3.32505 3.36553 3.40625 3.4472 3.48838 3.5298 3.57145 3.61333 3.65545 3.6978 3.74038 3.7832 3.82625 3.86953 3.91305 3.9568 4.00078 4.045 4.08945 4.13413 4.17905 4.2242 4.26958 4.3152 4.36105 4.40713 4.45345 4.5 4.54678 4.5938

Vx/Vy and ρy/ρx 1.99808 2.01493 2.03175 2.04852 2.06526 2.08197 2.09863 2.11525 2.13183 2.14836 2.16486 2.18131 2.19772 2.21408 2.2304 2.24667 2.26289 2.27907 2.2952 2.31128 2.32731 2.34329 2.35922 2.3751 2.39093 2.40671 2.42244 2.43811 2.45373 2.4693 2.48481 2.50027 2.51568 2.53103 2.54633 2.56157 2.57675 2.59188 2.60695 2.62196 2.63692 2.65182 2.66667 2.68145 2.69618

Ty/Tx 1.37422 1.38108 1.38797 1.39488 1.40182 1.40879 1.41578 1.4228 1.42985 1.43693 1.44403 1.45117 1.45833 1.46552 1.47274 1.47999 1.48727 1.49458 1.50192 1.50929 1.51669 1.52412 1.53158 1.53907 1.54659 1.55415 1.56173 1.56935 1.577 1.58468 1.59239 1.60014 1.60792 1.61573 1.62357 1.63144 1.63935 1.64729 1.65527 1.66328 1.67132 1.67939 1.6875 1.69564 1.70382

Ax*/Ay* and poy/pox 0.902552 0.898901 0.8952 0.89145 0.887653 0.883809 0.879921 0.875988 0.872014 0.867999 0.863944 0.859851 0.855721 0.851556 0.847356 0.843124 0.83886 0.834565 0.830242 0.825891 0.821513 0.817111 0.812684 0.808234 0.803763 0.799271 0.794761 0.790232 0.785686 0.781125 0.776549 0.771959 0.767357 0.762743 0.758119 0.753486 0.748844 0.744195 0.73954 0.734879 0.730214 0.725545 0.720874 0.716201 0.711527

poy/px 3.72445 3.76457 3.80497 3.84564 3.88658 3.9278 3.96928 4.01103 4.05305 4.09535 4.13791 4.18074 4.22383 4.2672 4.31083 4.35473 4.3989 4.44334 4.48804 4.53301 4.57825 4.62375 4.66952 4.71555 4.76185 4.80841 4.85524 4.90234 4.9497 4.99732 5.04521 5.09336 5.14178 5.19046 5.2394 5.28861 5.33808 5.38782 5.43782 5.48808 5.5386 5.58939 5.64044 5.69175 5.74333

ME4621: Semester II 2006-2007

Mx 2.03 2.04 2.05 2.06 2.07 2.08 2.09 2.1 2.11 2.12 2.13 2.14 2.15 2.16 2.17 2.18 2.19 2.2 2.21 2.22 2.23 2.24 2.25 2.26 2.27 2.28 2.29 2.3 2.31 2.32 2.33 2.34 2.35 2.36 2.37 2.38 2.39 2.4 2.41 2.42 2.43 2.44 2.45 2.46 2.47

My 0.572315 0.570679 0.569063 0.567467 0.56589 0.564334 0.562796 0.561277 0.559776 0.558294 0.55683 0.555383 0.553953 0.552541 0.551145 0.549766 0.548403 0.547056 0.545724 0.544409 0.543108 0.541822 0.540552 0.539295 0.538053 0.536825 0.535611 0.534411 0.533224 0.532051 0.53089 0.529743 0.528608 0.527486 0.526376 0.525278 0.524192 0.523118 0.522055 0.521004 0.519964 0.518936 0.517918 0.516911 0.515915

38

py/px 4.64105 4.68853 4.73625 4.7842 4.83238 4.8808 4.92945 4.97833 5.02745 5.0768 5.12638 5.1762 5.22625 5.27653 5.32705 5.3778 5.42878 5.48 5.53145 5.58313 5.63505 5.6872 5.73958 5.7922 5.84505 5.89813 5.95145 6.005 6.05878 6.1128 6.16705 6.22153 6.27625 6.3312 6.38638 6.4418 6.49745 6.55333 6.60945 6.6658 6.72238 6.7792 6.83625 6.89353 6.95105

Vx/Vy and ρy/ρx 2.71085 2.72546 2.74002 2.75451 2.76895 2.78332 2.79764 2.8119 2.8261 2.84024 2.85432 2.86835 2.88231 2.89621 2.91005 2.92383 2.93756 2.95122 2.96482 2.97837 2.99185 3.00527 3.01863 3.03194 3.04518 3.05836 3.07149 3.08455 3.09755 3.11049 3.12338 3.1362 3.14897 3.16167 3.17432 3.1869 3.19943 3.2119 3.2243 3.23665 3.24894 3.26117 3.27335 3.28546 3.29752

Ty/Tx 1.71203 1.72027 1.72855 1.73686 1.74521 1.75359 1.762 1.77045 1.77893 1.78745 1.79601 1.80459 1.81322 1.82188 1.83057 1.8393 1.84806 1.85686 1.86569 1.87456 1.88347 1.89241 1.90138 1.9104 1.91944 1.92853 1.93765 1.9468 1.95599 1.96522 1.97448 1.98378 1.99311 2.00249 2.01189 2.02134 2.03082 2.04033 2.04988 2.05947 2.0691 2.07876 2.08846 2.09819 2.10797

Ax*/Ay* and poy/pox 0.706853 0.70218 0.697508 0.692839 0.688174 0.683512 0.678855 0.674203 0.669558 0.664919 0.660288 0.655666 0.651052 0.646447 0.641853 0.637269 0.632697 0.628136 0.623588 0.619053 0.614531 0.610023 0.60553 0.601051 0.596588 0.59214 0.587709 0.583295 0.578897 0.574517 0.570154 0.56581 0.561484 0.557177 0.552889 0.548621 0.544372 0.540144 0.535936 0.531748 0.527581 0.523435 0.519311 0.515208 0.511126

poy/px 5.79517 5.84727 5.89963 5.95226 6.00514 6.05829 6.1117 6.16537 6.21931 6.27351 6.32796 6.38268 6.43766 6.4929 6.54841 6.60417 6.66019 6.71648 6.77303 6.82983 6.8869 6.94423 7.00182 7.05967 7.11778 7.17616 7.23479 7.29368 7.35283 7.41225 7.47192 7.53185 7.59205 7.6525 7.71321 7.77419 7.83542 7.89691 7.95867 8.02068 8.08295 8.14549 8.20828 8.27133 8.33464

ME4621: Semester II 2006-2007

Mx 2.48 2.49 2.5 2.51 2.52 2.53 2.54 2.55 2.56 2.57 2.58 2.59 2.6 2.61 2.62 2.63 2.64 2.65 2.66 2.67 2.68 2.69 2.7 2.71 2.72 2.73 2.74 2.75 2.76 2.77 2.78 2.79 2.8 2.81 2.82 2.83 2.84 2.85 2.86 2.87 2.88 2.89 2.9 2.91 2.92

My 0.514929 0.513954 0.512989 0.512034 0.511089 0.510154 0.509228 0.508312 0.507406 0.506509 0.50562 0.504741 0.503871 0.50301 0.502157 0.501313 0.500477 0.499649 0.49883 0.498019 0.497216 0.496421 0.495634 0.494854 0.494082 0.493317 0.49256 0.49181 0.491068 0.490332 0.489604 0.488882 0.488167 0.487459 0.486758 0.486064 0.485376 0.484694 0.484019 0.48335 0.482687 0.48203 0.48138 0.480735 0.480096

39

py/px 7.0088 7.06678 7.125 7.18345 7.24213 7.30105 7.3602 7.41958 7.4792 7.53905 7.59913 7.65945 7.72 7.78078 7.8418 7.90305 7.96453 8.02625 8.0882 8.15038 8.2128 8.27545 8.33833 8.40145 8.4648 8.52838 8.5922 8.65625 8.72053 8.78505 8.8498 8.91478 8.98 9.04545 9.11113 9.17705 9.2432 9.30958 9.3762 9.44305 9.51013 9.57745 9.645 9.71278 9.7808

Vx/Vy and ρy/ρx 3.30951 3.32145 3.33333 3.34516 3.35692 3.36863 3.38028 3.39187 3.40341 3.41489 3.42631 3.43767 3.44898 3.46023 3.47143 3.48257 3.49365 3.50468 3.51565 3.52657 3.53743 3.54824 3.55899 3.56969 3.58033 3.59092 3.60146 3.61194 3.62237 3.63274 3.64307 3.65334 3.66355 3.67372 3.68383 3.69389 3.70389 3.71385 3.72375 3.73361 3.74341 3.75316 3.76286 3.77251 3.78211

Ty/Tx 2.11777 2.12762 2.1375 2.14742 2.15737 2.16737 2.17739 2.18746 2.19756 2.2077 2.21788 2.22809 2.23834 2.24863 2.25896 2.26932 2.27972 2.29015 2.30063 2.31114 2.32168 2.33227 2.34289 2.35355 2.36425 2.37498 2.38576 2.39657 2.40741 2.4183 2.42922 2.44018 2.45117 2.46221 2.47328 2.48439 2.49554 2.50672 2.51794 2.5292 2.5405 2.55183 2.56321 2.57462 2.58607

Ax*/Ay* and poy/pox 0.507067 0.50303 0.499015 0.495022 0.491052 0.487105 0.483181 0.47928 0.475402 0.471547 0.467715 0.463907 0.460123 0.456362 0.452625 0.448912 0.445223 0.441557 0.437916 0.434298 0.430705 0.427136 0.42359 0.420069 0.416572 0.413099 0.40965 0.406226 0.402825 0.399449 0.396096 0.392768 0.389464 0.386184 0.382927 0.379695 0.376486 0.373302 0.370141 0.367003 0.36389 0.3608 0.357733 0.35469 0.35167

poy/px 8.39821 8.46205 8.52614 8.59049 8.6551 8.71996 8.78509 8.85048 8.91613 8.98203 9.0482 9.11462 9.18131 9.24825 9.31545 9.38291 9.45064 9.51862 9.58685 9.65535 9.72411 9.79312 9.8624 9.93193 10.00173 10.07178 10.14209 10.21266 10.28349 10.35457 10.42592 10.49752 10.56939 10.64151 10.71389 10.78653 10.85943 10.93258 11.006 11.07967 11.15361 11.2278 11.30225 11.37695 11.45192

ME4621: Semester II 2006-2007

Mx 2.93 2.94 2.95 2.96 2.97 2.98 2.99 3

My 0.479463 0.478836 0.478215 0.477599 0.476989 0.476384 0.475785 0.475191

py/px 9.84905 9.91753 9.98625 10.0552 10.12438 10.1938 10.26345 10.33333

40 Vx/Vy and ρy/ρx 3.79167 3.80117 3.81062 3.82002 3.82937 3.83868 3.84794 3.85714

Ty/Tx 2.59755 2.60908 2.62064 2.63224 2.64387 2.65555 2.66726 2.67901

Ax*/Ay* and poy/pox 0.348674 0.345701 0.34275 0.339823 0.336919 0.334038 0.33118 0.328344

poy/px 11.52715 11.60263 11.67837 11.75438 11.83064 11.90715 11.98393 12.06096

ME4621: Semester II 2006-2007

41

EXPERIMENT #4 To:

All Groups

Subject:

Pump Performance and Scaling Law Verification

Experimental objectives Pumps are used to move liquids by converting mechanical power to fluid power. They are machines encountered in many aspects of everyday life and industry. For example, Power Plants and Chemical Plants could not run, cities like New Orleans would not exist, and swimming pools would be unusable without them. The human body also includes a pump (heart), which is critical in sustaining life. In this experiment you are required to determine through measurements the Head, Efficiency and Power characteristics (dependence on flow rate) of a centrifugal pump rotating at two different rotation speeds of your choosing. Keywords Centrifugal Pump Performance Rotor Speed Volumetric Flow Rate Pressure (Head) Efficiency Power Available Equipment Armfield Pump Unit Reading Assignment Read the Armfield Pump Operating Manual [1] carefully during your experimental planning session. Do not operate the unit without reading the manual. Also read from references [2] or [4] on rotating machinery (turbomachinery) and in detail from Chapter 4 from reference [3] on Centrifugal Pumps. Useful Information and Definitions Centrifugal Pumps (see Figure 1) add kinetic energy to a liquid entering the machine axially via rotating blades. Then they convert this kinetic energy into Pressure and discharge the fluid in the radial direction. The kinematics of the fluid at the inlet and exit of the pump rotor are represented by velocity triangles as illustrated in Figure 2.

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The power delivered to the fluid by a pump is reflected into an increase in Head (equivalent hydrostatic pressure or power per unit weight flow rate of the fluid). The relationship between Head (H) and Volumetric Flow Rate (Q) at a fixed rotation speed constitutes one of the pumps characteristics. Other pump characteristics include Power (P) as a function of Volumetric Flow Rate and Efficiency (η) as a function of Volumetric Flow Rate. An example of H-Q and η-Q characteristics is shown on Figure 3.

Figure 1: Schematic of simple centrifugal pump.

Figure 2: (a) Inlet and (b) outlet velocity triangles for the pump of Figure 1. Instructions 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Read the manual carefully and acquaint yourself with the locations and type of sensors. Connect the Armfield unit to the data acquisition unit Initialize the DAQ system Set the Pump experiment to run a single pump only (No dual modes in this experiment) Set the pump to a fixed RPM and vary the flow rate by closing and opening the gate valve For each flow rate, measure the Pressure rise. Repeat steps 5-6 for different RPM values Plot Head vs. Flowrate for each RPM value. Compute the values at other RPM using similarity laws and check if the experiment and similarity laws provide same results. The report should contain detailed description of the pump performance curves and also should address the calculations using similarity laws.

ME4621: Semester II 2006-2007 11.

43

If you have time, investigate the dual mode operation by running the two pumps in serial or parallel mode at a single RPM and compare with single mode operation (extra credit!)

Figure 3: A Typical Pump performance curve References [1] Armfield Pump Manual [2] Fox, R. W., and McDonald, A. T., Introduction to Fluid Mechanics, Third Edition, J. Wiley, 1985. [3] Logan, E., Jr., Turbomachinery, 2nd Edition, Dekker, 1985. [4] M. C. Potter and D. C. Wiggert: Mechanics of Fluids, Third Edition, Brooks/Cole, 2001. ISBN 0-534-37996-6; TA357.P725 2001

ME4621: Semester II 2006-2007

44

EXPERIMENT #5 To:

All Groups

Subject:

Double Pipe (Concentric) Heat Exchanger

Prepared by:

S. V. Ekkad

Experimental Objectives The process of heat exchange between two fluids that are at different temperatures and separated by a solid wall is achieved by a device termed as Heat Exchanger. Heat exchangers are typically classified according to flow arrangement and type of construction. The simplest heat exchanger is one where the hot and cold fluids move in the same or opposite directions in a concentric tube (or double pipe) construction. In the parallel-flow arrangement, the hot and cold fluids enter at the same end, flow in the same direction, and leave at the same end. In the counter-flow arrangement, the fluids enter at opposite ends, flow in opposite directions, and leave at opposite ends (see Figure 1). In this experiment, you are expected to determine the heat exchange performance of parallel flow and counter flow concentric pipe heat exchangers and to compare their performance. You will use the commercial pipe heat exchanger apparatus available in the laboratory. Flow rates and water temperatures of both hot and cold water can be measured at various points along the flow circuit. The apparatus can be operated in the parallel-flow or counter-flow modes. Present the temperature distribution of the heat exchanger pipe from inlet to exit for both cold and hot flows with both flow arrangements. Also calculate the overall coeffcient of heat transfer, U, and the effectiveness, ε, at different flow rates for both flow arrangements. Keywords Heat Exchanger Parallel-Flow Counter-Flow Effectiveness NTU Available Equipment Heat Exchanger Apparatus Thermocouple Readouts Reading Assignment Read Chapter 11, sections 11.1, 11.2, 11.3, and 11.4 from reference [1].

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Procedure 1. 2.

3. 4. 5. 6.

Calibrate the flow meters using a stop watch and a known volume collector bucket. Set valves for parallel flow heat exchanger arrangement. Set the hot water flow rate to its maximum. Adjust to the required cold flow rates and make temperature measurements for different constant flow rates. Set the cold water flow rate and wait for 8-10 minutes for the system to reach thermal equilibrium. Record temperatures at thermal equilibrium state. Repeat steps 2-4 for three other cold water flow rates. Repeat steps 2-5 for the counter flow heat exchanger arrangement

Figures 1 & 2 show the temperature distribution along the heat exchangers from inlet to exit for both hot water and cold water for both parallel and counter arrangements.

Fig. 1 Parallel Flow Heat Exchanger [1]

Fig. 2 Counter Flow Heat Exchanger [2]

ME4621: Semester II 2006-2007

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Results 1. 2. 3. 4. 5.

provide plot of temperature vs. heat transfer area calculate (∆T)mean for the total heat exchanger Calculate total heat transferred for each configuration and flowrate Calculate and plot overall U values for each heat exchanger configuration Plot effectiveness versus NTUmin

Discussions 1. 2.

Discuss the possible best results you can obtain for each exchanger configuration. Why are you not getting the outlet water temperatures to be equal? Discuss your results and explain them with physical understanding of the heat transfer phenomena. Discuss also discrepancies in your results.

References [1] Incropera, F. P, and DeWitt, D. P., Introduction to Heat Transfer, 3rd Ed., Wiley & Sons, New York.

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EXPERIMENT #6 To:

All Groups

Subject:

Unsteady Multi-Dimensional Conduction Experiment

Prepared by:

S. V. Ekkad

Experimental Objectives Many heat transfer problems are time-dependent and such Unsteady, or Transient, problems typically arise when the boundary conditions of a system are suddenly changed. For example, if the surface temperature of a system is altered, the temperature at each point of the system will begin to change. The changes will occur until a steady-state temperature distribution is reached. Consider a hot metal billet that is removed from a furnace and exposed to a cool air-stream or a cold metal billet suddenly exposed to a hot liquid. Energy transfer by conduction will occur to or from the surface of the billet to the interior of the metal piece until a steady-state condition is reached. Such examples are common in many industrial heating and cooling processes. In this experiment, we will use an unsteady conduction experiment to estimate the thermal conductivity of a known material. Typically, with no internal generation and the assumption of constant thermal conductivity, the transient conduction equation reduces to:

∂ 2T ∂x

2

=

1 ∂T α ∂t

with initial condition, T(x,0)=Ti, and boundary conditions of

∂T ∂x

=0 x =0

T x = L = T∞ where T (x=0) is at the core of the solid and T (x=L) is at the outer wall. Lets define a dimensionless form of temperature as

θ=

T − T∞ and expressing θ as a function of x, Fourier number, and Biot number. The Heisler Ti − T∞

charts in Appendix D of Ref. 1 are created for different metal shapes with different Biot numbers. The Heisler charts were created as an easy way of evaluating one-dimensional conduction and not for multi-dimensional conduction. (Fig. 1)

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Fig. 1 Typical Heisler chart representing the transient responses for a slab of thickness 2L [1] You will use the Armfield Transient Conduction Unit {ref. 2} available in the Thermal Science Laboratory. The Unit consists of a heated water bath with integral flow duct and external circulating pump to ensure that hot water flows past the solid shape under evaluation at constant velocity and temperature. Seven solid shapes are supplied, manufactured in three simple geometries and two materials. Each shape is instrumented with a thermocouple to measure the temperature at the center of the shape. Monitoring the temperature at the center of the shape allows for analysis of the heat flow using the appropriate transient temperature/heat flow charts. The solid shapes supplied are: Small brass cylinder Large brass cylinder Small stainless steel cylinder Brass sphere Stainless steel sphere Brass rectangular slab Stainless steel rectangular slab With the present experiment, several questions need to be answered. Questions to ask: 1. 2. 3. 4.

Is the constant temperature boundary condition at the model external wall valid? If the constant temperature boundary condition is not valid, how do you determine the convective heat transfer coefficient of the water flow? Of what use is the heat transfer coefficient in this experiment? Is the use of Heisler charts valid for each of the shapes studied in the experiment?

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Keywords Unsteady conduction Thermal conductivity Time-dependent Temperature boundary condition Available Equipment Armfield Transient Conduction Unit Thermocouples A/D Data Logger Unit and Computer Reading Assignment Read Chapter 5 from reference [1]. Also read the Armfield Unit Manual [2] carefully and thoroughly before operating the unit. Procedure 1. 2. 3. 4. 5. 6.

7.

Read the manual carefully. If you do not know something, ask the instructor technician. Switch on the water heater. Attach the requisite geometrical shape thermocouple to the data logger unit and then attach the shape to the immersion rod Let the shape stabilize at room temperature Insert the shape suddenly into the hot water bath (ensure before this that the hot water is at constant temperature) Monitor the temperature of the shape and the thermocouple placed in the water adjacent to the shape. This is required to provide an accurate datum for measurement of time since immersion in the hot water. Repeat steps 3-6 for each of the other six shapes.

Results 1. 2. 3. 4.

Estimate the thermal conductivity of the material for each shape. Provide the temperature distribution versus time of the center of the shape Compare the effects of shape for same material Compare the effect of material for same shape

Discussions 1. 2. 3.

Discuss in detail the physical effects of transient conduction in heat treatment processes Discuss the effect of shape and material on conduction characteristics Discuss the differences between actual and experimental values for thermal conductivity for each shape and material and focus on the reasons for agreements and disagreements.

References 1. 2.

Incropera, F. P., and DeWitt, D. P., Introduction to Heat Transfer, 3rd Ed., Wiley & Sons, New York Armfield Transient Conduction Unit Manual, Thermal Science Laboratory.

ME4621: Semester II 2006-2007

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APPENDIX I LABORATORY PLANNING FORM

DATE:_____________

SECTION:__ _______

GROUP:___________________

EXPERIMENT NUMBER/TITLE:____________________________________________ GROUP MEMBERS/TASKS:___________________________________

Leader

_____________________________________ _____________________________________ _____________________________________ _____________________________________ _____________________________________ BRIEF STATEMENT OF OBJECTIVE:_______________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ TEST APPARATUS:

___________________________________________________

_____________________________________________________________ _____________________________________________________________ MEASURED QUANTITIES:________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________

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INSTRUMENTATION: ___________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ _____________________________________________________________ SKETCH OF APPARATUS AND INSTRUMENTATION SET-UP:

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STEP BY STEP LABORATORY PROCEDURE

_____________________________

______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ DATA REDUCTION:

___________________________________________________

______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ UNCERTAINTY ANALYSIS:

_______________________________________

______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________

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APPENDIX II FULL-FORMAT GROUP REPORT (1100 points total) 1.

Cover Page a. Standard engineering laboratory cover page (see Appendix V) b. All spaces must be typed or lettered neatly in black ink

2.

Title-Page Must contain the following: a.

b.

Identity information, i.e. Course (ME4621), section number (1, 2, 3, or 4), group number (1, 2, etc.), and experiment number Title of experiment Names of the group members and their task assignment number Execution date of the experiment Report submission date Abstract Think of the abstract as the part of your entire report that will be read first by an extremely busy person seeking technical information. On the basis of the abstract such a person will decide to read the rest of your report or file it into oblivion. Therefore the abstract should be a brief and succinct statement of the entire experiment. It should contain: Objective of the experiment Overview of the experimental methodology Results achieved conclusions/recommendations

You may find an example of the Title-page format at the end of this Appendix. 3.

Introduction a. b.

4.

Brief background and applications of the material to be investigated. This may include historical information and should certainly include references. Last paragraph should be a concise statement of the experimental objectives.

Theory a. b. c.

Explanation of physical principles involved in the investigation Presentation of equations to be used in the analysis. Qualitative presentation of the results of other investigators and/or theoretical predictions (when applicable).

ME4621: Semester II 2006-2007 5.

Experimental Apparatus and Instrumentation a. b.

Description of experimental set-up (including sketch or picture of apparatus and instrumentation as used in the experiment). Justification for the use of instrumentation tied to the quantities that had to be measured. For example: 1.

2.

3. c.

6.

54

A Hot-film anemometer was used for the measurement of the velocity profiles because it is more accurate than a pitot-static probe An electronic manometer was used to measure the free-stream pressure because it was more convenient and less subject to human reading errors. etc......

Additional details on specific items of apparatus and instrumentation if they are non-standard, unique or applied in an unusual fashion.

Experimental Procedure This is an itemized list of the steps required to acquire the necessary experimental data.

7.

Uncertainty analysis Present uncertainty analysis on all calculated quantities. Give uncertainty estimates for all calculated quantities based on experimental error estimates for every measured quantity.

8.

Presentation of Results a. b. c.

9.

Analysis and Discussion of Results a. b. c.

10.

Graphical or pictorial presentation of results with accompanying descriptions of what they represent (see example in Appendix IV) Comparison of your results with those of other investigators and theories developed in section 4 of the report. Tabular data may be presented here or in an appendix, whichever is fitting for the particular experiment.

Physical interpretation of the results presented in the previous section of the report. Discussion on the significance of the presented results. Give explanations of any discrepancies between your results and the theoretical predictions as well as the results of other investigations existing in the literature.

Conclusions and Recommendations a. b.

Comment on the outcome of the experiment. Identify probable sources of error and give suggestions on how the experiment can be changed to produce better results.

ME4621: Semester II 2006-2007 c.

11.

55

Give suggestions on how the experiment can be extended to produce useful results and further the investigation of the observed phenomena.

Reference Material a.

References This is a listing of external references which are actually cited in the text of the report. They should be listed sequentially in the order cited according to standard bibliographic form. Here is an example of the preferred format: 1. Mac Cormack, R.W. "The Effect of Viscosity on Hypervelocity Impact Crating", AIAA Paper 69-134, Reno, Nevada, January, 1969. 2. Roache, P.J., Computational Fluid Dynamics, Hermosa Publishers, Albuquerque, New Mexico, 1972, pp. 133-192.

b.

12.

Bibliography This is a listing of external materials which are used in the preparation of the report but are not specifically cited in the text of the report.

Appendices a.

Sample calculations of all data reduction and presentation procedures should be given here. These sample calculations should include one of every calculation which is performed in preparing the report. They should be arranged as follows: 1.

2. b.

Calculated quantity (e.g. Determination of velocity from pitot-static readings) Equation used Definitions of variables with units Numerical values of known quantities in equation Numerical result Next calculated quantity etc........

The actual Planning Form and Raw Data Sheet generated in the laboratory.

BRIEF FORMAT INDIVIDUAL REPORT 1. 2. 3. 4. 5. 6.

Title Page - one page Objective of the Experiment - 1/2 page Apparatus and instrumentation - 1/2 page Experimental Procedure - 1 page Discussion of results and significance - 1/2 page Evaluation of other group members

Do not report results in detail and do not include any plots. Remember, this report ought to show that you understand the experiment and its objectives!

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TITLE PAGE EXAMPLE

ME4621-2-3-1

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APPENDIX III SAMPLE PLANNING FORM

DATE: Sept. 1,1910________ SECTION: ____1____ GROUP: ________A________ EXPERIMENT NUMBER/TITLE: 1-Boundary Layer Velocity Profiles_______________ GROUP MEMBERS/TASKS:

Ludwig Prandtl - 1______________

Leader

Osborne Reynolds - 2___________ Theodore von Karman - 3________ Geoffrey I. Taylor - 4____________ ______________________________

BRIEF STATEMENT OF OBJECTIVE: Determine the velocity profiles within a flat-plate boundary layer at different distances downstream of the leading edge.______________ TEST APPARATUS:

Subsonic Wind Tunnel_________________________________ Flat Plate___________________________________________ Traversing Mechanism_________________________________

MEASURED QUANTITIES: Static, P, and Stagnation Pressure, P0. ________________ Temperature, T._____________________________________ Velocity, V, (Calculated).______________________________ ___________________________________________________ INSTRUMENTATION: Pitot-tube rack ______________________________________ Multiple tube manometer_______________________________ Thermometer_______________________________________ Pitot-static tube_____________________________________ ___________________________________________________

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SKETCH OF APPARATUS AND INSTRUMENTATION SET-UP:

STEP BY STEP LABORATORY PROCEDURE 1. Set up experiment and equipment as shown in sketch,_________________________ 2. Set wind tunnel speed at 50 ft/sec_________________________________________ 3. Place Pitot-static tube half-way between flat plate and ceiling___________________ of wind tunnel; move slightly up and then down making sure reading________________ does not change with this small change in position______________________________ 4. Record multi-tube manometer levels and temperature_________________________ 5. Move rack closer to leading edge by 1cm and repeat step 4._____________________ 6. Repeat steps 4 and 5 until readings from all tubes of the rack are the same_________ DATA REDUCTION: Find density of air from the temperature reading; Convert_______ manometer levels into pressure; Find dynamic pressures corresponding to each_______ rack-tube and the pitot-static tube (sub-tract static pressures from Pitot-tube stagnation Pressure); Find velocities from Bernoulli's equation._____________________________ UNCERTAINTY ANALYSIS:

dρ/ρ=[(dP/P)2+(dT/T)2]0×5, dP/P=[(dh/h)2+(dρm/ρm)2]0×5___

dV/V=0.5(1-P/P0)-1[(dP0/P0)2+(P/P0)2(dP/P)2+(1-P/P0)2(dρ/ρ)2]0×5__________________ h: manometer level, ρm: manometer fluid density, ρ: air density_____________________

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APPENDIX IV EXAMPLE FIGURE

Figure 1:

Critical mass flux as a function of pressure for three different qualities. Experimental data and predictions of the present analysis. The value of the quality for all the experimental points presented is within 5% of the value shown by the corresponding label.

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APPENDIX V LABORATORY REPORT COVER PAGE

COURSE

Experiment No.

SECTION

Group No.

REPORT TITLE

BY

ASSOCIATES

PERFORMED RECEIVED RETURNED COMPLETED

MECHANICAL ENGINEERING DEPARTMENT Louisiana State University Baton Rouge, Louisiana