4th Semester Mechanical Engineering (2013-December) Question Papers

USN

Time: 3 hrs.

2a.

3a.b.

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Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l4Engineering Mathematics - lV

Max. Marks:100

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O6MAT41

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data given

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Note: Answer FIVE full questions, selectingat least TWO questions from each part.' " - a-'-----'-- J- "-'- ------ r-'-'-

PART - AI a. Applying Taylor's series method, find'y'at x:0.1 by considering the series up to fourth.dv)^

degree term. Give, * = x + y' , y(0) : l. (06 Marks)dx

b. Find yat x:0.2 using Runge Kuttafourthordermethod. Given 1'= Il:, y(0): I andy+x

step size 0.2. , (07 Marks)

c. Use Milne's predictor Gorrector formulae to find y(0.4). Given t = ,,* + y), with

x 0 0.1 o7 0.3

v 1 t.1t69 1.2733 1.5049(Use corrector formula twice.)

/:2 :2\rf {iz) in a regutar tunction or'z' show,h"

[# .#) l f(z)l' = 4lf'G)i .

Find the analyic function flz): u + iv where u =sin 2x

cosh2v+cos2x'Find the bilinear transfo,rmation which maps the points z: l, i, -1 into the point w:2, i, -2.Also find the invariant points of the transformation. (07 Marks)

4a.

State and prove eauchy's theorem under complex values functionp integration. (06 Marks)

Expand f (z) =--== in Laurent's series valid for (i) lzl < l, (ii) I .lrl < 2.10t Marks)" (z-r)(z-2)

Evaluate lr"o'=',dzwhere'c'islz-11:lusingCauchy'sresiduetheorem. (07Marks)IQ_D'

r)

Solve *4* *9+ y = 0 using the method ofsolution in serdx' dx

With usual notation prove that P",r, = ## (x' - 1)' .

Express x' - 3x' + x in terms of Legendre's polynomials.

PART - B5 a. Fit a curve in the form y : a -t u* TFuy trr. method

below:x 1 1.5 2 2.5 a

J 3.s 4

v 1.1 1.3 t.6 2 2.7 3.4 4.1

.l nf1

of least squares for the

(06 Marks)

O6MAT41

5b. Obtain the two lilnes o resslonx 1 2 J 4 5

v 2 5 J 8 7

and hence find the coefficient of correlation between x and y. (07 Marks)c. The contents of the three urns are as given below:

Urn 1: 1 white ball,2 red balls, 3 green balls.IJrn2:2 white, 1 red and 1 green ball.Urn 3: 4 white, 5 red and 3 green balls.

Two balls are drawn from a randomly chosen urn and are found to the one white and one

green. Find the probability that the balls so drawn came from the third urn. (07 Marks)

for the data given below:

Find the mean and variance of Poisson distribution. (06 Marks)

In a certain town the duration of a shower is exponentially distributed with mean 5 minutes.

What is the probability that a shower will last for (i) 10 minutes or more, (ii) less than 10

minutes, (iii) between 10 and 12 minutes? (07 Marks)

iii) between 65 and75(07 Marks)

in the lot is expected to lie. (07 Marks)

(07 Marks)

6a.b.

7 a. A coin is tossed 1000 times and head turned up 540 times. Test the hypothesis that the coinis an unbiased one. (06 Marks)

c. The marks of 1000 students in an examination follows a norrnal distribution with mean 70

and standard deviation of 5. Find the expected number of students, whose marks will be:

i) less than 65 ii) more than75

fGiven A(z : 1) : 0.3413].

b. A sample of 200 tyres is taken from a lot. The mean life of tyres is found to be 40000 kms

with standard deviation of 3200 kms. I,s it reasonable to assume the mean life of tyres in the

lot as 41000 kms? Also establish 95% confidence limits with in which the mean life of tyres

c. Ten individuals are chosen at random from a population and the heights are found to the ininches 63, 63, 66, 67,68, 69, 70, 70, 7l and 7l In the light of this data discuss the

suggestion that the mean height in the population is 66 inches. If the population mean isunknown, obtain 90% confidence limits for this mean. (07 Marks)

8 a. The joint bability distribution for two random variables x and y is given below:

Find the (i) marginal probability distributions of x and y, (ii) covariance of x and y.

b. Find the unique fixed probability vector of the regular stochastic matrix (06 Marks)

c. A software engineer goes to his work place every day by motor bike or by car, he never goes

by bike on two consecutive days, but if he goes by car on a day then he is equally likely togo by car or by bike on the next day. Find the transition matrix for the chain of the mode oftransport. If car is used on the first day of a week find the probability that (i) bike is used, (ii)car is used on the 5th day. (07 Marks)

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1 0.1 0.2 0.2

J 0.3 0.1 0.1

USN MATDTP4Ol

Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.2O14

Advanced Mathematics - llTime: 3 hrs. Max. Marks:100

Note: Answer any FIVEfull questions.r\ure; AnJwer uny, rr r E luu quesru)ns.

L a.,., Frgvethat sin2cr+sin'B+sin'y =2 (06Marks)

b. If ,0r; mr, n1 and L2, m2, n2 arc direction cosines of two lines then plwe that the angle

betwoen,,them is cos 0: L&z * mrmz * n1n2. ::, :::,,:: (07 Marks)

c. Find the,,equation of the plane throughthe interaction of the planos 2x+ fy 5 andx-2y-32=- 8, also perpendicularto the plane x +y-z:2. (07Marks)

2 a. Prove that the equation of the plane in the intercept form is I * I +1 =7 .'abcb. Find the equation of the plane through the points (1, -2, 2) (-3. l, -2) and perpendicular to

the plane 2^ - y - z-t 6 : 0. (07 Marks)c. Find the angle between the following lines: , ,,,, ,

x-2 = ,, t =r:3 and += l:1=+ (ozMarks)3122*1 0

"",:,,:'::::::,...'.3 a' Findthesineoftheanglebetween d =21-2J+E and 6 =1-Zj+2k. (06Marks)

b. Find the value of i if the vectors a =4i+6J+2[. 6=3i+lOJ+5[' and c =-4i+5J+i[-are coplanar. (07 Marks)

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c. Prove the following: ,

i) (34-26)x (4a + z6l = 14(a+6)1i) (2a+ 36) x (a + 46) = 5(a + 6)

4 a. Aparticlernor.ralongthecurve i=(t'-4t)i+(t2+4t)J+(Sti-:t')[.finAthevelocityand acceleration at t : I and also find their magnitude. (06 Marks)

b. Find the unit normal veclor to the surlace *y3J :4 at the point (- l. -1.2). (oz wtarts)c. Findthedirectionalderivative of x2yz3 at (1, 1, 1) inthedirectionof i+ j+Zi Marks)

(06 Marks)

(07 Marks)

(06 Marks)

(07 Marts)

Find divF and curlF, where F = x3i+ y'J+ z'k .

Prove that curl grad Q : 0.

a.

b.

c.

d.

Find the constants a,b, c such that the vectorF =(x* y+afli+(x+ cy+22)k+(bx+ 2y- r)jis irrotational. (07 Marks)

Find the Laplace transform of the following:sin 4t cos3tcos hat

t e-t sin t1-cost

cEwqn'$'$--.aa/

LISJFI+*'r' "

(20 Marks)

a.

.b...d ,,

" k." ^-:- P rl L.-,,,,.=,

8a.

Find the inverse Laplace transform of

,""(,tl)"[s-l/s+1

7 +2#2S

...._., j;.!

subjecteff,t+=-thc conditions y(0) : y'(0) :0.:::" l::: ,, _1_-

Given that x:

(06 Marks)

(07 Mar.ks)

*ffi,ou'u"!' ........,,. ....

d'v -dv - - ,r___:+ 5": + 6y = )e-,dt'" dt1r. H

"l.,, (10 Marks)

ing Laplace transforms.

differential equation

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(10 Marks)

,,"'tt"'tt'

.=*= *"i-'

t ":""', .,,,1 _ii

... ..:r,h

.,;:::'! .,-..

::::...."r\rit'

(s+1)(s+2)(s-3)

,#"-sia

By.".@lying Laplce transforms, solve the::: j.

t*&

,tr.,", \..1"

.:::.. ::. t:3,

t{*ll*16*** ,a

::: iq,4::: .

{u dj

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...,"ttt"

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r,r's"r;qill$..

,,-1, --+,s

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. dx dv ,":Solve the simulppeous equations i*, =sint. ;+x =cost us

Given that x : l, y,.""J when t : 0. ==;.] *t

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Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l4Material Science and Metallurgy

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b.

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Define atoqric packing factor and calculate atomic radius and packing factor for FCC

9_t1r9ture. :',,..o,., . ,,,, ..

,,, (08 Marks)With neat sk#oties, explain the different types of point impef$'Ciions. (08 Marks)State and explain the second Fick's law of diffi;sion. (04 Marks)

Draw the stress-strain curve for mild steel under tension and show the elastic region, plastic

Note: Answer FIVEfull questions, selectingat least TWO questionsfrom each part.

PART _ A

reglon.

. PART-B ..Draw and explain the Iron-Iron carbide equilibrium diagram and label all thefields.

i) Stiffnessii) Elastic strengthiiit Resilienceiv) Modulus of resilience ,r-'i-" 'iiv) Toughness. ,,'..,;..';"' ,,"

Differentiate between slip and'tlvinning.

With neat sketches, explain the stages of moderately..,,,,4uctileload.

Yh?t is meant bry stress relaxation? Explain in briefly,Explain the various factors affecting fatigue.

Define solid"solutions. Explain the types of solid solutions with neat sketches. (10 Marks)Explaiufhe factors governing the formation of substitutional solid solufipns. (05 Marks)Staib;te Gibb's phase rule and explain the terms. t.-i (05 Marks)

Two metals A and B have their melting points at 600oC and 400'C respectively. Thesemetals do not form any compound or inter mediate phase. The maximum solubility in eachother is 4%o, whichremains the same until OoC, an eutectic reaction takes place between 650Z

A and 35%B at 300oC.Determine the following:D Draw the phase diagram of A - B and label all the important points and fields.iD Find the temperature at which a 20o/o A, 80% B alloy starts and completes

solidification.iii) Find the temperature at which the same alloy

solid.I of2

is composed of 50% liquid and 50%o

(I0 Marks)

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lOME/AU42A

6 a. Draw the T-T-T diagram for 0.8% C eutectoid steel and explain briefly. (10 Marks)b. Define hardenability. Explain with a neat sketch the Foming-end-quench test. (05 Marks)c. Explain with neat sketch the flame hardening process. (05 Marks)

'';.*;i' a. [rite.,,h:,*-r?s.ition,

structure and their applications offfi,

,ri l:,

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1rir

':": 'j

,,,,,,,,,,,,, (10 Marks)

i) White cast iron.' ' ".',',,,, ii) Malleable iron.

.::l' /... iii) S.G. iron.b'..,, ,,.W.rite the composition and properties of the following:b..., .,.W.rite the composition and properties of the following:

'0]lJettow ct - brasses ..' ,,,,''

|l=;*Hhl brasses e,,.=

iii) 'ffiltrVbrass. u,%t.-

8 a. Define conffisite material and explain the classification of cffic{ritb materials.b. What are the adVantages and limitation of composite materiql?c. Write a brief notd on FRP ,..=,\ '

-'l

(10 Marks)

(10 Marks)(06 Marks)(04 Marks)

""::,,!"*rf{<**

i:... \t::.

;:," ,::: \:i-..',..:

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USN lOME/AU43

Time: 3 hrs.

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Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2014Applied Thermodynamics

Note: 1. Answer FIVEfull questions, selectingat least TWO questions from each part.

2. Use of steam and vapour tables is not permitted

a. Defue,the terms: i) Stoichiometric ar; ii) Percent excess air; iii) Enthalpt of cNiv) Enthalpy of formation; v) Adiabatic flame temperature. (10J -'---'-'---'-'-' / "---------' --_-_r-------_-'

b. The volurnetric composition of dry flue gases obtained by the pombustion of an unknownhydrocarboin'is 1'2.7% COz,0.9o/o CO,3.9o/o Oz and 82.5% Nz. Determine:

D Composition 'of the fuel; ii) Theoretical air required for complete combustion;iii) Percentage of excess air required. (10 Marks)

't',, "a. With the help of P-V ard T-S diagram, derive an e(iration for theoretical air standard

efficiency of a semi diesel (dual) cycle in terms of compression ration, cut off ratio andexplosion ratio, with suitable'assumptions. (10 Marks)

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b. In an air standard diesel cycle tho compression ratio is 15 and the fluid properties at thebeginning of compression are 100 kPa and 300K. For a peak temperature of 1600K calculatei) the percentage of stroke at which cut-off occurs; ii) the cycle efficiency and iii) thework output/kg. ,,

, ,10 Marks)

a. Describe the following as applied to I.C. engine: i) Morse test; ii) Heat balanc. rl"o.rt*u.ug

b. During a test on a single eylinder 4 stroke oil engine the following observations were madeBore : 30cm, stroke :,450m, duration of trail: th, total fuel consumption:7.6k9 calorificvalue of fuel : 45,000 kJ/kg, total revolutions made : 12000, mean effective pressure 6 bar,net brake load: 1.47 kN. Brake drum diameter 1.8m rope diameter 3cm. Mass of jacket

cooling water circulated:550kg water enters at 15'C waiei',leaves at 60oC. Total airconsumption 360kg room temperature 20"C, exhaust gas temperut$ : 300'C. Calculate:i) Indicated and brake power; ii) Indicated thermal efficiency; iii) Mechanical efficiency;iv) Draw the heat balance sheet on minute basis. (12 Marks)

a. Why carnot cycle is not used as a reference cycle for steam power plant? ,,,,::,' (03 Marks)b. .,,, Sk.,.h the flow diagram and corresponding T - S diagram of a reheat vapour cycle and

,,," derive an expression for reheat cycle efficiency. (07 Marks)0. A 40MW steam power plant working on Rankine cycle operates between boiler pressure of

4MPa and condenser pressure of 10 kPa. The steam leaves the boiler and enters the steamturbine at 400oC. The isentropic efficiency of steam turbine is 85%. Determine:

:

i) The cycle efficiency; ii) The quality of exhaust steam from the turbine and iii) Steam .

flow rate in kg/hr considering pump work.tes oI steam.

Pressurebar

ts oc Specific volume

-'lkgSpecific enthalpy kJ/kg Specific entropy

kYke KV1 hr h,, h" Sf S.

lPSo

40 2s0.3 0.00125 0.049 t087.4 t7t2.9 2800.3 2.797 3.272 6.0690.1 45.83 0.0010 14.67s 191.8 2392.9 2584.7 0.649 7.502 8.1s 1

:"$--S

Properties of stea (10 Marks)

PART _ BState the advantages of multistage compression.

lOME/AU43

(04 Marks)5a.b.

v.

Derive the relation among volumetric efficiency, the pressure ratio and index ofcompression and expansion. Plot the variations of volumetric efficiency with clearance forvarious pressure ratio. (08 MarkS)

r: l.4 compression: expansion= n: 1.33. :

(08 Marks)

Atmospheric air at 1 bar and 2l"C istakgl into a single stage reciprocating compressor. It iscompressed according to the law PVl3 : C, to the delivery pressure of 6 bar. ifhe

compressor takes lm' of airlmin. The speed of the compressor is 300 rpm. Stroke todiameter ratio is equal to 1.5:1 mechanical efficiency of the compressor 0.85 motortransmission efficiency 0.9 calculate:i)-' ,' The indicated power and isothermal efficiency.ii) ,, The cylinder dimensions and power of motor required to drive the eompressor.

, ,,,,,,, , (08 Marks)

Discuss witkthe help of T-S diagrams the three methods of ir4prqving the thermal efficiency'1,::t 'i:'

of an open cyile.gas turbine plant. : ::::, '

(12 Marks)

A gas turbine unit,,,,has apressure ratio 6:1 and maximugl:cycle temperature of 610oC. Theisentropic efficiency of the compressor and turbine are 0.80 and 0.82 respectively. Calculatethe power output in kilowatts of an electric genefrltor geared to the turbine when the airenters the compressor at 1,5,"C and rate of 16kg/s".":Assume Cr: 1.005 for Cp: 1.11 for

6a.

b.

a. Write a short note on air cycle refrigeralion. (04 Marks)b. With the help of neat flow diagram explain the working of steam jet refrigeration system.

(08 Nlarks)c. An ammonia vapour compreqg'ion,refrigeratipg machine works between 25"C and -20"C.

The ammonia leaves the compressor in dry and saturated condition. Liquid ammonia isunder cooled to 21.5'C befire passing through throttle valve. The average specific heat ofliquid ammonia is 4.75 kJ/kg"C. Find the theoretical cop of machine. The lollowingproperties of NH: are,given. If the net refrigeration required is 400 x 103 kJ/h. Find themass of ammonia circulated/min. Assume cop actual is 75o/o of cop theoretical:

8a,b:

..c.

IIllIl. l\ssull}g u( UZ

Temp oC Liquid kJ/ks Vaoour kJlks KhrkJ/ke Sr hn So

25 537.6 4.612 1708.5 8.53*.'-20 328.4 3.854 r661.0 9.1 18

: ,,,' (08 Marks)

Derive the equations for relative humidity and specific humidity of moist air. (04 Marks)With neat sketch explain the working of air conditioning system for hot and dry weather.Present the process involved on a psychrometric chart (06 Marks)Calculate: i) relative humidity; ii) humidity ratio; iii) dew point temperature; iv) densityand v) Enthalpy of atmospheric air when the DBT is 35oC, WBT :23oC and the barometerrreads 750mm Hg.

2 of2

rt,(10 Marks) ,,

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Time: 3 hrs.

..,,, answer sheet.

PART _ AL a. Define degrees of freedom. Find the degrees of freedom

showq,i,n.Fig.Q1 (a)

IOME/AUIPIMITL44

Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2ol4Kinematics of Machines

.,,,,!.

Max. Marks:100Note: l. Answer FIVE full questions, selecting

2. Graphical solution may be obtained either on graph,..or on

{)o(.)

Lp'

C)

=(,)L

oXoo-(n=o-;-s\-69-r)bolioo.= c\(!$rOOYOoC-e()

o>*,a

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ootr(!(B

266rE(!J o.r

=9

AXtro.oi|a=toaqq

:(]5.v>\ (H

t50iu=sotr>=oo:(r<-i 6iooZ

li

o.

"' ,,

for the following mechanism as

' (10 Marks)

b.

2a.b.

3

,,1

',....

"',rO *u*"r,

Define the following terms with examples:i) Kinemati" pui.,,,, ii) Mechanism -') Structr*re iv) Inversion

.,... t"*..,ii'. ... ;,:t.:t (10 Marks)

Describe wiftaeat sketch two inversion of double slider-crank chain mechanism. (10 Marks)Derive 4a'eipression for necessary condition of correct steeririg _explain Ackermann

A four bar mechanism shown in Fig. Q3 crank BC rotates with an angular velocity of100 radlsec and an angular acceleration of 4400 radlsec2 at the instant when the crank makesan angle 53o to the horizontal. Draw the acceleration polygon and determine the linearacceleration of points E and the angular acceleration of link 3.

E

,t--4100 rillrc/-u = F0 yad

l.r.c

Fig. Q3

4a.b.

c.

la.b.

Write a note on Kennedy's theorem.List the properties of instantaneous centre of rotation.

B and ii) Angular velocity of connecting rod AB.

In a slider crank mechanism shown in Fig. Q4 (c) the crank OA : 300 mm and connectingrod AB : 1200 mm the crank OA is turned 30o from inner dead centre. Locate all theinstantaneous centres. If the crank rotates at 15 radlsec clockwise, find i) velocity of slider

maximum acceleration during outstroke.,r*r,<**

2 of2

IOME/AUIPIMITL44(05 Marks)(05 Marks)

(10 Marks)

(12 Marks)

(06 Marks)

Fig. Qa (c)

ttt,,, i.t,.,..,,. PART - B5 a. berilre-an expression for displacementarralysis of a4bar mechanism using complex algebra

methOd. (10 Marks)b. For a si@e slider mechanism, of Fig. Q5 (b) determine the velocity and acceleration of

piston, angufar acceleration of connecting rod. Take crank length : 50 mm, connectingrod:200 mm, Crank speed: 300 rpm (constant), Crank angle 30o. (10 Marks)

[,Fig. Qs (b)

"""l)errve an equatron to determme'Ength oI are ot contact tor matrng of 2 spur gear. (08 Marks)Two gear wheel mesh externally and:.,are to give a velocity ratio of 3. The teeth are ofinvolute form of module 6 mm and standard addendum one module. Pressure angle: 18o.Pinion rotates at 90 rpm. Findi) Number of teeth on each wheei so that interference is just avoided.ii) Length of path of contacl, .

iii) Maximum velocity of sllding between teeth.iv) Number of pairs of teeth in contact.

Explain with neat sk*tih classification of gear trains.In an epicyclic geai train, the internal wheels A, B and the cornpgund wheel C and D rotateindependentl,y'about the axis 'O'. The wheel E and F rotate'CIh-a pin fixed to the arm G.E gear wi . ,A and C, and F gears with B and D. All the wheels have same pitch and thenumbero,f teeth on E and F are 18, C and D are 28,26 respectively.i) Sketch the arrangement.ii) Number of teeth on A and B.iii) If arm (G) makes 200 rpm clockwise and gear A is fixed, find speed of gear: Biv) If arm (G) makes 100 rpm clockwise and gear A make 50 rpm CCW, find the speed of

gear B. (14 iVlarks)

A cam rotating at uniform speed of 300 rpm operates a reciprocating follower through aroller 1.5 cm diameter. The follower motion is defined as below:i) Outward during 150" with UARM.ii) Dwell for next 30o

iii) Return during next 120o with SHM.iv) Remaining dwell period.Stroke of the follower is 3 cm. Minimum radius of cam is 3 cm. Draw the cam profile whenthe follower axis is offset to the left by 1 cm and determine maximum velocity and

(20 Marks)

USN

Time: 3 hrs. Max. Marks:100

lOME/4U45

06 Marks)

(12 Marks)(08 Marks)

Fourth Semester B.E. Degree Examination, Dec.2013 lJan.2014Manufacturing Process - ll

Note: Answer FIVE full questions, selectingat least TWO questions from each part.

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PART _ AI a. Explain with a neat sketch the nomenclature of a single point cutting tool, highlighting the

significance of different angles. (08 Marks)

b. With necessary sketches, explain the types of Toolwear. . . (08 Marks)

c. Briefly de.sc:ibe the various types of chips produced during metal ng operations4 Marks)

',.,,,,2 a. What are the desirable properties or characteristics of an idealciitting tool materiulfru

*u.u.yb. Briefly explain the desirable properties and purpose of cutting fluids. (06 Marks)

c. With a neat sketch, explain different heat affected zones during orthogonal cutting.(08 Marks)

3a.b.

Differentiate between turret lathe and capsten:lathe. (06 Marks)Explain with the help of a neat sketclt, the Whitworth quick return mechanism of a shaper.

(08 Marks)c. Compare shaper and planer in ter,mspf their operation, types of workpiece and applications.

, l-,. (06 Marks)

a. Draw a neat diagram of a radial drilling machine. Name and explain the parts and itsprinciple of operation. (07 Marks)

b. Explain with sketches tkre lollowing operations in a drilling machine:(i) Reaming (ii) Boring (iii) Counter boring. (iVJ Trepanning. (07 Marks)

c. Describe twist drill nomenclature using sketches. (06 Marks)

..:::

,il pART-B ,,,,,,,,,,,,,,,i,,,,,,

5 a. Differentiate between:(i) Up milling and down milling ii) Simple indexing and compound,i+dexi58

Marks)b.\Mithaneatsketch,exp1aintheworkingofanuniversa1dividinghead.c. Show the calculation for setting dividing head to mill 69 teeth (division) on a spur gear

blank by compound indexing. Index plate with circles of holes patented by the Porous and

Plate No. 2 - 21,23,27,29,30, 33Plate No. 3 - 37,39, 41,43, 47,49

6 a. With respect to grinding process, differentiate between:(i) Glazing and loading(ii) Dressing and truing of wheels(iii) Cylindrical grinding and centreless grinding.

b. Explain the different factors to be considered in the selection of a grinding wheel.

7a.b.

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Sketch and explain the process of super finishing.What is Honing? Explain with sketch.List the operations and application of polishing and buffrng.

lOME/AU45

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principle of a electron beam mactiining

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(EBM) and what are its limitations.,,"8,riefly describe the principle of electro-discharge

afld',,,what are its advantages and disadvantages.1n'

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lOME/AU46B

Max. Marks:100Note: Answer FIVE full questions, selecting

at lesst TWO questions from each part.

PART-A " ,.

Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4Fluid Mechanics

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a. Define following and mention their units:(i) 1\4ass. density(iv) Bulk.modulus (v) Capillarity

b. Explain effect of variation of temperature on viscosity of liquid and gases.

cylinder at 100 rpm, determine,,the viscosity of the fluid.

c. A 15 cm diameter. vertical cylinder rotates concentrically inside another cylinder ofl5.l0cm. Both cylinders are 25 cm high. The space between the cylinders is filled with aliquid whose viscosity ii unknown. If a torque of 12 N-m is required to rotate the inner

(10 Marks)

(04 Marks)

(06 Marks)

(06 Marks)

a. Define: (i) Gauge pressure (ii) Vacuum ppiior. (iii) Absolute pressure. (03 Marks)

b. A hydraulic press has a ram of 30 cm diameter and a plunger of 5 cm diameter. Find theweight to be lifted by the hydraulip press. When the force applied at the plunger is 400 N.

(03 Marks)

c. Derive an expression for total pressure and centre of pressure on an inclined plane surfacesubmerged in liquid. (08 Marks)

d. A pipe line which^ is 4 meter in diameter contains a gate valve. The pressure at the centre ofpipe is 19.6 N/cm2. Ifihe pipe is filled with oil of spgr. 0.87, find the force exerted upon thegate and position of cbntre of pressure.

a. Define following terms:(i) Buoyaaoy (ii) Centre of buoyancy (iii) Meta centre lin|Msta centric height.

i,...,,!, ,,, (04 Marks)b. Explain the condition for stability of submerged and floating bodies.c. A eone of specific gravity S, is floating in water with its apex do as a diameter

Derive Euler's equation of motion. Also derive Bernoulli's equation. \stry ,z'110 Marks)

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A pipe of diameter 400 mm carries water at a velocity of 25 m/sec. The pressures at thepoints A and B are given as 29.43 N/cmz and 22.563 N/cm2 respectively, while the datumhead at A and B are 28 m and 30 m. Find the loss of head between A and B. (07 Marks)

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lOME/ALT46B

PART _ B

Explain: (i) Geometric similaritymodel and protot)?e.

(ii) Kinematic similarity

A vertical venturimeter has an area ratio 5. It has a throat diameter of 10 cm. When oil ofspecific gravity 0.8 flows through it, the mercury in the differential gauge indicates a

difference in height of 12 cm. Find the discharge through venturi. Take e 6 : 0.98. (06 Marks)

The functional torque T of a disc of diameter D rotating at a speed N in a fluid of viscosity p

(iii) Dynamic similarity(06 Marks)

and density p in a turbufent flow is given by

T = Dsx,p4l=+= I, ,LD'NP-]

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Derive Darcy Weisbach equation for flow tkough pipe. ,, ,

What do you mean by hydraulic gradient line and total energy line?

A horizontal pipe line 40 m long is connected to a watff tank at one end and dischargesfreely into the atmosphere at the other end. For fiist 25 m of its length from the tank, thepipe is 150 mm diameter and its diameter is suddenly enlarges to 300 mm. The height ofwater level in tank is 8 m above the centie of pipe. Considering all losses of head which

(08 Marks)

(08 Marks)

(02 Marks)

occur, determine the rate of flow. TAke f : 0.01 for both sections of pipe. (10 Marks)

For a fluid flow through a pipe; show that maximum fluid velocity is twice the averagevelocity. Also derive Hagen Poiseuille's equhtion (12 Marks)

Determine (i) pressure gradient (ii) the shear stress at the two horizontal parallel plates and(iii) the discharge per meter width for the laminar flow of oil with a maximum velocity of2 m/sec between tWo horizontal parallel fixed plates which are 100 mm apart.p: 2.4525 N-s/m2. (08 Marks)

Explain the terms:(i) Lift :(ii) DraS (iii) Displacement thickness (iv) Momentum thickness. (08 Marks)

Define the terms sonic flow, subsonic flow and supersonic flow. (03 Marks)

A flat'plate 1.5m x 1.5m moves at 50 kmph in stationary air of density 1.15 kg/m3. If thecoefficient of drag and lift are 0.15 and 0.75 respectively, determine(i) The lift force, (ii) The drag force, (iii) The resultant force, (iv) Power required tothe plate in motion. (09 Marks)

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