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Time: 3 hrs.

Fourth Semester B.E. Degree Examination, June/July 2013

If w: z3 find dddz.

If the potential function is $ = 16*

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Max. Maiks:100

(06 Marks)(07 Marks)

. Find the stream function. (07 Marks)

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I a. Use modified Euler's method to ,olre !l = * + y, y(0) = 1 at:-'x '= 0.1 for three iterationsdx

takingh:0.I. (06 Marks)

dv6. Solve l=*+y,x:O y=1 at x:0.2 using Runge-Kutta method' Take h:0.2." dx (07 Marks)

c. Using Milne's predictor-corrector method furd y(0.3) correct to thLree decimals given,(07 Marks)

Note: 1. Answer FIVE full questions, selectingdt leost TIVO questions from each part.

2. Use of Statistical tables permitted

x -0.1 0 0.1 0.2

v 0.908783 1.0000 1.1 1 14s 1.25253

^dv! 6. Approximate y and z at x : 0.? using Picard's method for the solution sf :l- = , ,

*=*'rr-., wirh y(0): l. z(0)- l/2. Perform two steps (yr. y2.:Zt.z2l. (l0Marks)dxUsing Runge-Kutta meihod solve y" : x(y')' - f at x = 0.2 with xo - 0, y0 : 1, 26 : 0 takeh : 0.2. ( l0 Marks)

If (z) : u + iv is anall.tic prove that Cauchy-Reimann equations u1 = Vy, uy : -v* are true.

b.

b.

C.

4 a. Find the bilinear transformation which maps the points z = I . i. - I onto the poinls * = j. o. -i.(06 Marks)

b. Discuss the conformal transformation w: e'. Any horizontal strip of height 2n in.z-planewill map what portion of w-plane.

c . State and prove Cauchy' s integral formula.(07 Marks)(07 Marks)

(06 Marks)

(07 Marks)(07 Marks)

6 PART- B

{ a. Prove that J'''=-ia sinx.t Vnxb. State and prove Rodrigues formula for Legendre's polynomials.c. Express f(x) : xa + 3xr - x2 + 5x - 2 in terms of Legendre polynomial.

2 +y

1of 2

lOMAT4I

6 a. The probabilities offour persons A, B, C, D hitting targets are respectively 112, 113,114,1/5.What is the probability that target is hit by atleast one person if all hit simultaneously?

(06 Marks)b. i) State addition law ofprobability for any two events A and B.

iil Two different digits from 1 to 9 are selected. What is the probability that the sum of.the two selected digits is odd if '2' one ofthe digits selected. (07 Marks)

c. Three machine A, B, C produce 50%, 30%, 20%o of the items. The percentage of defectiveitems arc 3, 4,5 respectively. If the item selected is defective what is the probability that it is

ritom machine A? Also find the total probability that an item is defective.

7a. Theliil.f of x is

Find k. Also fildp(x > 5), p(3 < x < 6). (06 Marks)

6. A die is thrown Stiines. Find the probability that '3' falls,i.1 Exactly 2 timesii) At least onceiii) At the most 7 times. (07 Marks)

c. In a certain town the duration gf shower has mean 5 minutes. What is the probability thatshower will last for i) 10 minutes or more; ii) less than l0minutes; iii) between 10 and 12

(07 Marks)

minutes-

What is null hypothesis, alternatiye hyliiithesis significance level? (06 Marks)

The nine items of a sample havc the following values: 45, 47, 50, 52, 48, 47, 49, 53, 51.Does the mean ofthese differ'significantly from the assumed mean of47.5. Apply student'st-distribution at 5% level ofsignificance. (to os for 8df:2.31). (07 Marks)

c. In experiments on a pea breading, the following frequencies of seeds were obtained:

Round-yellciw Wrinkled yellow Round green Wrinkled green Total315 101 108 32 556

8a.b.

ls the experiment is in the agreement of theory which/-9:3:3:1 (xjr,, 3df = 7.815).

(07 Marks)

predicts pioponion of fiequencies

(07 Marks)

x 0 1 2 J 4 5 6p(x) k 3k 5k 7k 9k 11k 13k

2 of2

USN IOI0/IF.4zAIAU42A

Max. Marks:100

materials.(08 Marks)

Calculate the hardness(06 Marks)

(05 Marks)

(10 Marks)(05 Marks)(05 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013

Material Science and Metallurgy

Time: 3 hrs.Note: Answer FIVE full qaestions, selecting

at least TWO questions from eoch part.

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PART _ Aa. With neat sketch, explain body centered cubic face centered cubic and closed packed

hexagonal structures with examples. (09 Marks)

b. Derive expression for atomic packing factor of BCC, FCC and HCP structure. (07 Marks)

c. Brielly explain the different tlpes ofpoint defects. (04 Marks)

2 a. With the help of stress-strain diagram,'explain the behaviour of ductile and brittle

b. The lollowing data have been obtained in hardness test ofspecimens.number. Assume dia olball indenror: l0mm.

Material Trt:e Load (kgf) Impression (mm)

A Brinell 500 4.6B Vicker's 5 0.28

c. Define the following terms Toughness, Resilience, Proofstress and ductility. (06 Marks)

3 a. With neat diagram, explain the fracture in the following: i) Ductile; ii) Brittle; iii) Fatigue.(12 Marks)

b. Explain the three stages ofcreep with a neat sketch and its characteristics. (08 Marks)

4a.b.

c.

With neat diagram. explain the process olnucleation.

d. Briefly explain the rules behind the solid solubility.

b. What is level rule? Explain how it is useful.c. What are phase diagrams? How are they classified?

Write a note on Gibb's phase rule with an example. (04 Marks)

With the help of cooling curve. explain how soliditjcation process begins in pure metals.(06 Marks)(05 Marks)

PART-B5 a. Construct the Ag-Cu phase diagram using following data:

Melting point of Ag : 960.5'CMelting point of Cu : 1085'CEutectic point : 779.4oCEutectic composition : 28.lYo CttMaximum solubility of Ag in Cu and Cu in Ag is 8%.Maximum solubility of Cu in Ag and Ag in Cu is 2%.Assume the liquidus, solidus and soh'us lines are straight. Calculate:'i) Amount of eutectic in 20%o Cu', 80% Ag alloy at 700oC and

iD Percentages and compositions of solid phases in 60%o Ct and 40%o Ag alloy at 400'C.

1of2

loIME4zAlAA42A

6 a. Draw Iron-Carbon equilibrium diagram and explain primary crystallization of steelhypoeutectic cast iron and hypereutectic cast iron. (10 Marks)

b. Define the following annealing, normalizing, tempering, carburizing and nitriding.

" (10 Mar[s)

Y' tY , a. How cast iron are classified? What are the properties of cast iron? (08 Marks)

"-"tf),h. How generally steels are classified? Corsider at least two composition mixtures, q€_&ion its'fJ, application and advantages. .. 'i{$8 Marts)

c.{p6p1ain the compositioq properties and uses of at least two copper based alloyi. (04 Marks)ul)*

S a. Ddrffiqn expression for load distribution in a composite for longitrlSfirih. loading of fiberreinfdffi composite. (lo Marks)

b. With;Hdpdagram, explain the hand laminating process. (10 Marks)lI '-t.i..''"l,, .,-. r.

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(10 Marks)

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Fourth Semester B.E. Degree Examination, June/July 2013

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Applied Thermodynamics

Time: 3 hrs. Max. Marks:100Note:1. Answer FIVE full questions, selecting

at least TWO questions from each port.2, Use of thermodynomic data hand book is permitted.

PART _ A1 a. Explain the following:

i) Enthalpy of formation ii) Conibustion efficiency iii) Enthalpy of combustioniv) Complete combustion v) Incomplete combustion (10 Marks)

b. The products of combustion of hydrocarbon fuel of unknown composition have thefollowing composition on dry basis:CO, : 8.0%. CO : 0.9 %, O: = 8.8 %,Nr:82.3%Calculate: i) Airfuel ratio ii) Composition of fuel on mass basis.

iii) The percentage oftheoretical air on mass basis. (10 Marks)

2 a. Derive an expression of air standard efficiency of a dual cycle, stating the assumptionsmade. (10 Marks)

b. A diesel engine operating on an air standard diesel cycle has 20 mm bore and 30 mm stroke.

The clearance volume is 4.2x10-a m3. The fuel is injected for constant pressure for 5oh ofthe stroke, calculate the air standard efficiency. If the cut-off is delayed from 5% to 8%,what will be the effect on efficiencv? (10 Marks)

a. Explain the following: i) Motoring test method ii) Willian's line method. (08 Marks)b. A two stroke diesel engine was motored when meter reading was 1.5 kW. Test on engine

was carried lbr one hour and data observed were as follows: Brake torque = 120 N-m;Cp(gas) : 1 .05 kJ/kg-K, Speed : 600 rpm, Room temperaturc = 27"C,Fuel used : 2.5 kg, A : F ratio :32:1, Calorific value :40.3 MJlkg,Cooling water: 818 kg, Rise in temperature of cooling water: 10"C,Exhaust gas temperature - 347"C.Determine brake power, indicated power, brake thermal effrciency. And draw the heat

balance sheet on minute basis. (12 Marks)

4 a. Sketch the flow diagram and corresponding T-S diagram ofa reheat vapour cycle and derivean expression for the reheat cycle efficiency. What are the advantages gained by reheatingthe steam in between stages? (10 Marks)

b. A steam power station uses the fbllowing cycle: steam boiler outlet : 1 50 bar, 550'CReheat at 0.1 bar, using the Mollier diagram and assuming the ideal process find,i) Quality of steam at turbine exhaust.ii) Cycle efficiency.

I of2

rOME/AU43

PART - Ba. Derive an expression for minimum work I/P by two stage compressor with intercooler.

(10 Marks)b. The following data refer to a single stage double acting air compressor in which air is drawn

at 1 bar and compressor in which air is drawn at 1 bar and compressed to 16 bar, according

to the law PVr25 =C. Input to compressor is 50 kW. The speed of the compressor is 300rpm. The piston speed is 180 m/min. The volumetric efficiency is 8070. Calculate thediameter and stroke ofthe cvlinder. (10 Marks)

a. With neat sketches, explain turbojet and ramjet propulsions. (10 Marks)b. A'gas turbine receives air at 100 kPa and 300 K and compresses it to 620 kPa. With

compreqsor efficiency of 88%. The fuel has a heating value of 44180 kJ/kg and fuel air ratiois 0.017 kg of fuel per kg of air. The turbine efficiency is 90%. Calculate the compressorwork, turbiiie work and thermal effrciency. (10 Marks)

a. Explain the effect of super heating and sub-cooling with the aid of T-S and P-H diagrams.

b' Explain steam jet re .geration. [8:ffi[:]c' A vapour compression refrigeration uses Freon-12, has its temperature - 1OoC and 30"C. Thevapour enters the compressor dry and under cooled by 5"C in the condenser. For thecapacity of I 5 TO R. findi) CoPii.) Mass of Freoniii) Power required Cp (vapour.l : 0.56 kJ,&g-K and Cp lliquid) : 1.003 kJ,&g-K (t0 Marks)

a. Define the following: ' -

i ) Wet bulb temperatureii) Dew point temperatureiii) Retative humidityiv) Specific humidity .

v) Degree ofsaturdtion.

b. A sling thermonieter reads 40'C DBT and 28'C WBT. Find the following:(10 Marks)

(10 Marks)i) Specific humidityiii) Dew'point temperature

ii) Relative humidityiv) Vapour density

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USN lOME/AU/PM/TL44

(06 Marks)

Time: 3 hrs. Max. Marks:100Notezl. Answer FIVE full questions, selecting

at least TllO questions from each part.2. Graphical Solutions can be done either on

Graph Sheets or on Answer Book itself.PART-A

I a. Define : i) Machine and ii) Mechanism. State an example for each. (06 Marks)

b. Five binary .links ol lengths 5 cm, 8 cm, 1 5 cm, 19 cm and 28 cm are available forconstructing,.'6 crank-rocker mechanism. Select four links required for the construction ofthis mechanism. Sketch (need not be to scale) the mechanism and clearly show the fixedlink, crank and rocker. (06 Marks)

c. Sketch a 'Double slider crank chain'. A mechanism is obtained from this by fixing a binarylink having two turning pairs. State an application for this mechanism and skelch the same.

,- (08 Marks)

2 a. The length ofthe fixed link ofa crank and slcitted-lever mechanism (quick return motion) is250 mm and that of the crank is 100 mm. Determine : i) angle between extreme positions ofslotted lever, and ii) Ratio of the time of cutting stroke to that of return stroke. (06 Marks)

b. Draw a neat proportionate 'Peauceliier Mechanism'. Indicate the geometric relations amo ng

the links and show the point tracing the straight line. Prove that the point traces a straightline perpendicular to the fixed link. (14 Marks)

3 In the slotted-lever quick-reium mechanism shown in Fig. Q3, the crank OuA rotates at a

constant speed of 30 rpm (CCW). For the position shown, determine the velocity andacceleration of the point C. Given O:A: 12 cnr, O:O,r = 30cm, O+B:60 cm and BC - 15 cm.The line ofmovement ofC is 30 cm above the point 02. (20 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013Kinematics of Machines

Fig. Q3

What is instantaneous centre ofrotation? State Kennedy's theorem.

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4a.b. A binary link of a mechanism having two turning pairs at A and B is in the shape of an

isosceles triangle as shown in Fig. Qa (b) (complete mechanism is not shown). Velocity ofA is 20 cm/s along AB in the direction shown in the Fig. Q4 (b). Determine theinstantaneous centre of the link if the path of B at the instant is along BC. Also determinethe magnitude and direction of, i) angular velocity of the link ii) Velocity of C. (06 Marks)

1of2

PART - BIn the 4-bar mechanism shown in Fig. Q5, link AB rotates uniformly at'2 radians per second inclockwise sensq: Using complex algebra write loop closure equation for this. Determinemagnitude and dirtictions ofangular velocity and angular acceleration of links BC and CD usingvector algebra. Also state whether the magnitudes of angular velocity of these links tend toincrease or decrease at the.instant. (20 Marks)

B

C AD:10 cmi AB : 7.5 cmCD: 15 cm

a. state and prove lu* of ,"-inr. Fig' Q5

(0E Marks)b. The number of teeth on each of the two equal spur gears in mesh is 40. The teeth have 20.

involute profile and the module is 6 mm. If the length of arc of contact is 1.75 times thecircular pitch, find the addendum. (08 Marks)

c. Compare involute and, cycloidal tooth profile of a gear with respect to, i) Pressure angleii) Interference. (04 Marks)

An epicyclic gear'train has a fixed arurular wheel 'C' concentric wjth sun wheel 'A'. A planetwheel 'B' gearsu/ith'A' and 'C' and can rotate freely on a pin carried by an arm 'D' whichrotates about aii axis co-axial with that of 'A' and 'C'. If T1 and T2 are the numbers of teeth on

'A' and 'C' respectively, show that the ratio of speeds of 'D' to 'a' 6 -J, . If the leastr, +T,

number of teeth on any wheel is 18 and T1+T2 = 120, find the greatest and least spgeds ofDwhen wheel 'A' rotates at 500 rpm. (20 Marks)

a. Draw neat sketch for each ofthe following:i) Plate or disc cam with a translating follower.ii) Wedge cam with translating follower.iii) Cylindrical cam with translating follower.

Q.No.a @) Contd...

Fie. Qa (b)ExplainExplain the procedure to construct 'Klein's construction to determine theacceleration of a slider Crank mechanism in which crank is rotating uniformly.

the procedure construct 'Klein's construction

acceleration ofthe follower during the lift.*****

2 of 2

lOME/AUiPM/TL44

AB : 500 mmAC: BC

ZCAB:30"

veloiity and(08 Marks)

(06 Marks)b. Draw the profile of a cam operating a knife-edge follower having a lift of 30 mm. The cam

raises the follower with SHM for 150o of the rotation followed by a period of dwell for 60o.The follower descends for the next 1000 rotation of the cam with uniform velocity, againfollowed by a dwell period. The cam rotates in an anticlockwise sense at a uniform velocityof 120 rpm and has a least radius of 25 mm. What will be the maximum velocity and

(14 Marks)

I]SN

PART _ Bconstructional features of horizontal

lOME/AU/TL45

Max. Marks:100

(08 Marks)(06 Marks)

(10 Marks)(10 Marks)

(08 Marks)

(08 Marks)(04 Marks)

spindle column and(08 Marks)(06 Marks)(06 Marks)

(04 Marks)

(08 Marks)(08 Marks)

(08 Marks)(06 Marks)(06 Marks)

(10 Marks)(10 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013

Manufacturing Process - I!

Time: 3 hrs.

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PART-AI a. Briefly explain the different types of chips produced during metal cutting with neat sketches.

(06 Marks)

b. In an orthogonal cutting operation, following data have been observed. Un cut chip

thickness - 0.127 mm; Width of cut - 6.14 mm; Cutting speed '2.6 mlsec; Rake angle :20o; Cutting force-: 589 N; Thrust force : 225 N; Chip thickness : 0.226 mm. Determine

2a.b.

3a.b.

shear angle, frictioti angle and chip velocity.c. With a neat sketch, explain crater wear and flank wear.

List the desired propertiea"if cutting tool materials and explain any four. (10 Marks)

List the techniques to meaS0re tool-tip temperature and explain tool-work thermocoupletechnique with a neat sketch. (10 Marks)

With a neat sketch, explain the constructional features of a Capstan lathe.

Explain hydraulic driving mechanism ofa shaper with a neat sketch.

4 a. With a neat sketch, explain the corstructional features of a radial drilling machine tool.

6a".b.

c.

b. With neat sketches. exptain the following operations:i) Drilling ii) Bgring iii) Counter sinking - iv) Trepanning.

c. Write a note on CNe machines.

a. With a neat sketch, explain theknee milling machine.

b. Differentiate up milling and down milling with a neat sketch.c. List the methods ofindexing and explain any one.

Explain the types of abrasives used in grinding wheel.With a neat sketch, explain the constructional features of a centreless grinding machine.

ta.b.c.

8a.b.

Explain the factors to be considered while selecting a grinding wheel.

What are the advantages and limitations of broaching process?

Explain the principle of lapping with a neat sketch.Explain the principle ofhoning with a neat sketch.

Explain laser beam machining with a neat sketch.Explain ultrasonic machining with a neat sketch.

USN lOME/AU46B

Max- Marks: I OO

(10 Marks)sleeve of 120mm long at 200 rpm. If the

is 1.5mm, find the power lost in friction. The(10 Marks)

Fourth Semester B.E. Degree Examination, June/July 2OI3Fluid Mechanics

Time: 3 hrs.

Note: Answer FfW full questions, selectingal least TWO qaestions from each part.

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PART_A

1 a. Define the following properties of fluid:i) Specific weight.ii) Specific gravity.iiD Vapour pressure.iv) Capillarity.v) Surface tension.

b. A shaft of 250mm diameter rotates inside a

thickness of oil film between shaft and sleevedynamic viscosity of oil used is 8 poise.

2 a. Obtain the total pressure and the centre ofpressure on an inclined plain surface immersed ina fluid. (10 Marks)

b. A differential U{ube mercury manometer is used to measure the difference of pressurebetween two water pipes A and B. Find the pressure at A ifthe level difference in mercuryin the manometer is 150mm as shown in figure. The at B is 300 kPa. (10 Marks)

S= o'8

s =0 9

3a.b.

4a.

b.

Explain the method to find the metacentric height experimentally. (08 Marks)

The stream function for a two-dimensional flow is given by V :2xy. Find the velocity a1 thepoint P(4, 2). Also find the velocity potential function. (12 Marks)

Obtain the Euler's equation of motion along a stream line and hence derive Bernaulisequation for a steady incompressible fluid flow. (10 Marks)A 10m long water pipe is laid at a slope of3 in 4. The diameters ofthe lower end and upperend are 120mm and 180mm respectively pressure gauges fixed at the lower end and upperend reads 0.2MPa and 0.3MPa respectively. Determine the flow rate of water through the

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prpe.

1 of 2

(10 Marks)

5a.b.

PART - B

Derive an expression for discharge through a rectangular notch.

A flat plate 2m x 2m moves at 40 km/h in a stationary air of densitycoefficients ofdrag and lift are 0.15 and 0.75 respectively determine:i) The lift forceiD The drag forceiiD The resultant forceiv) The power required to keep the plate in motion.

lOME/AU46B

(I0 Marks)

(10 Marks)1.2 kg/m3 . If the

(10 Marks)

6a.b.

Using Buckingham's n-theorem prove that the frictional torque T of a disc of diameterD rotating at a speed N in a fluid ofviscosity pL and density p in a turbulent flow is given by

r=o'N'06[=51 (roMarks)I o'Np I

Derive Darcy's equation for the loss of head due to friction in a circular pipe. (10 Marks)Water is supplied to a town having a population of I lakh from a reservoir 6km away tomthe town and is stipulated that half of the daily supply of 180 litres per head should bedelivered in 8 hrs. What should be the diameter ofthe supply pipe? The loss of head due tofriction in the pipe line is 12m. Take f : 0.002. (10 Marks)

7 a. Derive Hagen-Poiseuille's equation for viscous flow through a circular pipe. (10 Marks)b. A pipe of diameter 240mm and length 20km is laid at a slope of I in 250. An oil of specific

gravity 0.85 and viscosity 180cp is pumired up at a rate of 18 litres/sec. Find the head lostdue to friction and the power required to pump the oil. (10 Marks)

8 a. Explain the following:i) DragiD Liftiil) Momentum thicknessiv) Mach numberv) Mach cone.

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