CITY UNIVERSITY

SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES

PART I

AERONAUTICAL ENGINEERING AIR TRANSPORT ENGINEERING

AUTOMOTIVE AND MOTORSPORT ENGINEERING ENERGY ENGINEERING

MECHANICAL ENGINEERING

ENGINEERING LABORATORY

INSTRUCTION BOOKLET

CONTENTS Page Instructions to Students 2 Safety in Laboratories 3 Instructions for Writing Reports 4 Electrical, Electronic and Information Engineering Uncertainties in Measurement 5 Transistor Characteristics 9 Fluid Mechanics Fluid Flow in a duct of Varying Cross Section 12 Engineering Mechanics Trifilar Suspension 14 Synchromesh gearbox 16 Rolling Wheel 17 Strength of Materials Tensile Test 19 Thermodynamics

The determination of brake power, brake thermal efficiency, air-fuel ratio, 21 and engine volumetric efficiency in a diesel engine

Materials Science Formative Materials Laboratory 24 Aerodynamics Pressure Distribution around a Symmetrical Aerofoil 32 Date of Issue: September 2008

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CITY UNIVERSITY SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES

PART 1 – ENGINEERING LABORATORY

INSTRUCTIONS TO STUDENTS

General Guidance Each student will attend laboratory classes as scheduled on the Laboratory Rota. A total of 6 experiments will be performed. Each student must possess a hardbacked log-book, which may be purchased from the University bookshop. This log-book must be brought to the laboratory for every laboratory class. In the laboratory each student must keep a continuous record in the log-book as the experiment is performed. The practice of plotting graphs of measured variables in the log-book as the experiment is done should be followed. Usually one member of the group will be assigned to this task. Well proportioned free hand sketches or diagrams of equipment and mechanisms should be made in the log-book during the laboratory class. At the end of the class the log-book must be signed by the lecturer in charge. Careful attention must be given to warnings against the harmful treatment of instruments and damaging or unsafe procedures. Safety consciousness must be cultivated at all times. Each student must read the section Safety in Laboratories (see next Section) and must abide by these instructions. Coursework Requirements Two of the experiments must be written up as full length reports and 4 as brief reports. To pass this course students must attain 40 %. Note that it advisable to submit a full set of reports; it is difficult to make up the loss of marks caused by omissions. Missing the scheduled laboratory class will normally result in a zero mark for the particular experiment. If a laboratory class is missed for whatever reasons, the student should contact the lecturer in charge immediately. The laboratory classes can only be rearranged in case of an acceptable excuse supported by appropriate evidence (from GP, etc). Submission of Reports With a few exceptions, any laboratory experiment may be written up as a full length report; it is advisable to do at least one full length report during the first term. Both full length and brief style reports must be written on A4 loose leaf paper and fixed in a standard buff report folder. Full length reports should be submitted to the lecturer concerned within three weeks of the date of the laboratory class and brief or letter style reports within two weeks. Marked reports will either be returned during lecture periods or be available for collection from a member of staff. The log-book must not be handed in. Assessment of Reports Credit will be given for literacy, numeracy, clarity of illustrations and organisation of the report. It should be borne in mind that a large proportion of marks will be awarded for the critical appraisal and understanding displayed in the “Discussion” and “Conclusion” sections of your report. The instructions for writing reports (see later) should be followed closely otherwise marks may be deducted.

2

SAFETY IN LABORATORIES In co-operation with the Health and Safety at Work Act 1974

and the University Safety Regulations

Introduction In the interests of safety it is necessary for all students to have their names recorded for attendance in laboratory work. Students are expected to conduct themselves in a responsible manner at all times. Thoughtlessness or careless behaviour may endanger others. All accidents, however slight, must be reported immediately to the Laboratory Technician Supervisor. Regulations 1. A student may not work in a laboratory unless at least one other person is present. Permission must be

obtained from the School of Engineering’s Safety Officer, Mr Rod Stokes, before working in a laboratory or workshop outside scheduled class times.

2. Smoking is forbidden at all times. 3. The wearing of scarves and loose clothing is forbidden. Neckties must be secured to prevent danger of

entanglement in machinery and equipment. Loose hanging hair must be secured to prevent entanglement. Briefcases, books, coats, umbrellas, etc., must be placed in such a location as to prevent tripping-up of personnel.

4. The unauthorised handling of equipment is forbidden. With the exception of personnel using authorised

equipment under the supervision of the lecturer in charge, students must not attempt to:

(a) Replenish fuel tanks. (b) Alter the settings of power plant controls, i.e. speeds, feeds, loads, frequencies, etc. (c) Alter the settings of valves in steam, water and air lines. (d) Alter electrical instrumentation settings or circuits. (e) Use/handle any hazardous substance. (f) Perform any other hazardous operation.

5. Spillages of all substances; in particular, mercury, petrol, diesel oil, and all chemical compounds, must

be reported to the Laboratory Technician Supervisor immediately. 6. Do not obstruct exits, passages or walkways. 7. Students should note the positions of Exits, Emergency Exits and Fire Extinguisher Points on entering

the workshop laboratory. 8. Students should not enter the void areas under CXLG18 and CM CXLG19. 9. Should the Fire Alarm Bells sound, leave the laboratory immediately and proceed to the nearest Fire

Exit. DO NOT ENTER A LIFT. 10. The Health and Safety at Work Act imposed a “duty of care” on all members of the University,

including student members. The School Safety Officer must be informed of any hazardous or potentially hazardous situation.

3

INSTRUCTIONS FOR WRITING REPORTS

Marks may be deducted if these instructions are not followed

Full length reports should contain 1000-2000 words and conform to the following layout: Title, Abstract, Introduction, Theory, Experimental arrangements, Results, Discussion, Conclusions, References and Appendices (including specimen calculation and raw data). Figures may be inserted in the text near where referred to or placed together at the very end of the report. Brief reports should contain 500-1000 words and conform to the following layout: Title, Introduction, Results, Discussion, Conclusions, Appendices, (specimen calculation and raw data) and Figures. Any relevant theory should be written into the Introduction of a brief report, although not as much detail is required as in the Theory section of a full length report. The Abstract should include brief details of results and conclusions as well as the objective of the experiment. It is better to write this last rather than first. The Introduction should include an outline of the background to the experiment to be made and a clearly stated objective. The laboratory instruction sheet should not be used as an introduction or used in the main report. Some initiative is required, and the laboratory instruction sheet should not be simply copied into the report. Theory is not always necessary and its inclusion will depend on the experiment to be done. It should contain only the main equations; intermediate steps should be omitted and verbal description used to link these equations. Results should not include tables of raw or unprocessed data which are contained in the log-book but these should be included in an Appendix; any results which are represented graphically should not be included in Tables. A specimen calculation for one representative data point should be included, preferably in an Appendix. The unit of any dimensional quantity should always be used. The Discussion should deal with the results obtained and should not be regarded as an extension of the introduction. An estimate of the accuracy of the results and an appropriate error analysis should be included. The Conclusions should summarise the whole report and some conclusion should be reached; it must not be an extension of the discussion. It may be helpful to consider the conclusion as answering questions raised in the introduction. All Figures including diagrams, graphs and sketches should be labelled consecutively, Fig.1, Fig.2, etc. For graphs, a brief title must be included and axes labelled to show quantity and units used. Figures and tables should have a caption (ie. a brief title). Experimental points must be marked by any of the following symbols 0 Δ + x ; dots should never be used. The different symbols are used to denote different conditions on the same graph. Unless printing the report in colour, avoid the use of different colours since they do not photocopy well. Also, black and white photocopies will lose all colour detail. Theory should be denoted by a continuous line, dashed lines being used for joining up experimental points if required. More relevant material on writing reports and error analysis can be found on the CitySpace – ME1104 Engineering Laboratory, which can be accessed internally as well as externally.

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CITY UNIVERSITY

SCHOOL OF ENGINEERING

G1 UNCERTAINTIES IN MEASUREMENT

The object of this test is to measure resistance by three methods:- A Using a voltmeter and an ammeter, B. By substitution, C. Using a Wheatstone Bridge. Also to assess the uncertainty of each measurement (i.e. the range in which the resistance may lie), and to verify that the three results are compatible, (i.e. that there is a common intersection of the three ranges). Apparatus: A, B and C Metal oxide or carbon compound resistor R of known tolerance, A and B 100mA moving coil ammeter A only 10V moving coil voltmeter B only Standard resistance box with tolerance ±0.2% of setting. C only Wheatstone Bridge with tolerance ±0.1% of setting. Procedure: PART A. Using a voltmeter and an ammeter. 1. Connect the circuit as shown in Fig.1, wiring the voltmeter last.

2. Set the power supply output to minimum and have the circuit checked by a member of staff before

switching on. 3. Switch on and set the output voltage such that the voltmeter and ammeter readings are well up the scale

(to minimise the constructional error as a percentage of the indication). 4. Take one reading of each instrument to get V and I’. Since I’ is not the current through R we must

correct it by substracting Iv, where:

( ) FSDV/VIV ×Ω

=

Hence obtain I, and compare your value with the change in currents which are observed by disconnecting the voltmeter.

5. Each meter has a Constructional Uncertainty. For the voltmeter, a single-range instrument, this is ±1.0% of PSD. For the ammeter, a multi-range instrument, this is ±1.5% of FSD.

6. Each meter has a Reading Uncertainty, which is about ±1/5 or ±1/10 of a small scale division.

5

7. Nominally, R=V/I. Allowing for the two uncertainties it follows that:

ty Uncertain Reading-ty UncertainonalConstructi-Ity UncertainReadingty UncertainonalConstructiVRMAX

++=

ty Uncertain Readingty UncertainonalConstructiIty UncertainReadingty UncertainonalConstructiVRMIN ++

−−=

8. Use these two results to express the resistance in the form Ro+δRΩ. PART B. Substitution method – comparison with a standard. 1. Connect the circuit as shown in Fig.2., making sure that you include the 100Ω resistor.

2. Set the power supply output to minimum and the standard resistance to maximum. Turn on the supply

with the switch set to position ‘a’ and adjust the output to give the ammeter mid-scale deflection on the 30mA range.

3. Switch to position ‘b’ and adjust the standard resistance until the current is the same as before. Remember that the ammeter is used only as an indicator in Part B.

4. Determine the range over which the standard resistance may be adjusted without noticeably affecting the current reading. This is called the Determination Uncertainty. Express the resistance in the form Ro +δRΩ, where Ro is the centre of this uncertainty range and R is half the value of the range.

5. You are comparing the test resistance with that of a standard which has a Constructional Uncertainty, and this must be taken into account by adding ±0.2% of its setting to the uncertainty range.

6. Repeat this with the ammeter showing near full-scale deflection and again with the minimum deflection using the 100mA range. Remember that the exact value of current is irrelevant and it is important only that the pointer should return to its original position after each switch change.

PART C. Wheatstone Bridge – Comparison with a standard. 1. The circuit shown in Fig.3 is already connected within the portable instrument, and it is necessary only

to connect the resistance to be measured to the terminals marks ‘X’. 2. Set the ratio arms P and Q to be 1:1, using any of the four available values. 3. Press the ‘Battery’ Key and observe the direction and amount of deflection on the galvanometer. 4. Adjust the decade dials, press the ‘Battery’ key again and find whether the deflection is greater or less. 5. Repeat this until you have obtained an approximate balance point, shown by minimum deflection of the galvanometer pointer.

6

6. While holding the battery key down, press the ‘Full Sensitivity’ switch so that any out-of-balance current is effectively increased, then make a final adjustment of the dials to establish the best balance position.

7. Change to P/Q ratio to 1:10, set the dials to 10 times the balance value and repeat the procedure to establish final balance.

8. Assess the Determination Uncertainty as in Part B. and remember to take account of the Constructional Uncertainty of the bridge by adding in ±0.2% of its setting to the uncertainty range.

Conclusions: 1. Compare the results of the three methods A, B and C with the resistance specification using a bar chart

to show the mean resistance, the range of uncertainty and the common intersection, if any. 2. For clarity, use only the resitance range with ±10% of the nominal value. 3. Treat the three results of Part B separately to show how accuracy of measurement of resistance is

related to the size of the pointer deflection. 4. Comment on the range, accuracy and sensitivity of the methods. Appendix: The resistance of a conductor is defined as the ratio of the potential across it in volts to the current through it in amps. These are measured by voltmeter and ammeter in Part A, and the accuracy of the measurement obtained depends on (a) the Constructional Uncertainty of the instruments (set by the manufacturer), (b) The Reading Uncertainty (estimated by the observer). (c) The Systematic Error (how much the original conditions are changed by introducing the instruments

into the circuit).

The Classified Accuracy of the instruments used in this experiment is ±1% of PSD for single-range and ±1.5% of PSD for multi-range instruments (See B.S. 89). That means that the manufacturer guarantees the actual voltage or current to be within the given tolerance at any point on the scale. So, for example, if the indication is 50mA on the 100 mA range of the multi-range ammeter, then the actual current is between 48.5mA and 51.5mA. The Reading Uncertainty depends effectively on the width of the scale markings and their distance apart. The observer can estimate this as a fraction of a division, usually ±1/5 or ±1/1/0 depending on the instrument used. The Systematic Uncertainty depends on the manner of connection of the meters so, for example, in Fig.4. the ammeter reads the true current through the resistor but the voltmeter reads the voltage across resistor and ammeter, and in Fig.5. the voltmeter reads the true voltage across the resistor but the ammeter reads the current through the voltmeter as well as the resistor.

7

It is easier to make an allowance for the voltmeter current, so this is done in the experiment. An alternative method of measuring resistance is to make a comparison with a known resistance and accuracy. Here the accuracy obtained depends on (a) the smallest change which can be made in the standard resistance, or the smallest change which can be

detected, whichever is the larger. (b) the Constructional Uncertainty of the standard resistance. Detection of current change depends on the sensitivity of the axmeter, and this is low because the instrument has to carry total circuit current. For the axmeter used the deflection is about 1mm per mA on the 100 mA range. It is essential in this method that the supply is stable during testing, since any fluctuation between tests will affect the results. The Wheatstone Bridge, as its name implies, uses a bridge circuit. The current passing through the galvanometer is dependent on the values of the resistances which form the arms and is reduced to zero when the bridge is balanced. This is therefore called a Null Method. Because the detector carries only the out-of-balance current it can be made much more sensitive, usually about 1mm per μA. The ratio arms can be set to 10Ω, 100Ω, 1,000Ω. or 10,000Ω, the adjustable dial decade resistances be set to any value between 1Ω and 9999Ω in steps of 1Ω. All of the bridge resistances are made to close tolerances, giving the instrument an overall Constructional Uncertainty of ±0.1% of dial setting. The colour code is a method of identifying the resistive value of a component by using coloured bands. In this experiment the resistor being tested has four bands; the group of three indicate the most significant digit, the second most significant and the number of following zeroes, and the single band indicates the tolerance. It is not necessary to learn the colour code but it is useful to understand how it works. The colours used are:

Black = 0 Brown = 1 Red = 2 Orange = 3 Yellow = 4 Green = 5 Blue = 6 Violet = 7 Grey = 8 White = 9

For example, a resistor carrying the code orange, white, yellow with a tolerance band or red has a nominal value of 3 9 0000, or 390,000Ω ±2%. Further reading on measurement I. Topping 001.434 J.P. Holman 001.421 Brinkworth 001.434 N.C.Barford 001.422 BAR

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CITY UNIVERSITY SCHOOL OF ENGINEERING

ET2 TRANSISTOR CHARACTERISTICS

The object of this test is to measure the small-signal current gain and the output characteristics of a transistor. Apparatus: Chassis with ZTX 300 transistor, 3mA And 50μA moving coil ammeters, 10V moving coil voltmeter. Circuit:

Broken lines are connections to be made.

Schematic complete circuit

9

Procedure: 1) Complete the circuit by making the dotted connections shown in the diagram. 2) Note that the 50μA meter can easily be damaged, so make sure that the circuit is checked by a member

of staff before the supply is switched on. 3) The base current IB can be varied by potentiometer R1 and the collector-emitter voltage VCE by R3,

although the controls are not independent. A. Determination of current gain 1) Take readings of IC and IB keeping VCE constant at 2V and plot a graph of IC against IB. 2) The slope of the curve at any point is the small-signal current gain of the transistor in the common-

emitter connection (usually denoted by hfe). Measure the slope at the point IC=1mA. The manufacturers of the ZTX300 quote the dc current gain as being between 50 and 300 at IC=10mA, VCE=6V, and the gain falls to about 60% of these values at IC=1mA.

B. Measurement of output characteristics 1. Take readings of VCE and IC with IB constant at several values up to 50μA and for the full range of

VCE from 0 to 10V. Note that for each value of IB there is little variation in IC when VCE is greater than 0.5V.

2. Disconnect the 50μA meter (so that IB = 0) and take a further set of readings of VCE and IC. 3. Plot IC against VCE for each value of IB on a single sheet. The family of curves obtained is known as the

output characteristics of the transistor. 4. Assume the transistor is used in a simple common-emitter amplifier circuit with a collector load resistor

of 3kΩ. Draw a load line on the output characteristics and suggest a suitable operating point for the transistor. What would be the maximum r.m.s. signal voltage available at the collector?

Appendix Transistors are made from crystals of semiconducting materials, the most common being silicon and germanium. Atoms of these elements have 4 valency electrons in their outermost shell and in a crystal each atom shares its 4 valency electrons with 4 equidistant adjacent atoms. Conduction is made possible by the removal from an atom of an electron (by thermal or electric forces) which can then move relatively freely through the crystal structure. By the removal of an electron a “hole” is created in the crystal structure which can effectively move to an adjacent atom by the movement of an electron in the opposite direction. Thus conduction is possible by the movement of electrons and holes. The conductivity of semi conducting materials can be increased by the addition of impurity atoms with 5 or 3 valency electrons. If impurity atoms with 5 valency electrons are added, there is a surplus of electrons which therefore carry the majority of the current, and the semiconductor is called n-type. If atoms with 3 valency electrons are added, there are additional holes in the crystal structure; the majority carriers are therefore holes and the semiconductor is p-type. A junction between p-type and n-type regions in a crystal acts as a rectifier. If the junction is forward biased, i.e. the p-region is made positive with respect to the n-region, the holes from the p-region and electrons from the n-region can easily cross the junction, the resulting current rising rapidly as the bias voltage is increased. If the junction is reverse biased, majority carriers are prevented from crossing the junction and the current of minority carriers is very small.

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A transistor consists of a thin base region of one type of semiconductor between two regions of the opposite type known as the emitter and the collector. The figure shows each type diagramatically with the usual circuit symbols. The arrow on the emitter denotes the direction of positive current.

Consider the n-p-n transistor:- The base emitter junction is normally forward biased so that electrons flow from the emitter into the base. The collector is made positive with respect to the base so that most of the electrons in the base are attracted to the collector and the base current is relatively small. Increasing the collector voltage has little effect on the collector current since the number of electrons available depends on the base-emitter voltage. Thus varying the base current and hence the base-emitter voltage procedures proportional variations in the much larger collector current. If a load resistance is connected in series with the collector, variations in collector current produce corresponding variations in the voltage across the load. This is the basis of a transistor amplifier. Similar considerations apply to the p-n-p transistor, except that the supply voltage is of opposite polarity and the current carriers are holes.

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CITY UNIVERSITY

SCHOOL OF ENGINEERING

Fluid flow in a duct of varying cross-section

Introduction The purpose of this experiment is to demonstrate the relation between pressure and fluid velocity in a duct of varying cross-section. In this case the duct consists of a pipe of constant diameter, then a short contraction to a narrow throat followed by a long diffuser and finally a pipe of the same size as the original one. This arrangement is called a Venturi and can be used for the measurement of flow rate but the general arrangement, i.e. contraction followed by diffuser typifies many situations from flow in a pipeline to flow over a wing. The relationships involved are the continuity equation and Bernoulli’s theorem. The continuity equation expresses the idea that the fluid must remain continuous and is essentially a statement of the conversation of mass. For an incompressible flow, involving a liquid or a gas at low velocity, the continuity equation is:

A v = const. = Q (1) Where A is cross-sectional area, v mean velocity and Q is the volumetric flow rate. Thus the velocity is inversely proportional to the duct cross-sectional area. Bernoulli’s theorem or equation expresses the principle of conservation of energy for a steady flow but the energy involved is restricted to mechanical energy only. It is:

.constv21gzP 2 =++

ρ (2)

Where p is static pressure, ρ density, z elevation above an arbitrary datum and v is fluid velocity. The first term is the fictitious potential energy due to pressure per unit mass, the second term is the gravitational potential energy per unit mass and the third term is the kinetic energy per unit mass. The equation applies strictly only when the flow is inviscid or frictionless, but can be applied to real flows if proper allowance is made for losses, i.e. irreversible conversion of mechanical energy into heat. For this experiment, the duct is horizontal so gravitational effects are absent and the gz term disappears. It is convenient to express the static pressure p as an equivalent head of liquid h (=p/ρg). So Bernoulli’s equation becomes

const.2gvh

2

=+ (3)

The Experiment Study the apparatus and make a sketch. Adjust the flow rate to 44 l/min and read the manometer heights h1 to h10. Repeat for flow rates of 34 and 24 l/min. The pressure tapping locations and corresponding internal diameters of the duct are shown below: Tapping No.

1 2 3 4 5 6 7 8 9 10

Distance x/mm

0

80

122

164

238

312

386

460

534

607

Diameter d/mm

41

41

28

15.5

21.4

27.8

34.1

40.5

40.5

40.5

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Calculations and graphs Calculate the velocities v1 and v10 using the continuity equation (1) and the information in the table above. Plot graphs of: i) (hn - h1) versus x

ii) 21

1n

v)h2g(h −

versus x

iii) ⎥⎥⎦

⎤

⎢⎢⎣

⎡−

⎭⎬⎫

⎩⎨⎧

+− 1

vv

v)h2g(h

2

1

n21

1n versus x

For n = 1 to 10. Use different symbols for each flow rate. Graph (i) represents the change in static head along the duct for each flow rate separately. Graph (ii) uses a normalised static head and shows that the variations are actually very similar. For a frictionless fluid they would be identical. Superimpose the ideal static head variation given by 1-(d1/dn)4. Graph (iii) shows the variation of normalised total head along the duct, i.e. the constant in equation (3). The Report When writing the Introduction for a brief report, it is necessary only to précis the laboratory instruction sheet but for a full length report it will be necessary to do some background reading of the relevant sections of the textbook. When writing the Discussion, comment on the physical significance of the results, e.g. when a fluid is accelerated to a higher velocity the pressure is reduced. Comment on the comparison between theory and experiment shown in graph (ii) and on the significance of the change in total head shown in Graph (iii). Estimate the accuracy of a few selected data points, e.g. at the throat. Perform an appropriate error analysis. Reference Schmidt, Henderson and Wolgemuth. Introduction to Thermal Sciences. Sections 5.3, 6.3 and 7.5.1.

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City University SCHOOL OF ENGINEERING

MECHANICAL ENGINEERING LABORATORY – ENGINEERING MECHANICS

Title The trifilar suspension. Type of Report The laboratory supervisor will specify whether the report is to be formal or informal. Introduction The trifilar suspension is used to determine the moment of inertia of a body about an axis passing through its mass centre. The apparatus consists of a circular platform suspended by three equi-spaced wires of equal length. The body under consideration is placed with its mass centre exactly over the centre of the platform. The platform is given a small rotational displacement about the vertical axis through its centre, and is released. The periodic time of the subsequent motion is obtained by measuring the time taken to complete a definite number of oscillations. Then from the formula given below, the moment of inertia of the body on the platform can be calculated. The periodic time is given by the expression

⎟⎟⎠

⎞⎜⎜⎝

⎛++

⋅=MMII

rL2 T

0

02g

π

Where L = Length of the suspension wires, r = Radius from the centre of the platform to the attachment points of the suspension wires, Io = Moment of inertia of platform, Mo = Mass of platform, I = Moment of inertia of body, M = Mass of body, g = Acceleration due to gravity. Objective To obtain a value for the moment of inertia of a connecting rod about an axis through the centre of mass. Experimental Equipment Two specimens are to bee used: 1. a uniform bar of rectangular or circular cross-section, 2. a connecting rod. Scales, stop-watch, calipers, metre rule. Procedure Weigh each specimen. Locate the mass centre of the bar and of the connecting rod by balancing it on a knife edge. As the bar is of a regular shape, a value for the moment of inertia can be calculated and compared with that obtained using the trifilar suspension. For the connecting rod this is not possible so a second estimate is obtained by swinging the connecting rod as a compound pendulum, in the following way:

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Suspend the connecting rod from a knife edge by means of the small-end bearing. Give it a small angular displacement from the vertical, and release it. Obtain the periodic time of the subsequent motion. Repeat this procedure with the connecting rod suspended from the knife edge in the big-end bearing. Then measure the position of the mass centre relative to the two points of suspension. Then the moment of inertia with respect to the point of suspension is given by the expression

lgM4TI 2

2

⋅⋅⋅=π

Where T = Periodic time, M = Mass g = Acceleration due to gravity, l = Distance from point of suspension to mass centre. Notes on Experimental Work 1. The mass of the platform is 1.125 kg or 1.252 kg with the V pieces. 2. Io may be measured by timing the oscillations of the platform when unloaded. 3. The brass V-shaped supports must remain with the platform. If they obstruct the placing of a specimen,

lift them out and insert them underneath the platform. Notes on Theoretical Work 1. Moment of inertia (Iyy) of a rectangular bar about the axis yy through G is given by

( )22yy w

12MI += l

2. Parallel axes theorem applied to the bar 2

yyy1y1 mdII += Where d = l/2.

The parallel axes theorem should be applied to the connecting rod to relate moment of inertia through the centre of mass G to the moments of inertia through the axes of suspension in the compound pendulum test. Report 1. Include all readings and results in your report. 2. Compare the values of I obtained experimentally and by the use of

Standard results in the case of the regular body. 3. Compare the values of I obtained for the connecting rod by the trifilar suspension method and the

compound pendulum method. 4. There should be only small discrepancies in the results; postulate causes. A quantitative analysis of the

errors should be made. 5. Give an example of another engineering object for which the trifilar suspension technique would be

useful. Reference Anderson, J.S. and Bratos-Anderson, M., Solving problem in vibrations, Longman Scientific, 1987, p.16

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City University

SCHOOL OF ENGINEERING

MECHANICAL ENGINEERING LABORATORY – ENGINEERING MECHANICS

Title The synchromesh gearbox. Type of Report The laboratory supervisor will specify whether the report is to be formal or informal. Introduction The modern automobile gearbox is the result of many years of research and development. Two of the stages in this development are available in the laboratory in the form of an old ‘crash’ gearbox and a more recent synchromesh constant mesh gearbox from a Ford ‘Capri’. Objective To write a clear, illustrated description of a modern synchromesh gearbox. This should include good engineering sketches (or drawings) of the complete gerabox, and of such sub-assemblies or details as your consider desirable for a full explanation of the functions of the important components. A visual comparison should be made with the ‘crash’gearbox. The method of gear selection, and the ‘flow path’ for each gear should be described and illustrated. Calculations For each of the four forward gears, and reverse,

The ratio: srevolutionshaft output srevolutionshaft input

Should be found both by direct counting and by calculation based on the numbers of teeth on the gear wheels which are actually transmitting the drive. Reference AA Book of the Car, Drive Publications.

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City University SCHOOL OF ENGINEERING

MECHANICAL ENGINEERING LABORATORY – ENGINEERING MECHANICS

Title The rolling wheel. Type of Report The laboratory supervisor will specify whether the report is to be formal or informal. Introduction The rolling wheel experiment is concerned with the simultaneous translational and rotational motion of a body under the action of constant forces. The ‘bodies’ used are cylindrical wheels mounted on relatively small axles, and a small turbine rotor. From measurements of the time (t) taken to move from rest through a known distance (s) down a slope set at a particular inclination (d), the acceleration (f) can be found from s = 1/2 f t2. From theory,

2mrI1

sin gf+

=α

Where g = gravitational acceleration, I = moment of inertia of rolling body, m = mass of rolling body, r = radius of axle. Objective To obtain the moment of inertia of the turbine rotor. Experimental Equipment Parallel rails, spirit level and metric rule. Calipers, stop-watch, micrometer screw gauge. Several specimen cylindrical wheels and one turbine rotor. Procedure Set the rails level both longitudinally and transversely with the spirit level. Raise one end a known distance. Mark off a reasonable distance along the slope. Take at least three readings of the time taken for each specimen to cover this distance from rest, and find the average time. Observations Note the principal physical dimensions and mass of each specimen. Record the times taken to roll through the set distance, and the inclination of the rails. Report Whilst the principal result is a prediction of the moment of inertia of the turbine rotor, the results of homogeneous solid circular cylinders can be used to confirm or contradict the theoretical expression given. The error in the experimental estimate for the moment of inertia should be calculated. An attempt should also be

17

made to calculate the moment of inertia of the turbine rotor from measurements of its mass and physical dimensions. Appendix The moment of inertia of a homogeneous solid circular cylinder of mass M and radius R about its centroidal polar axis is given by

2MRI

2

=

or 2MkI =

In this case 2R/k = Where k is the radius of gyration about the polar axis.

The moments of inertia of bodies which rotate about the same axis can be calculated individually and then added together. Therefore the moment of inertia of the turbine wheel can be estimated by regarding it as the sum of a number of solid circular cylinders which approximate to the actual shape.

18

City University SCHOOL OF ENGINEERING

ENGINEERING LABORATORY I – MATERIALS

Title Tensile Test. Type of Report Consult lecturer. Introduction The tensile test is conducted to determine the basic stress-strain response of a material. Object To perform tensile tests on standard steel, aluminium alloy or copper test pieces (state which one only). Experimental Equipment 1. Tensile testing machine. 2. Lindley extensometer,

1 division measures 0.001 mm extension 1 revolution measures 0.1 mm extension Instructions will be given on fitting the extensometer correctly. Handle it with great care. Secure it to a convenient part of the machine so that it cannot fall when the gripping screws loosen. The hinged (straight) arm should be uppermost. Procedure Details of the material tested and name and serial number of the testing machine and extensometer are to be recorded. Graph of load v. extension must be plotted by one member of the team as the test proceeds. Make sure that you fully understand the controls of the testing machine before proceeding. Sequence of Operations 1. Estimate the mean diameter of the specimen by not less than six micrometer screw gauge

readings. 2. Fix the Lindley extensometer to the specimen (see Experimental Equipment). 3. Insert the specimen into the upper jaws of the testing machine and secure the extensometer. 4. Adjust the zero of the load scale as necessary. 5. Engage the lower jaws of the testing machine with the specimen. 6. Check that the extensometer is functioning correctly by applying a small load ( 1 or 2kN and

unloading. 7. Proceed methodically and unhurriedly with the test until the specimen fractures.

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Observations Record the loads required to produce the following extensions:

Steel Steps of 5 divisions from 0 to 100 divisions Steps of 25 divisions from 100 to 400 divisions Al Alloy Steps of 20 divisions from 0 to 200 divisions Steps of 10 divisions from 200 to 300 divisions Steps of 25 divisions from 300 to 400 divisions Copper Steps of 10 divisions from 0 to 200 divisions

Then remove the extensometer and use dividers set to 501/2, 51, 52, 53 mm and so on up to failure. Measure the elongation of the 50 mm gauge length spanning the fracture and diameter of the ‘neck’ of the fractured specimen. Report In your report, 1. Carefully define the following quantities: Young’s modulus, yield stress, o.1% proof stress, tensile

strength, percentage elongation and percentage reduction of area after fracture. 2. With the aid of neat, well-proportioned line diagrams describe the principal features and mode of

operation of the testing machine and extensometer. Omit all unnecessary detail. Give the pieces of equipment their correct names.

3. Two separate graphs should be plotted of the load versus extension for the range of 0 to 0.4 mm and 0 to 16 mm.

Graphs and tables should be identified by numbers which should be referred to under DISCUSSION.

4. In the DISCUSSION section comment on the different portions of the graphs. Make any comments you think appropriate on the uses of the materials.

5. Under CONCLUSIONS state concisely and in general terms what useful information you have obtained and to what extent the experiment was successful.

6. In the APPENDICES, (i) neatly tabulate your results, (ii) show specimen calculations of all derived quantities.

Design Exercise Using Test Results A tie bar 2 m long has to be able to withstand a tensile force of 100 kN with a factor of safety of 2. Determine whether the mild steel or aluminium alloy would be the more satisfactory for the following design criteria:

(i) weight to be kept to a minimum; (ii) cost to be kept to a minimum; (iii) extension under load to be a minimum

Material Density Cost as bar Elastic Limit Elastic Modulus Kg/m3 £/kg MN/m2 GN/m2 Mild Steel 7800 2.00 from test data. Aluminium Alloy 2700 4.50

20

THE CITY UNIVERSITY

SCHOOL OF ENGINEERING

MECHANICAL ENGINEERING LABORATORY – THERMODYNAMICS

EXPERIMENT 2A

TITLE The determination of brake power, brake thermal efficiency, air-fuel ratio, and engine volumetric efficiency in a diesel engine.

INTRODUCTION Engine tests are carried out in order to evaluate the parameters which are used to illustrate some particular characteristic of the engine. One such parameter is the air-fuel ratio (A/F), defined as Mass flow rate of air through engine A/F = ----------------------------------------------- Mass flow rate of fuel through engine The air –fuel ratio gives the mass ratio of air to fuel usage in a given engine. Another important engine parameter is the brake thermal efficiency ηbt, defined as Power available at engine crankshaft

ηbt = ------------------------------------------------- net chemical power of fuel supplied

This gives an overall efficiency for the engine, and so, in the case of an older engine, includes the effects of wear and usage on the performance of the engine. The brake power and chemical power supplied are not measured directly but are calculated from the experimentally determined values of the engine variables on which they depend, i.e.

ηbt = LCVLCV

T

⋅⋅=

⋅

⋅⋅

⋅

⋅

f

sh

f

W

m ρυ

ω

where T = torque exerted by the engine crankshaft

.

= engine shaft power (kW) shW

= mass flow rate of fuel (kg/s) .

fm

= volume flow rate of fuel (m3 /s) .υ

LCV = lower calorific value of the fuel (kJ/Kg) fρ = fuel density (kg/m3 )

The volumetric efficiency is the ratio defined as follows: Actual mass of air supplied to the engine

ηv = --------------------------------------------------------- Theoretical mass of air supplied to the engine

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The theoretical mass of air supplied to the engine is calculated from the cylinder geometry and the air density at ambient conditions. Accordingly, the theoretical mass of Air = (n/2) (π/4) D2 S ρa N/60 (kg/s) where D = cylinder diameter (bore) (m) S = stroke (m) N = engine rpm (rpm) n = number of cylinder ρa = air density at room temperature (kg/m3 ) Hence one of the objectives of undergraduate laboratory work is to enable the student to familiarise himself/herself with the construction, use reliability and accuracy of the measuring instruments, which must be Used to determine the magnitude of such experimental variables as the engine speed, or rate of air and fuel consumption.

OBJECTIVE To conduct a test on a four cylinder diesel engine running at constant speed in order to determine its speed, brake power, rate of fuel consumption, rate of air flow through engine, and brake thermal efficiency.

EQUIPMENT Engine: Ford/Peugot four cylinder, four stroke, 2.3 litre diesel engine. Bore: 94 mm, Stroke: 83 mm

MEASUREMENTS Engine power: Heenan-Froude water dynamometer. Engine speed: Tachometer. Temperatures: Thermocouples. Fuel consumption: Stopwatch and 50, 100 and 200 ml pipettes. Air flow: Air drum with 60 mm orifice and inclined water manometer. Atmospheric pressure: Mercury barometer. Fuel specific gravity: Hydrometer. Procedure (a) The engine is warmed up and run at a steady speed of 2500 rev/min and at a high throttle opening until all temperatures have stabilised.

(b) A set of readings and their units are taken as follows:

Air inlet temperature T3 (Celsius) Air manometer reading ha (mm water) Atmospheric pressure Pa (mm Hg)

Heenan-Froude dynamometer Added mass m (kg) Spring balance reading L (N) Engine speed N(rev/min) Fuel: Lower calorific value LCV = 43 MJ/kg Density ρ (kg/l) Volume V (ml) Consumption time t (s)

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Full load

T3 (oC) ha (mmw) Pa(mmHg) m(kg) L (N) N (rpm) V(ml) t(s) (1) (2) (3)

Part load

T3 (oC) ha (mmw) Pa(mmHg) m(kg) L (N) N (rpm) V(ml) t(s) (1) (2) (3) (b) Readings should be repeated a further two times. (c) The fuel pump rack is then partly closed, the temperatures allowed to stabilise for about ten minutes, and a

further set of readings taken.

CALCULATIONS

Air Mass flow rate = 5.11 x 10-3 ( )2733 +TPh aa kg/s

(a) Shaft Power

( )602.447NLmgWsh ×

+=& kW

REPORT

Summary: Summarise entire report including Conclusions. Introduction: Comment on energy costs and engine tests. Theory: See Introduction section of experiment. Apply the first law thermodynamics and develop a

full equation for the break thermal efficiency Errors: Discuss the different sources of error and analyse the errors due the limited sensitivity of the

measurement devices. Discussion: The following may be of interest

(b) QUOTE FIRST AND SECOND LAWS OF THERMODYNAMICS; apply them to this

experiment. (c) Why does the brake power not equal the chemical power supplied? (d) Changing the power in diesel engine is achieved by changing the mixture quality while in

the petrol engine is achieved by changing the quantity (throttling) discuss this point from the results? Which is better?

(e) Comment on the values obtained for the brake thermal efficiency. (f) Why is it better to achieve high volumetric efficiency?

Conclusions: Give important quantitative results and compare your values with the typical values published

for similar engine. R.D. Lockett September 2001

23

CITY UNIVERSITY

SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES

MECHANICAL LABORATORY 1 – MATERIALS SCIENCE

Title: Formative Materials Laboratory

SECTION 1: Mechanical Properties of Plain Carbon Steels Experimental details: Three normalised steel tensile specimens will be tested and they have the following carbon contents:

Code AN, 0.1% C Code DN, 0.4% C Code N, 0.8% C

The tensile tests will be performed using a Houndsfield tensile testing machine. Examine the machine carefully and determine how the tensile force and the elongation of the specimen is measured. Before testing, the gauge length and the cross-sectional area of the specimens must be measured. From the force elongation data, plot an engineering stress/strain curve for each specimen. Note the form of the fracture surfaces and the extent of necking. The broken specimens can be fitted together and re-measured to obtain an alternative measure of elongation to fracture. Hooke’s law suggests that the force should be proportional to Δl but at the beginning of the test there is pronounced upward curvature. The reason for this is that the various linkages in the load train are straightening out and bedding in at the start of the test. It is not until this is completed that proportionality between force and elongation is observed. To correct for this the straight line portion should be extrapolated down to the horizontal axis as in Figure 1. This procedure gives the true origin on the elongation axis.

Figure 1: Correcting the force elongation curve to find the true origin

Background In a tensile test a specimen of material having a uniform cross-section is stretched, usually at a constant rate, until it fractures. During the stretching the force required and the increase in the specimen length or elongation, are both measured. The ends of the specimen are machined to a larger cross-section to give it a dumbell shape as in Figure 2. The enlarged ends are gripped by the machine and the deformation is confined to the length of uniform cross-section in the middle (Section C in figure below).

A C

B Figure 2: Tensile test specimen. The specimen generally has a circular or rectangular cross-section. Section C is the gauge length of the specimen, the region that will experience the deformation

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The essentials of a tensile testing machine are shown schematically in Figure 3. It consists of a rigid frame and a cross-head which is driven by a screw or other means. One end of the specimen is connected to the moving cross-head and the other to the fixed frame via the load-cell. A load-cell is a device for measuring force. It may be thought of as a hard spring whose deflection is proportional to the force. The elongation of the specimen is measured by monitoring the separation of two points on the specimen ends or less accurately by the movement of the cross-head. In a modern tensile machine the force and elongation are measured and sent automatically to a computer or an x - y plotter.

Force Load cell

Moving cross-head

Rigid frame

Specimen Grips

Fixed cross-head

Figure 3: The essentials of a tensile machine Stress and Strain When a static load or slowly changing load is applied uniformly over the cross section of a member a materials mechanical properties may be ascertained by a stress/ strain test. Engineering Stress may be defined mathematically as: F

0AF

=σ Engineering Strain may be defined mathematically as:

Figure 4

Where; Ao is the initial cross-sectional area in metres2 lo is the initial length in metres F is the force in Newton’s li is the new specimen length in metres Δl is the change in length metres

Ao

l lo

00

0

ll

llli =

− Δ=ε

F

25

Typical stress strain behaviour of steels

σ

ε

Ductile

Brittle

Figure 5: Graphical representation of a ductile

Figure 5, is a typical force/ deflection curve for a “ductile” and brittle steel. It can be seen that the ductile steel has a very large area under the stress/ strain curve corresponding to the work done in deforming the material or the energy absorbed. Conversely the Brittle steel has a much smaller area under the curve representing a much reduced deformation energy. In certain engineering applications energy absorption is an important design specification. For example, crumple zones in cars.

and

brittle steels stress/ strain curve

Figure 6: Graphical representation of a ductile steel showing the key areas of a stress/ strain curve. A – Young’s modulus; B – Upper yield stress; C- Lower yield stress; D- Ultimate tensile stress; E – Fracture stress; and O to E – Strain to failure.

A

B D

C

E σ

ε

σUTS

O

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SECTION 2: Light Microscopy Laboratory - Microstructure of plain carbon steels Introduction: The properties of a material depend on its chemical composition and on what we can loosely call its structure. The word structure refers to a wide variety of things. The crystal structure (the way the atoms and/or molecules are arranged spatially) is a particularly important structural feature and so is what we call microstructure. This latter term refers to things which can be made visible using microscopes of one kind or another. The optical microscope is capable of resolving structural features as small as 1μm (μm, micrometer = 10-6 meter) while the electron microscope can resolve objects only a few nanometres (nm, 1nm = 10-9 meter) in size. The microstructure and the chemical composition of a material are not, of course, independent. However, it is almost always true that the microstructure can be varied very widely without changing the chemical composition. It is perfectly possible to have an engineering component made of the correct material of the correct composition but which has the wrong microstructure and therefore the wrong properties for the application. There are many examples of spectacular disasters which are a consequence of this fact. The science of engineering materials is the business of unravelling the relations between properties and structure, while the engineering technology of materials is the art of controlling the properties of materials by controlling their structure and hence ensuring that the properties are those required for the application. Steel is an alloy of iron and carbon. There are always other alloying elements and impurities present in com-mercial plain carbon steels and their amounts may exceed the carbon content. Nevertheless in plain carbon steels the element carbon exerts by far the most powerful effect on the microstructure and therefore on the properties. Steel is essentially a composite material consisting of two phases, a very hard, brittle compound, iron carbide or cementite, and a relatively soft phase called ferrite, which is iron with a very small amount of carbon in solid solution. The amount of cementite increases with carbon content. The size, shape and distribution of cementite in the material is part of the microstructure. Microstructure: Most materials and almost all metals are crystalline in nature. This means that the atoms or molecules of the material are arranged in a three-dimensional repeating pattern in space. However, the typical engineering material will not consist of one crystal like a diamond in an engagement ring, but of many millions of individual crystals aggregated together. These crystals may have the same kinds of atoms arranged in the same repeating pattern in space but in each individual crystal the pattern will be differently oriented in space. See Figure 1.

Figure 1: A cross-section through a polycrystalline material. a) The boundaries of the individual crystals or grains are shown. b) A square grid is used to show the spatial orientation of the pattern in which the atoms are arranged. Note that in a real crystal the pattern is oriented at random in three dimensions not two as illustrated above. The individual crystals in a polycrystalline aggregate are called grains. Their size and shape are important aspects of microstructure. Large grains usually mean relatively poor mechanical properties while fine grains are associated with good mechanical properties. See Figure 2. The size of grains varies widely. Grains whose size is of the order of millimetres are found in cast metals, while grains as small as a few micrometers across are found in some hot-worked alloys.

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Figure 2: Cross-sections through two samples of a material of identical composition but with different grain sizes. The material might be, for example, pure iron. The material on the right would have better mechanical properties than the material on the left. It is important to understand that the grains of a polycrystalline material fill space (there are no gaps between grains) and that the inter-atomic forces, which hold the atoms together inside, a grain also operate across the grain boundary. At ordinary temperatures the grain boundaries are not significantly weaker than the grains themselves. In an alloy there is more than one element. Steel is an alloy of iron and carbon for instance. When there are two elements present it is possible for the material to have two different crystalline phases existing at the same time and the alloy will be a sort of natural composite material. In plain carbon steels there is a phase called ferrite, which has the same crystal structure as pure iron and is simply iron with a small amount of carbon in solid solution, and there is a phase which is the chemical compound iron carbide, Fe3C, or cementite. The microstructure is therefore rather more complicated than that of pure iron. The amount of cementite, the shape and size of the individual cementite particles as well as their distribution will constitute an important aspect of the microstructure. Ferrite is soft and ductile while cementite is hard and brittle. Hence the amount of cementite will have a very important influence on mechanical properties. Observation of microstructure: Putting a piece of metal or alloy under a microscope will not reveal its microstructure. Very careful preparation of the surface is required if any useful observations are to be made. The procedure is as follows:

1 A sample of the metal or alloy is cut with a hacksaw so that one face is the surface on which observation is required.

2 The surface is then flattened and the hacksaw marks removed by fixing a file in a vice and rubbing the sample on the file. It is not possible to produce a surface of the required degree of flatness by putting the sample in the vice and rubbing the file on it.

3 The sample surface is then rubbed on water lubricated silicon carbide paper bedded on a flat surface. The rubbing is carried out at right angles to the file marks until these have disappeared. The sample is then rubbed on another, finer grade of silicon carbide paper at right angles to the scratches from the first. Again the rubbing (or grinding) is carried out until all the scratches from the previous operation have been removed.

4 The process is repeated on successively finer grades of silicon carbide paper. During this process the surface becomes progressively more mirror-like and shiny. However, even after the finest paper the surface looks like a ploughed field under the microscope.

5 The surface is cleaned and then polished using fine diamond powder impregnated in a polishing cloth lubricated with paraffin. Two or even three grades of diamond will be used. At the end of this process the surface is optically flat with scratches less than the wavelength of light. The surface is now completely mirror-like and nothing whatsoever is visible under the microscope. This is because the microscope can only give information about the shape of the surface for an opaque material. We need therefore to find some means of making the surface topology reflect the underlying structure of the material. This is done in step 6 below.

6 The polished surface is now cleaned and then attacked with a chemical etching reagent usually a dilute acid solution. The etching reagent attacks the surface in a non-uniform manner. Atoms are more easily removed from grain boundaries for instance so a groove is formed at the grain boundary. Different grains are attacked at different rates and in different ways depending on their orientation, hence contrast between grains is developed.

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The effect of etching is illustrated schematically in Figure 3.

Figure 3: Illustrating the effect of etching a polished surface. The surface groove makes grain boundaries appear as a dark line under the microscope and the different surface patinas on the grains make some appear dark and others light. The iron carbon phase diagram: In order to understand microstructure it is necessary to understand phase diagrams. The phase diagram does not tell everything we want to know about structure, far from it, but without it we cannot begin to understand structure. The phase diagram gives information on what phases are present in equilibrium as a function of temperature and chemical composition. For an alloy of two components (a binary alloy) the phase diagram is a sort of two dimensional map plotted with temperature as a vertical axis and chemical composition as the horizontal axis. The map is divided into regions or phase fields which are separated from each other by lines called phase boundaries. A part of the phase diagram for the iron/carbon system is shown in Figure 4.

Figure 4: The part of the iron/carbon diagram relevant to steels. The horizontal axis extends from zero to about 2.11% carbon (by mass). Iron carbon alloys with more than 2.11% carbon are called cast irons. Alloys with less than about 0.022%C are called ingot irons. Note that the diagram is not drawn accurately to scale. Pure iron can exist in one of two crystalline forms. Ferrite, or α iron, stable below 912oC, has the iron atoms arranged on the corners of a cube with an additional atom in the very centre of the cube (body-centred cubic, or bcc iron). Austenite, or γ iron is stable between 912oC and 1394oC and has the atoms arranged on the corners of a cube with additional atoms in the centres of the cube faces (face-centred cubic, or fcc iron). Carbon will dissolve interstitially in both phases but γ can dissolve much more than α. The two structures are shown in Figure 5. Each field in the diagram of Figure 4 is labelled with the phase or phases which are stable within its boundaries. The γ field, for example is the region above the line AEF. It can be seen from the phase diagram that carbon increases the range of stability of the γ phase. With 0.77% C γ is stable down to 727 oC.

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Figure 5: The atomic arrangement in α iron (α and χ) and in γ iron (β and δ). The upper Figures, a and b, use small spheres to show the exact location of the atom centres in the cube. The lower Figures, c and d, attempt to show the “correct size” of the atoms relative to the size of the cube. In some fields two phases co-exist together. In the field ABE both the α and the γ phases exist together and the microstructure would show a mixture of the two. In a two phase field we can determine a number of things from the diagram; these are 1) the compositions of both phases present and 2) the relative amounts of both phases. This is done using the lever rule which is illustrated in Figure 6.

Figure 6: Illustrating the use of the lever rule in the α plus γ phase field. The line AB is the “lever” and G the “fulcrum”. The alloy composition is C, the composition of the α phase Cα and the composition of the γ phase Cγ. The point representing the alloy is first plotted. This is the point C,T or point G in Figure 6. This means we have an alloy of composition C held at a temperature T. To determine the composition of the two phases present in equilibrium a horizontal line AGB is drawn through the point C,T. The compositions of the phases, Cα and Cγ, are the points at which this line intersects the phase boundaries i.e. A and B. This is true wherever G lies between A and B. The amounts of the two phases are given by the lever rule. The mass fractions of α and γ are Xα and Xγ respectively and these are given by:

αγ

αγ

αγ

αα

CCCCX

CCCCX

−−

=

−−

=

The analogy with the mechanical lever can be clearly seen.

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Suppose the alloy of composition C were heated above the point D in Figure 6, and then allowed to cool slowly. It would consist only of γ until the point D was reached. α phase would then appear, usually on the γ grain boundaries. As the temperature falls the lever rule tells us that increasing amounts of α are formed. As the α phase has very little carbon in solution the carbon content of the remaining γ phase increases as the temperature drops and more and more of the low-carbon α phase is formed. This is indicated by the arrows on the phase boundary. Eventually the composition of the γ phase will reach the lowest possible value where the phase boundary intersects the horizontal line HEI in Figure 4. Inspection of Figure 4 shows that this happens at 727oC and the γ composition is then 0.77% C. This temperature is known as the eutectoid temperature, the composition 0.77% C as the eutectoid composition and the line HEI in Figure 4 the eutectoid horizontal (it is exactly horizontal). Further cooling will take the alloy into the α + Fe3C field so all this γ phase must now disappear. It therefore decomposes isothermally (undergoes the eutectoid reaction) to form a mixture of α and Fe3C.

γ (0.77%) ⇒ α(0.022%C) + Fe3C(6.67%C)

727 °C The product of this reaction is a very fine scale mixture of α and Fe3C. This mixture is given a name - pearlite. It consists of thin plates of Fe3C sandwiched between thin plates of α. Often the plates are too thin to be resolved by the optical microscope and pearlite simply appears dark or grey under the microscope. Steels which contain less carbon than 0.77% are called hypoeutectoid steels. They pass through the α plus γ phase field on cooling and hence must contain α phase which separated from γ before the eutectoid reaction took place. This so called pro-eutectoidα, is massive compared to the α formed by the eutectoid reaction and is easily distinguished from it under the microscope. The carbon content of a plain carbon steel can be estimated from the microstructure using the lever rule. Your assignment: You are to submit a 3 page report (The minimum text size is 12) to include the following:

1. ONE stress strain graph of all 3 specimens plotted in MS Excel (converted from the load displacement data of your experiment); and

2. A table of mechanical properties identified from this graph with appropriate units for each property (refer to Section 1, Fig. 6).

3. Sketches of the microstructure of the 3 plain carbon steels (this will be carried out during Laboratory Section 2: Microscopy of Plain Carbon steel), the sketches must be done in PENCIL, 10% deduction will be incurred if this is done in any other means.

4. A brief description of how the structure and properties are related.

31

CITY UNIVERSITY

SCHOOL OF ENGINEERING AND MATHEMATICAL SCIENCES

PRESSURE DISTRIBUTION AROUND A SYMMETRICAL AEROFOIL INTRODUCTION The purpose of this experiment is to measure the static pressure distribution around a symmetrical aerofoil, find the normal force and hence determine the lift-curve slope. For zero angle of attack the flow pattern and the pressure distribution are symmetrical about the aerofoil’s chord line and the normal force is zero. When the angle of attack is increased a small amount by (say) raising the leading edge of the aerofoil, the flow pattern becomes unsymmetrical because the sharp trailing edge causes the flow over both surfaces of the aerofoil to leave the trailing edge parallel to the chord line. The resulting unsymmetrical flow pattern produces high velocity and hence low pressure over the upper surface, and low velocity and hence high pressure on the lower surface. This results in a relatively large force normal to the chord line and a small force parallel to it. The lift force is defined as the force at right angles to the direction of flow and this is approximately the same as the normal force for small angles of attack. As the angle of attack is increased the lift increases until at a certain angle the flow on the upper surface breaks away, or separates from the aerofoil. At this point the lift decreases and the drag increases sharply. THE EXPERIMENT An aerofoil of chord c = 3.5” is mounted in the working section of a small wind tunnel (T8), which is run at a suitable wind speed. The pressure distribution is measured by means of wall tappings located at certain points on the surface of the aerofoil at mid-span (see Table 1 below). These tappings are connected to a multitube manometer in such a way as to show qualitatively the pressure distribution around the aerofoil. The dynamic pressure is also determined from the multitube manometer by reading the difference between the tunnel reference pressure (hs) and atmospheric pressure (ha). Each group will record the pressure distribution for 5 angles of attack and calculate the corresponding values of the lift coefficient. ANALYSIS OF RESULTS The results are analysed in terms of the pressure coefficient, i.e. non-dimensional pressure defined by:

22/1 UPPCP ρ∞−

=

where P is the local pressure at the point of interest, P∞ is the static pressure in the freestream and U is the freestream velocity. The coefficients may be determined directly from the manometer readings as follows:

sa

sP hh

hhC

−−

=

where h is the reading for the tapping being considered, ha is the atmospheric pressure reading and hs is the static pressure in the tunnel working section. Note that there is no need to convert individual readings to pressure. The tunnel speed is determined using:

θρρ sin)(21 2

asm hhgU −=

where hs and ha must be in SI units, θ is the inclination of the manometer to the horizontal, ρm is the density of the manometer fluid (usually about 830 kg/m3) and ρ is the density of air, which may be determined from the equation of state as follows :

32

RTP

=ρ

where P is the pressure in the lab, T is the lab temperature, and R is the gas constant for air (287 kJ/kgK). Note that all quantities must be in SI units. Plot a graph of CP against x/c for each angle of attack, where c is the chord of the aerofoil and x is the distance measured from the leading edge (obtained from Table 1). Plot each graph as two different series: one for the upper surface pressure distribution and one for the lower surface. Next, determine the lift coefficient, CL, for each angle. It may be shown that the lift coefficient, defined as:

cULCL 22/1 ρ

=

is given by :

∫ ⎟⎠⎞

⎜⎝⎛−=≈

cxdCCC PNL

Therefore, the lift coefficient may be determined by measuring the area enclosed within the curve of CP against x/c. This may be done most conveniently by counting the number of squares inside the curve and multiplying this number by the representative area of each square. Note that the sign of the lift coefficient will be positive when the peak negative pressure coefficient is on the upper surface and negative when the peak negative pressure coefficient is on the lower surface. Use the results to plot a graph of CL against angle of attack, α, and determine the gradient of the linear portion around zero degrees. This is the lift-curve slope. Finally, determine the aerofoil Reynolds number:

Re Ucν

=

where U is the tunnel speed, c the chord length (in meters) and ν is the kinematic viscosity of air (usually taken as 1.5 x 10-5 m2/s at room temperature). DISCUSSION • Study each of the pressure coefficient plots and look for:

o the stagnation point (where Cp = +1). o the flow separation point (if any) i.e. where the pressure distribution on the upper surface

becomes constant. o the value of CP at peak suction (i.e. the maximum negative value). o the value of CP at the trailing edge.

In all cases, comment on any changes with varying angle of attack. • Which region of the aerofoil contributes the most to the lift force? Explain your answer. • Study the lift curve and determine the angle of attack for no lift (where CL = 0) and for the stall point (where

CL is a maximum). Comment on any unexpected findings. • Compare the value of the lift curve slope with the theoretical value (i.e. 2π per radian or 0.1097 per degree)

and comment on any differences. • Compare the aerofoil Reynolds number with typical values for full-scale aerofoils. Comment on the

importance of Reynolds number. • Perform an appropriate error analysis of the results obtained and estimate the error in the pressure coefficient,

lift coefficient and lift curve slope.

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Table 1: Pressure tapping positions for the symmetric aerofoil in tunnel T8 Hole No x in y in

0 0 0 Leading Edge1 0.05 0.0652 0.18 0.123 0.53 0.194 1.23 0.25 Upper Surface5 1.75 0.236 2.45 0.157 3.15 0.058 0.09 0.099 0.26 0.1410 0.88 0.2811 1.49 0.24 Lower Surface12 2.1 0.213 2.8 0.1114 3.5 0 Trailing Edge

References [1] Houghton and Carpenter, Aerodynamics for Engineering Students (Butterworth Heinemann). [2] John D. Anderson, Fundamentals of Aerodynamics (McGraw-Hill).

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