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2a.

1OMAT41

December 2Ol2

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Fourth Semester B.E. Degree Examination,

Engineering Mathematics

Time: 3 hrs.Note: Answer FIVEfull questions, selecting

ut least Tl'yO questions from each part.

PART _ A

I a. Using the Taylor's series method, solve the initial value problem

the point x:0.1

c.

0)ooLa

()

o!

oX

dv

-lb!'a6.= a'l

:boE()-O

Ep

;,i :l()(l)

6-O=-coi

-o>6!6=

3o'-^

o- 5-

o''oFl

o=adLO

Y

^:oo-tr40iD=o. eitr>Xo5:U<-i 6i

ooz

oo.

b. Employ the fourth order Runge-Kutta method to solve !Idx

x: 0.2 and x :0.4. Take h:0.2.

c.

.rl _rl \-::--r-

= *. y(0) : I at the pointsy'+*'

(07 Marks)

i, -1 onto the points i, 0, -i(06 Marks)(07 Marks)

(07 Marks)

Given 9 = *r + y', y(0) : 1, y(0.1) : l.1169,y(0.2) :1.2773,y(0.3) : l.5049.Find y(0.a)1Jox

using the Milne's predictor-corrector method. Apply the corrector formula twice. (07 Marks)

Employing the Picard's method, obtain the second order approximate solution of the

following problem at x: 0.2.

(06 Marks)

Using the Runge-Kutta method, find the solution at x : 0.1 of the differential equation

d'y , dy- ', -x' -' -Zxv =1 underthe conditions y(0): 1, y'(0):0. Take step lengthh:0.1.dx' dx

(07 Marks)

Using the Milne's method, obtain an approximate solution at the point x : 0.4 of the

problem #.3":l-6y=0, y(0):1, y'(0):0.1. Given that v(0.1): i.03995,

y(0.2): 1.138036, y(0.3) :1.29865,y'(0.1) :0.6955, y'(0.2):1.258, y'(0.3) : 1'873'(07 Marks)

3 a. If (z) : u * iv is an analyic function, then prove that = ;r'1zl' .

(06 Marks)

dv dzI!-=x1-yz, =y+zx, y(0):1, z(0):-1.dxJ'dx

b.

4 a. Find the bilinear transformation that maps the points 1,

respectively.b. Discuss the transformation W: e'.

c. Evaluate Ismfz' f co-4dz

, where c is the circle lzl:3.,. (r-l)'(z-2)

r2 / ^ 12

[frrr,t,.J .[*rr(z)r,J

b. Find an analytic function whose imaginary part is v = e* {(r' - y') cos y -2xy sin y} .

c. If t(z): u(r, 0) + iv(r, 0) is an analytic function, show that u and v satisfy ,h.(oJ#;,tT,]

9}.*19g*14 = o. (07 Marks)Ar' r& r'00'

Max. Marks:100

\

t\

1OMAT4l

5A.

b.

(06 Marks)

-n2)Y=o in

(07 Marks)

(07 Marks)c.

6 d:'(06 Marks)

b.--A has contains 10 white balls and 3 red balls while another bag contains 3 white balls and'qW;.aiulls. Two balls are drawn at ransom from the first bag and put in the second bag and

then a ball is drawn at random from the second bag. What is the probability that it is a white

ball? (07 Marks)

c. In a bolt factory there are four machines A, B, C, D manufacturing respectively 20%o, l5oh,

25% 40% of the total production. Out of these 50 , 40 , 3o/o and 2o/o respectively are

defective. A bolt is drawn at random from the production and is found to be defective. Find

the probability that it was manufactured by A or D. (07 Marks)

7 a. Th. probubility distributi m variable X is given by the following table:

Determi*, the value of k and find the mean, variance and standard deviation. (06 Marks)

b. The probability that a pen manufactured by a company will be defective is 0.1. If 12 such

pens are selected, find the probability that (i) exactly 2 will be defective, (ii) at least 2 willbe defective, (iii) none will be defective. (07 Marks)

c. In a normal distribution,3lo/o of the items are under 45 and 8o/o are over 64. Find the mean

and standard deviation, given that A(0.5) :0.19 and A(1 .4):0.42, where A(z) is the area

under the standard normal curve from 0 to z>0. (07 Marks)

PART _ B

Express the polynomial 2x3 -x' -3x+2 in terms of Legendre polynomials.

Obtain the series solution of Bessel's differential equation *' !* *$ * 1*'dx' dx

the form y: AJn(x) + BJ-"(x).I - d' ,x'-l)'.Derive Rodrique's formula P.(*) = 2.r! d*l

, A tt .

${ate the axioms of probability. For any two events A and B, prove that

., PIA u B) = P(A) + P(B) - P(A ^

B) .

8a.

b.

A biased coin is tossed 500 times and head turns up 120 timbs. Find the 95% confidence

limits for the proportion of heads turning up in infinitely many tosses. (Given that z": I.96)(06 Marks)

A certain stimulus administered to each of 12 patients resulted in the following change in

blood pressure:5, 2, 8, -1, 3, O, 6, -2, 1, 5, 0, 4 (in appropriate unit)

Can it be concluded that, on the whole, the stimulus will change the blood pressure. Use

to.os(l l):2.201. (07 Marks)

A die is thrown 60 times and the frequency distribution for the number appearing on the face

x ls glve followine tablen bv thex I 2 3 4 5 6

Freouencv 15 6 4 7 11 t7Test the hlpothesis that the die is unbiased.

(Giventhat 1lo,(5) =11.07 and X3o,(5) =15.09)

nXi 1

1 0 1 2 J

p(xi) 0.1 k 0.2 2k 0.3 k

c.

,r*{<{<*

(07 Marks)

USN

Fourth Semester B.E. Degree Examination, December 2012Engineering Mathematics - IV

O6MAT41

Max. Marks:100

of v at .* : 0.1 and

(06 Marks)

(06 Marks)

regions i) z <lzl<l

(07 Marks)

(07 Marks)

(06 Marks)

(07 Marks)

(07 Marks)

Z,

ooo!o.

()c3()!

bor

s-=6

'-o '

=oo,-t.= a-i

gdioEeO

=P

o2

a=

oc)

50c

a6

-aoLOo€:? C)sQ.Fg

o..

edC.-

h12t.2X9c50o=

tr>=o5-(r<- C.l

oo

a

Time: 3 hrs.Note: Answer FIVEfull questions, selecting

ut least TI,YO questions from each part.

PART _ A

1 a. Given that +=x2 +y' and y(0)=1, to find an approximate valuedx

x:0.2 by Taylor's series method.

b. UsingEuler'smodifiedmethod, solveforyatx:0.1 if {y - y-*,y(0): l,carryoutthree

dx v+xmodifications. (07 Marks)

c. Given I=(t+y)*'andy(1):1,y(l.1):1 .233,y(1.2):1548,y(1.3):1.979,determineox

y(1.4) by Adams - Bash forth method. (07 Marks)

a. Show that an analyic function with constant modulus is constant. (06 Marks)b. Findtheanallticfunction f(2)=u+iv,if u=e-*{(x'-y')cosy+2xysiny} (07Marks)c' Find the bilinear transformation which maps the points z: 1, i, -1 into the points w: i, 0, -i

and hence find the image lrl.t. (07 Marks)

3 a. Using the Cauchy's integral formula, to evaluate l, tlil"

=, dz where c : lzl=2.l (,-1)(z-2)

b. obtain the Laurent's series for the function f (z) = ." =' -in thez- +52+6

ii) lrlrt.c. Determine the poles of

(, -1)' (z + 2)and the residues at

4 a. prove that e%ex'= it'J,(x).

b. Show that J, (><) = ;;*, (x) + J,-, (r)l

c. Explain the polynomial 2x3 - x' -3x + 2 in terms of Legendre's polynomials.

PART _ BFit a straisht line to the follow

x: 0 I 2 aJ 4

v: 1.0 1.8 aaJ.J 4.5 6.3

fa('sa//s

i2t

5a. ing data:

I of2

(06 Marks)

t\

O6MAT41

5 b. prove that tan e=(l-t'l++, where y, o,, o, have their usual meanings and

I r /o;+o;explain the significance of r = t1 and r: 0' (07 Marks)

c. A certainproil.- is givento four students for solving. The probability of their solving the

problem are f , % , i, and /, respectively. Find the probability that the problem is solved.(07 llarks)

a. The probability-t.lP(x) = Yne ,

distribution.b. Derive the mean and variance of the binomial distribution.

c. If x is an exponential variate with mean 4, evaluate i) P(0<x<1) ii)

iii) P(-m<x<l0).

7 a. Define the terms: i) Null hypothesis ii) Level of significance and iii) Confidence limits.(06 Marks)

A sugar factory is expected to sell sugar in 100 kg bags' A sample of 144 bags taken from a

day'i output ,ho*r'the averag. ,nd S.D. of weights of these bags as 99 and 4 kg

respectively. Can we conclud. tt ut the factory is working as per standards? (Table value of

,: t.ga at S%oLog) Q7 Marks)

The following table gives the number of aircraft accidents that occurred during the various

days of the -week. iind ,rh.ther the accident are uniformly distributed over the week.

c.

density function P(x) of a continuous random variables is given by,

-oo<x<co, prove that Yo=/z' Find the mean and variance of the

(06 Marks)(07 Marks)

P(x>2) and(07 Marks)

(07 Marks)

independent(06 Marks)

(07 Marks)

8a.

( X3o, = 9 '41 for 4 d'f')

Day Sun Mon Tue Wed Thu Fri Sat Total

No. of accident t4 t6 8 t2 11 9 l4 84

ibution for the following table:

Determine the marginal distribution of x and y and verifY that x and Y are

variables.b. Find the fixed probability vector of the following regular stochastic matrix.

ly, y^ %

A =l Y, .,9'o /,Io 1,;aQ

c. Define theI

i) Regular stater,fi*..

ii) Periodic state iii) Recunent state and iv)

***{<r<

Transient state.(07 Marks)

The ioint bi itv dtstrt lo

vx

21J 4

1 0.06 0.15 0.09

2 0.14 0.35 0.21

( /

usNilT-1 "_il_

'l'itrrrl: .1 hrs.

N*te : ,{n.rwcr r:r1y .l?Ffi.firf/ ryrres/rdns, se/rclirrg g#rns/

it. ll:xplain lndiln Srirr:dard {lSglgrvith tire n*lrt rli*gran"t.

lr. ( ,)lllI;tlr' llrc lull,,rrirrr:

l9{r3} itbng rvith 1hq cr}nccpi ol'lilriit" sizc and t*lerancc.{05 Marks)

l0M 842 B/A U42B/tlM42rI'L4:

Max" M*rlis: l0{)

T'lr'{) questir;xs -{iorrr rw'y'r ;rnr/"

{{}6 l{arks}{0"1 &lxrks}

(lii ${*rks}

ii) lntcrchlrrgcabilitl xn(j sclccli\r*{05 Murkr}

{{Xr }lnrksi{{)$ }t*r$s}

Fsrunth ,$emrster" II.E. Ilegree liraminationn l]*c*mb*r 2012fllle*hanicat Mea$ursment and MetroloEy

s:r{

7

$ir€3{}-.r

.1

€*aJ!.,,: c,

.g*

i:=

*.6't:

f*r?J'

:{i),Ur.5

*,5

tux:{ipara

!{

;(7-

i

j

l,^g'1" {rl. l.:xpl*in inlclnitri*rral prolitt,vpe nlctcr. rvith skctch,b' Wfral arc Air3'paints'l Wlrtre ure th* rirv poinls loc*tur.l9n 6{.}0rnr1 l;ar'Jc. Lising a ser ul":v-lli? slipr gaugrs. builii the 1irll*r.ving dimensions :

i; Ji)..i I l5 ii) 6tr{.108 iii) 5t.4q6 ir,) 78.1665.

i) lJLriiri i-t11 t{)lcr$ncr iincl {'orrrpr:uiitl lolcr.arre r:

ils$crnbIy,{]. State the "l';tyk:r's prirrciple arrd dtsign tlrc gaugcs t$ n"Ieosltrc lh* fit rlcsignatccl hr, Sl)f,r lx

llLrir-:h is prurluccd bl lrltsr prridrrrtir:rr. {lir'*n i) 5fJrrrrl lies hr:ti.;r*n }{) tr:5{}rr.rr"rr

iit ;'{).:l5dD, tt.tlUiL> iii) lrr,rndnrrrcrrri:lrlcr:iation 1}r hrk is ll[]'irr.iv) l-undarncnllll r.ki,'iirlirn lirr shrrli is -5.51)"'rr,vj "l'olerance gr*de iirr l"l'4 and I't^lt is "'ji" rncl ..15i".

Wrilctlrelype *l'I'lt lbr5{i}:+15enci cxprcssthcvalucirunilalcraliiirlsrrsion. {tt}t}Iarks}

:1. [xpiain thr r,r,urling r;l'a signra eompil.iilor. r.vi{h a skeleh. {t{} x*rks}h. \\'ith * neat diagr"alr. expllin thc principlc ol'u.*rkirrg ol"r.vD"l. {{}6 M;rrkr)t:. S*i**l th* siv-*s ol' anglc giursrli lcquirccl to hr"tild" lhc .irrglc .j7(r -l l' .1". shor.r. th*

Brrin!|cmclll oi"*liirgcs. {{}.t }lrrkr}

ii- l\iith a ne;tt sketuh. txplain thr rvt;r"king prinripL: olnn rurtu collinrelcr. {{}f: Mrrks}h. l)rllnc'"cl{cctir'u: iJilrnclcl" anil "l:rst sizc r.virc'-. l}crivc i:n cx1:rcssiun Lr r"lctcrnrir:c ths hrsl

sirc u,irc dilrurltr'. {{lll }.trrksic' ilor'l'iii} villl rllcitsttl'c lltc cltorr"l thickncss ril'spur g*irr toolir Llsing gr:ar loolh vrnliar".)

l:xplain *'illr I skrtch. {{x} M$rks}

il.

I"{ll'l'* $

l:xplilin tl"le coiti:*pl i:1"'gr:n*ruli/-r:d rncasurerni::lil sl,stelr).'. rvith trlnck diagriitn lijkin$ lltcrvorking ol'hcLrrdun pt*ssurr galrgir as lrr rramg:le . {{}fl Mrrk*}Lxplrrr, &ll\ llrrcc s\'$tL:ill r{s}l{}ilsd r:haraclcri.sli".:. {{}s i\{arks)(.I*ssily- i:nd ruh clirssit'r .rrilrs. l-:rplirirr liriclll.circh lype ol'!trr.)r" witl:,-rrrrrrr;.lic;rrrd lrou, i1

tar: i:e reduucd. {{}$ t\{*rks)

t).

C.

it. 5ik*lch and explairr tlic platftrnr halancc nrcthcd rr{'r:rclsurinu lirrce.b. wirh a rrcal skcrch. r:xplairr lhc rr,urking uI'h1.,draulic rlr,il;rrnorllcli:r.

ira

{o\#/r.{{*Iol l

\

t 0 M A{2 I}/A U 42 B/P M ,t2lT L42

c. Write a nolecnX *Y ploters. (0ll illarks)

Explain the inherent problcm prescnt in mechanical inrcrmeeli;rre rrroclilying systems.

Hxplain the rvr:rking rl"'Carhoel* I{ay Oscilloscope". ff H:XlWlal ixe electronic amplifiers? With a neat sketch, expl*in chcppcr amplifir3r. (88 Marks)

litate *nd explain the [au,s ol'thermocouple. (06 Mnrks]Explain th* principlc and u'nrking o{"unhonclcrl an<J horrrled elcctrical slrain ga1rges.

(06 Mnrks)

a.

b.

c.

h.

c. Wri{e noies on &ny two o{'the li:llowing :

i) Gauge tactur unel cross sensitivity.

iil l**p*r*ture compsns:rrion in resistan*e type strain g{}uges.iiii Calibration r:rf srrai:'r g$uges.iv) Wheal str:ne briclge arrongement fbr strain rne{isur"e$.}ent" {0S Marhs}

*#_ !q'

I '. t:*-..'"'---..- .*:*b%,: _.-q,: , ,f}' '\r1 -^

2 of?

(

b.

c.

()oo

a

(.)

()L

3e

-*tEoo.= o.l

b9!oc-o

a:;

o()

ootr

PG

!(g

o!

:qtro-o-iOEaoalt

LO5-6v,^:bo-cao'o)=o. iitr>=oU

(r<-i 6i

OoZ

oo.

USN

/lOME/AU43

Fourth Semester B.E. Degree Examination, December 2Ol2

Applied ThermodynamicsTime: 3 hrs. Max. Marks:100

Note: l. Answer FIYEfull questions, selectingat leust TWO questionsfrom each part.

2. (Jse of thermodynamic data book is permitted.

PART _ AL a. Define: i) Stoichiometric air-fuel ratio ii) Enthalpy of combustion

iii) Enthalpy of formation iv) Combustion efficiencyv) Adiabatic flame temperature. (10 Marks)

b. A sample of fuel has the following percentage composition by weight:Carbon :83oh, Hydrogen : 7lo/o, Oxygen :3oh, Nitrogen :2%, Ash: 1oZ

i) Determine the stoichiometric air fuel ratio by mass.

ii) If 20oZ excess air is supplied, find the percentage composition of dry flue gases by

volume. (10 Marks)

2 a. Derive an expression for air-standard efficiency of limited pressure cycle. (10 Marks)

b. The pressur.i on the compression curve of a diesel engine are at 1/8th stroke l.4bat and at

7/8th stroke 14bar. Estimate the compression ratio. Calculate the air standard efficiency and

mean effective pressure of the engini if the cut-off occurs at llllth of the stroke. Assume

initially air is at 1 bar and 27oC. (10 Marks)

3 a. List out the methods used for measuring friction power of an IC engine. Explain motoring

test. (05 Marks)

Explain Morse test.- (05 Marks)

During a trial of 60 minutes on a single cylinder oil engine having cylinder dia 300 mm,

stroke 450 mm and working on two-stroke cycle, the following observations were made:

Total fuel used: 9.6 litresCalorific value of fuel:45000 kJ/kgTotal number of revolutions : 12624

Gross mean efTective pressure : 7 .24 bar 4Pumping mean effective pressure: 0.34 bar t1Net load on brake : 3150 NewtonDiameter of brake drum: 1.78 m \ ':

Diameter of rope:40 mm \Cooling water circulated: 545 litresCooling water temperature rise : 25oC

Specific gravity of oil = 0.8

Heat carried away by the exhaust gases : I5oh total heat supplied.

Determine IP, BP and mechanical efficiency. Draw up the heat balance sheet on minute

basis. (10 Marks)

4a.

b.

With a schematic diagram, explain the working of reheat vapour power cycle and deduce an

expression for cycle efficiency. (10 Marks)

Aiurbine is suiplied with steam at a pressure of 32 bar and a temperature of 410oC. The

steam then expands isentropically to a pressure of 0.08 bar. Find the dryness fraction at the

end of expansion and thermal efficiency of the cycle.If the stiam is reheated at 5.5 bar to a temperature of 400"C and then expanded

isentropically to a pressure of 0.08 bar, what will be the dryness fraction and thermal

efficiency of the cycle? (10 Marks)

/

5 a. Show that for a

PART _ B

multistage compressor

,F 'F ,< * ,1.

a ^f ,)

lOME/AU43

where Z : stage pressure ratio,

(08 Marks)

humidification and then by cooling,capacity of the humidifier in kg/h,

(10 Marks)

,=[+l)-

x = number of stages, +: overall pressure ratio.P,

b. What are the advantages of multistage compressor? (04 Marks)

c. Air at standard atmospheric conditions is compressed and delivered to a receiver of 0.4 m

diameter and 1 m long until a final pressure of 10 atm is reached. Assuming ideal conditions

with no valve pressure drops, compute the power needed to drive the compressor for

(i) isothermal compression, (ii) polytropic compression with n: 1.32.

Assume that the receiver temperature is maintained atmospheric throughout and fillingtakes place in 5 min. atmospheric temperature is 25oC. Also calculate isothermal efficiency

of the compressor. (08 Marks)

6 a. With a neat block diagram and T-S diagram, explain how inter-cooling increases thermal

efficiency of gas turbine plant. (06 Marks)

b. With a neat sketch, explain the working of Ram Jet. (04 Marks)

c. In a gas turbine plant working on Brayton cycle with a regenerator of 75o/o effectiveness, the

atr at the inlet to the compressor is at 0.1 MPa, 30oC, the pressure ratio is 6 and the

maximum cycle temperature is 900'C. If the turbine and compressor have each an efficiency

of 80%, find the percentage increase in the cycle efficiency due to regeneration. (10 Marks)

7 a. With a neat schematic diagram, explain the working of steam jet refrigeration. (10 Marks)

b. A Freon-l2 refrigerator producing a cooling effect of 20 kJ/s operates on a vapour

compression cycle with pressure limits of 1.509 bar and 9.607 bar. The vapour leaves the

evaporator dry saturated and there is no under-cooling. Determine the power required by the

machine. If the compressor operates at 300 rpm and has a clearance volume of 3%o of stroke

volume, determine the piston displacement of the compressor. Assume volumetric efficiencyof compressor as 88o/o.

Properties of Fo reon

TemperatureOC

P

bar

V"m'/ks

hrkYke

hs

kJ/keSg

kJ/keKS-

kJ/keKcp

kJ/keK-2040

1.5099.607

0.1 088 17.874.53

178.61

203.050.073

0.27160.70820.683 0.747

(10 Marks)

of winter air conditioning system.(10 Marks)

b. For a hall to be air conditioned, the following conditions are given:

Out door condition:40oC DBT, 20"C WBTRequired comfort condition :20oC DBT, 60% RHSeating capacity of the hall : 1500

Amount oioutdoor air supplied : 0.3 m3/min/person

If the required condition is achieved first by adiabaticestimate: i) capacity of the cooling coil in TOR, ii)iii) condition of air after adiabatic humidification.

T2:

8 a. With a neat schematic diagram, explain the workingRepresent the processes on psychrometric chart.

-:,.--

/

()(.)

o

0.

C)

()

ox

)ll=A.! cr

:boE6)e0EEo3o=.=oAPoc)

OE50tr

-o,6

-4()OE

o-a

;oo=aiGE!o

>'3a0-tr oL)

o=o. ;itr>o.

U<- C']

ooZ

Loa

USNIOME/AU|PMITL44

Fourth Semester B.E. Degree Examination, December 2012

Kinematics of Maehines

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

at least TWO questions from each part.2. Gruphical solution moy be obtained either

on graph sheet or on the unswer book itself,

PART _ AI a. Differentiate between:

i) Degree of freedom and mobility of mechanism'ii) Kinematic chain and kinematic pair. (08 Marks)

b. Explain with a neat sketch, the single slider mechanism and its three inversions. (12 Marks)

line motion'. Prove that a point on the Peaucellier's mechanism traces2 a. Define 'Exact straightan exact straight line.

b. Define 'Quick return motion'mechanism.

(10 Marks)

in a mechanism and using a neat sketch explain the drag link(10 Marks)

3 In the mechanism shown in Fig.Q3, the slider 'C' is moving to the right with a velocity of1 m/sec and an accelerationof 2.5 m/sec2. The dimension of the various links are AB :3 m,

inclined at 45o with the vertical and BC : 1.5 m inclined at 45" with the horizontal. Determine

i) The magnitude of vertical and horizontal component of the acceleration of the points 'B' and

ii) The angular acceleration of links AB and BC.

ft(20 Marks)

rZl--k; l"Sr-r

D +--C

Fig.Q3j8g{-

4 a. State and prove 'Kennedy's theorem'. (06 Marks)

b. Explain the analysis of velocity and acceleration of a piston in a single slider mechanism

using Klein's construction. (06 Marks)

c. For a pin jointed four bar mechanism having the following dimensions. Fixed link AD : 4rn,

Driving link AB : 1.5m, Driven link CD :2.5m, connecting rod BC : 3m and angle BAD

is 60'. Link AB rotates at25 rpm. Determine using instantaneous centre method i) Angular

velocity of link 'CD' and ii) Angular velocity of link BC.

I of2

(08 Marks)

\

\

IOME/AUIPNIITL44

PART _ B

The crank of an engine is 200 mm long and the ratio of connecting rod length to crank radiusis 4. Determine the acceleration of the piston when the crank has turned through 45" from theinner dead centre position and moving at 240 rpm by complex algebra method. (20 Marks)

6 a. Derive an equation to determine the length of path of contact by a pair of mating spur gear.(08 Marks)

b. Two mating spur gears have 30 and 40 involute teeth of module 12 mm and 20" obliquity.The addendum on each wheel is to be made of such a length that the link of contact on eachside of pitch point has half the maximum possible length. Determine the addendum heightfor each gear wheel and length of line of contact. (12 Marks)

In an epicyclic gear train, the internal gears A, B and the compound gears C - D rotatesindependently about a corlmon axis O. The gears E and F rotates on pins fixed to the arm 'G'which turns independently about the axis 'O'. E gears with A and C, F gears with B and D. Allgears have the same module. The number of teeth on gears C, D, E and F are 28, 26, 18 and 18respectively.i) Sketch the arrangement.ii) If 'G' makes 100 rpm clockwise and gear 'A' is fixed, find speed of gear 'B'.iiD If 'G' makes 100 rpm clockwise and gear 'A' makes 10 rpm C.C.W. find the speed of

gear 'B'. (20 Marks)

A roller follower cam with a roller diameter of 10 mm is rotating clockwise. The lift of the camis 30 mm and the axis of the follower is offset to the right by a distance of 5 mm. The followercompletes the lift with SHM during 120o of cam rotation. The dwell at lift is 60o of cam rotation.First half of the fall takes place with constant velocity and second half with UARM during 120o

_pf cam rotation. The rest is the dwell at fall. Draw the cam profile. (20 Marks)

2 of2

USN

Time: 3 hrs.Note: Answer FIVEfull questions, selecting

at least TWO questions from each part.

PART _ A1 a. Distinguish between the following and mention their units:

i) Specific weight and mass density.ii) Surface tension and capillarity.iii) Dynamic viscosity and kinematic viscosity.

b.

c.Obtain an expression for capillarity rise.

Fourth Semester B.E. Degree Examination, Decemb er 2Ol2Fluid Mechanics

lOME/AU46B

Max. Marks:100

(09 Marks)(03 Marks)

(10 Marks)

(10 Marks)

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In a 50mm long journal bearing arrangement, the clearance between the two at concentriccondition is 0.lmm. The shaft is 2.0mm in diameter and rotates at 3000 rpm. The dynamicviscosity of the lubricant used is 0.01 pas and the velocity variation in the lubricant is linear.Considering the lubricant to be Newtonian, calculate the frictional torque the journal has toovercome and the corresponding power loss. (08 Marks)

2 a. Obtain an expression for the force exerted and centre of pressure for a completelysubmerged inclined plane surface. (10 Marks)

b. A cylindrical roller gate 3m in diameter is placed on the dam is such a way that water is justgoing to spill. If the length of the gate is 6m, calculate the_;ngggltrr{e and direction of theresultant force due to water acting on it. 4fXN (r0 Marks)

s3 a' 'r'*L:-ry,,t:ffi';,"ru,", ,ifil ,:;$li Xii) Metacentre \o\ r"- /-iiii) Metacentric height. \iff ;/ (04 Marks)

'6)

b. A solid cylinder of diameter 4m has a height of 3m. Fi ric height of thecylinder when it is floating in water with its axis vertical. Take specific gravity of thecylinder as 0.6. (08 Marks)

c. Explain the different types of fluid flows. (08 Marks)

4 a. Obtain an expression for Bernoulli's equation from Euler's equation of motion and alsomention the assumptions made. (10 Marks)

b. A pipe 300m long has a slope of 1 in 100 and tapers from lm diameter at the high end to0.5m at the low end. Quantity of water flowing is 5400 litres per minute. If the pressure at

5a.b.

the high end is 70 kPa, find the pressure at the low end.

PART - BDerive an expression for discharge through venturimeter.The resisting force 'F' of a supersonic plane dunning flight can be considered as dependentupon the length of aircraft '/', velocity 'v' , ak viscosity 'v' , atr density 'p' and bulk modulusof air 'K'. Express the functional relationship between these variables and the resistingforce.

1 ^f.)

(10 Marks)

t-

lOME/AU46B

a. Derive Darcy-Weisbach equation for loss of head in a pipe due to friction. _ (10 Marks)

b. A 5pm diameter pipe takes off abruptly from a large tank and rum 8m' then expands

abruptly to 10cm diameter and runs 43m, and next discharge directly in to open air with a

velocity of 1.5 m/s. Compute the necessary height of water surface above the point

dischaige. Take t : 0.0065 in the Darcy equation' (10 Marks)

a. prove that the maximum velocity in a circular pipe for viscous flow is equal to two times the(10 Marks)

average velocity of the flow' lel fixed plates which are kept at ab. en oi-l of viscosity 10 poise flow between two paral

distance of 50mm apart. Find the rate of flow of oil between the plates if the drop of

;;;;;. in a length oi t.Z- be 0.3 N/cm2. The width of the plates is 200mm' (10 Marks)

a. Define:i) Lift and drag.

ii) Displacement, momentum and energy thickness'

iiO trrtaitr number, mach cone and mach angle' r ^ (10 Marks)

b. A man descends to the ground from an aeioplane with the help of a parachute while is

homispherical having a diameter of 4m againsf the resistance of air with a uniform velocity

of 25 m/s. Find the ri.iglrt of the man if the weight of the parachute is 9.81 N. Take Ct : 0'6

and density of air: t.ZSkglm3. (10 Marks)

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