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# 4th Semester Mechanincal Engineering (2012-December) Question Papers

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## 4th Semester Mechanincal Engineering (2012-December) Question PapersDocument Transcript

• i.i.{ t { Cc?n^^ lia( 1OMAT41 USN Fourth Semester B.E. Degree Examination, December 2Ol2 Engineering Mathematics -lv Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting ut least TlyO questions from each part. 0) o o PART _ A L a I a. Using the Taylors series method, solve the initial value problem at () the point x:0.1 -::--r- rks) .rl _rl o ! b. Employ the fourth order Runge-Kutta method to solve !I = *. y(0) : I at the points oX dx y+* x: 0.2 and x :0.4. Take h:0.2. (07 Marks) dv c. Given 9 = *r + y, y(0) : 1J 1, y(0.1) : l.1169,y(0.2) :1.2773,y(0.3) : l.5049.Find y(0.a) b!-l ox a6.= al using the Milnes predictor-corrector method. Apply the corrector formula twice. (07 Marks) :bo E() -O 2a. Employing the Picards method, obtain the second order approximate solution of the following problem at x: 0.2. Ep dv I!-=x1-yz, dz dxJdx =y+zx, y(0):1, z(0):-1. (06 Marks) ;,i :l ()(l) b. Using the Runge-Kutta method, find the solution at x : 0.1 of the differential equation 6-O =- coi dy , dy - , -x - -Zxv =1 underthe conditions y(0): 1, y(0):0. Take step lengthh:0.1. -o dx dx >6 (07 Marks) !6= c. Using the Milnes method, obtain an approximate solution at the point x : 0.4 of the3o-^ problem y(0):1, y(0):0.1. Given that v(0.1): i.03995, o- 5- #.3":l-6y=0, o y(0.2): 1.138036, y(0.3) :1.29865,y(0.1) :0.6955, y(0.2):1.258, y(0.3) : 1873 oFl (07 Marks) o= ad r2 / ^ 12 LO 3 a. If (z) : u * iv is an analyic function, then prove that .[*rr(z)r,J = ;r1zl . Y [frrr,t,.J ^: oo- tr40 (06 Marks) iD= o. ei b. Find an analytic function whose imaginary part is v = e* {(r - y) cos y -2xy sin y} . tr> Xo 5: U< c. If t(z): u(r, 0) + iv(r, 0) is an analytic function, show that u and v satisfy ,h.(oJ#;,tT,] -i 6i 9}.*19g*14 = o. (07 Marks) o o Ar r& r00 z 4 a. Find the bilinear transformation that maps the points 1, i, -1 onto the points i, 0, -i o (06 Marks) o. respectively. b. Discuss the transformation W: e. (07 Marks) co-4dz c. Evaluate Ismfz f , where c is the circle lzl:3. (07 Marks) ,. (r-l)(z-2)
• t 1OMAT4l PART _ B5A. Express the polynomial 2x3 -x -3x+2 in terms of Legendre polynomials. (06 Marks) b. Obtain the series solution of Bessels differential equation * !* *\$ * 1* -n2)Y=o in dx dx the form y: AJn(x) + BJ-"(x). (07 Marks) I d ,x-l). tt - ,A (07 Marks) c. Derive Rodriques formula P.(*) = . 2.r! d*l6 d: \${ate the axioms of probability. For any two events A and B, prove that B) . (06 Marks) ., PIA u B) = P(A) + P(B) - P(A 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 n m variable X is given by the following table: Xi 1 1 0 1 2 J p(xi) 0.1 k 0.2 2k 0.3 k 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 will be 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 (07 Marks) under the standard normal curve from 0 to z>0.8a. 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) b. 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) c. A die is thrown 60 times and the frequency distribution for the number appearing on the face x ls glve n bv the followine table x I 2 3 4 5 6 Freouencv 15 6 4 7 11 t7 Test the hlpothesis that the die is unbiased. (Giventhat 1lo,(5) =11.07 and X3o,(5) =15.09) (07 Marks) ,r*{<{<*
• USN O6MAT41 Fourth Semester B.E. Degree Examination, December 2012 Engineering Mathematics - IV Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting o ut least TI,YO questions from each part. o o ! o. PART _ A 1 a. Given that +=x2 +y and y(0)=1, to find an approximate value of v at .* : 0.1 and dx () c3 () x:0.2 by Taylors series method. (06 Marks) if {y - y-*,y(0): !bor b. UsingEulersmodifiedmethod, solveforyatx:0.1 l,carryoutthree dx v+xs- modifications. (07 Marks)=6-o,-t =oo c. Given I=(t+y)*andy(1):1,y(l.1):1 .233,y(1.2):1548,y(1.3):1.979,determine.= a-i oxgdi y(1.4) by Adams - Bash forth method. (07 Marks)oEeO=P a. Show that an analyic function with constant modulus is constant. (06 Marks)o2 b. Findtheanallticfunction f(2)=u+iv,if u=e-*{(x-y)cosy+2xysiny} (07Marks)a= c Find the bilinear transformation which maps the points z: 1, i, -1 into the points w: i, 0, -ioc) and hence find the image lrl.t. (07 Marks)50c 3 a. Using the Cauchys integral formula, to evaluate tlil" dz where c : lzl=2.a6 l, l (,-1)(z-2) =,-ao LO (06 Marks) o€:? C) b. obtain the Laurents series for the function f (z) = ." the regions i) z <lzl<lsQ.Fgo.. = z- +52+6 -in ii) lrlrt. (07 Marks)ed Z,C.- c. Determine the poles of and the residues at (07 Marks)h12t.2 (, -1) (z + 2) fa(X9c50 sa/ /so=tr> 4 a. prove that e%ex= itJ,(x). i2t (06 Marks)5-=o(r< b. Show that J, (><) = (x) + J,-, (r)l (07 Marks)- C.l ;;*,o (07 Marks)o c. Explain the polynomial 2x3 - x -3x + 2 in terms of Legendres polynomials.a PART _ B 5a. Fit a straisht line to the follow ing data: (06 Marks) a x: 0 I 2 J 4 aa v: 1.0 1.8 J.J 4.5 6.3 I of2
• t O6MAT41 5 b. prove that tan e=(l-tl++, 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 f problem are , % , and /, respectively. Find the probability that the problem is solved. i, (07 llarks) The probability density function P(x) of a continuous random variables is given by, a. P(x) = Yne , -oo<x<co, prove that Yo=/z Find the mean and variance -t.l of the (06 Marks) distribution. (07 Marks) 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) P(x>2) and (07 Marks) iii) P(-m<x<l0). 7 a. Define the terms: i) Null hypothesis ii) Level of significance and iii) Confidence limits. (06 Marks) 144 bags taken from a A sugar factory is expected to sell sugar in 100 kg bags A sample of dayi output ,ho*rthe averag. ,nd S.D. of weights of these bags as 99 and 4 kg (Table value of respectively. Can we conclud. tt ut the factory is working as per standards? ,: t.ga at S%oLog) Q7 Marks) various c. The following table gives the number of aircraft accidents that occurred during the -week. days of the iind ,rh.ther the accident are uniformly distributed over the week. (07 Marks) ( X3o, = 9 41 for 4 df) Day Sun Mon Tue Wed Thu Fri Sat Total No. of accident t4 t6 8 t2 11 9 l4 84 8a. The ioint bi itv dtstrtibution for the following table: lo 1 v 2 J 4 x 1 0.06 0.15 0.09 2 0.14 0.35 0.21 Determine the marginal distribution of x and y and verifY that x and Y are independent (06 Marks) variables. b. Find the fixed probability vector of the following regular stochastic matrix. y^ ly, % (07 Marks) A =l Y, .,9o /, Io 1,;aQ c. Define the I i) Regular state ii) Periodic state iii) Recunent state and iv) Transient state. r,fi*.. (07 Marks) ***{<r<
• ( / usNilT-1 l0M 842 B/A U42B/tlM42rIL4: "_il_ Fsrunth ,\$emrster" II.E. Ilegree liraminationn l]*c*mb*r 2012 fllle*hanicat Mea\$ursment and MetroloEy litrrrl: .1 hrs. s Max" M*rlis: l0{) : : ,{n.rwcr r N*te r:r1y .l?Ffi.firf/ ryrres/rdns, se/rclirrg g#rns/ Tlr{) questir;xs -{iorrr rwyr ;rnr/" 7 { l,^g1" { \$ir rl. l.:xpl*in inlclnitri*rral prolitt,vpe nlctcr. rvith skctch, €3 {{}6 l{arks} {}-.r b Wfral arc Air3paintsl Wlrtre ure th* rirv poinls loc*tur.l9n 6{.}0rnr1 l;arJ {0"1 &lxrks} c. Lising a ser ul":v-lli? slipr gaugrs. builii the 1irll*r.ving dimensions : .1 i; Ji)..i I l5 ii) 6tr{.108 iii) 5t.4q6 ir,) 78.1665. (lii \${*rks} it. ll:xplain lndiln Srirr:dard {lSglg l9{r3} itbng rvith 1hq cr}nccpi ollilriit" sizc and t*lerancc. €* rvith tire n*lrt rli*gran"t. {05 Marks) aJ lr. ( ,)lllI;tlr llrc lull,,rrirrr: !., i) lJLriiri i-t11 t{)lcr\$ncr iincl {orrrpr:uiitl lolcr.arre r: ii) lntcrchlrrgcabilitl xn(j sclcclir* ,: c, ils\$crnbIy, {05 Murkr} {]. State the "l;tyk:rs 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 .g* 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, i:= vj "lolerance gr*de iirr l"l4 and It^lt is "ji" rncl ..15i". *.6 t: Wrilctlrelype *lIlt lbr5{i}:+15enci cxprcssthcvalucirunilalcraliiirlsrrsion. {tt}t}Iarks} f*r :1. [xpiain thr r,r,urling r;la signra eompil.iilor. r.vi{h a skeleh. {t{} x*rks} ?J h. ith * neat diagr"alr. expllin thc principlc olu.*rkirrg ol"r.vD"l. {{}6 M;rrkr) :{ i) t:. S*i**l th* siv-*s ol anglc giursrli lcquirccl to hr"tild" lhc .irrglc .j7(r -l l .1". shor.r. th* ,U Brrin!|cmclll oi"*liirgcs. r.5 {{}.t }lrrkr} *,5 ii- liith a ne;tt sketuh. txplain thr rvt;r"king prinripL: olnn rurtu collinrelcr. {{}f: Mrrks} tux h. l)rllnc"cl{cctiru: iJilrnclcl" anil "l:rst sizc r.virc-. l}crivc i:n cx1:rcssiun Lr r"lctcrnrir:c ths hrsl :{ ip sirc u,irc dilrurltr. {{lll }.trrksi ar a c ilorliii} villl rllcitsttlc lltc cltorr"l thickncss rilspur g*irr toolir Llsing gr:ar loolh vrnliar".) !{ l:xplain *illr I skrtch. {{x} M\$rks} ; ( I"{lll* \$ 7- il. l:xplilin tl"le coiti:*pl i:1"gr:n*ruli/-r:d rncasurerni::lil sl,stelr).. rvith trlnck diagriitn lijkin\$ lltc i rvorking olhcLrrdun pt*ssurr galrgir as lrr rramg:le . {{}fl Mrrk*} j t). Lxplrrr, &ll llrrcc s\$tL:ill r{s}l{}ilsd r:haraclcri.sli".:. {{}s i{arks) C. (.I*ssily- i:nd ruh clirssitr .rrilrs. l-:rplirirr liriclll.circh lype ol!trr.)r" witl:,-rrrrrrr;.lic;rrrd lrou, i1 tar: i:e reduucd. {{}\$ t{*rks) it. 5ik*lch and explairr tlic platftrnr halancc nrcthcd rr{r:rclsurinu lirrce. {{Xr }lnrksi b. wirh a rrcal skcrch. r:xplairr lhc rr,urking uIh1.,draulic rlr,il;rrnorllcli:r. {{)\$ }t*r\$s} Iol l {o #/ r.{{* a
• t0M A{2 I}/A U 42 B/P M ,t2lT L42 c. Write a nolecnX *Y ploters. (0ll illarks) a. Explain the inherent problcm prescnt in mechanical inrcrmeeli;rre rrroclilying systems. b. Hxplain the rvr:rking rl"Carhoel* I{ay Oscilloscope". ff H:Xl Wlal ixe electronic amplifiers? With a neat sketch, expl*in chcppcr amplifir3r. (88 Marks) c. litate *nd explain the [au,s olthermocouple. (06 Mnrks] h. Explain th* principlc and unrking o{"unhonclcrl an<J horrrled elcctrical slrain ga1rges. (06 Mnrks) 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} 2 of? _ !q *# I . t:*-.."---..- .*:*b%,: ,: , ,f} _.-q r1
• ( / USN lOME/AU43 Fourth Semester B.E. Degree Examination, December 2Ol2 Applied Thermodynamics Time: 3 hrs. Max. Marks:100 Note: l. Answer FIYEfull questions, selecting at leust TWO questionsfrom each part. 2. (Jse of thermodynamic data book is permitted. () PART _ A o o L a. Define: i) ratio Stoichiometric air-fuel ii) Enthalpy of combustion a iii) Enthalpy of formation iv) Combustion efficiency v) 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 () L i) Determine the stoichiometric air fuel ratio by mass. 3e ii) If 20oZ excess air is supplied, find the percentage composition of dry flue gases by volume. (10 Marks) -*t 2 a. Derive an expression for air-standard efficiency of limited pressure cycle. (10 Marks) Eoo b. The pressur.i on the compression curve of a diesel engine are at 1/8th stroke l.4bat and at .= o.l 7/8th stroke 14bar. Estimate the compression ratio. Calculate the air standard efficiency and b9! oc mean effective pressure of the engini if the cut-off occurs at llllth of the stroke. Assume -o (10 Marks) initially air is at 1 bar and 27oC. 3 a. List out the methods used for measuring friction power of an IC engine. Explain motoring test. (05 Marks) a:; o() b. Explain Morse test.- (05 Marks) c. During a trial of 60 minutes on a single cylinder oil engine having cylinder dia 300 mm, ootr stroke 450 mm and working on two-stroke cycle, the following observations were made: Total fuel used: 9.6 litres PG Calorific value of fuel:45000 kJ/kg Total number of revolutions : 12624 !(g o! Gross mean efTective pressure : 7 .24 bar 4 :q tro- Pumping mean effective pressure: 0.34 bar t1 o-i Net load on brake : 3150 Newton OE Diameter of brake drum: 1.78 m : ao alt Diameter of rope:40 mm LO Cooling water circulated: 545 litres Cooling water temperature rise : 25oC 5-6 v, ^: bo- cao Specific gravity of oil = 0.8 Heat carried away by the exhaust gases : I5oh total heat supplied. o)= o. ii tr> =o U Determine IP, BP and mechanical efficiency. Draw up the heat balance sheet on minute basis. (10 Marks) (r< -i 6i 4a. With a schematic diagram, explain the working of reheat vapour power cycle and deduce an expression for cycle efficiency. O o (10 Marks) Z b. Aiurbine is suiplied with steam at a pressure of 32 bar and a temperature of 410oC. The o steam then expands isentropically to a pressure of 0.08 bar. Find the dryness fraction at the o. 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)
• lOME/AU43 / PART _ B5 a. Show that for a multistage compressor ,=[+l)- where Z: stage pressure ratio, x = number of stages, +: P, overall pressure ratio. (08 Marks) 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 filling takes 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 900C. 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 efficiency of compressor as 88o/o. Properties o F reon T2: of Temperature P V" hr hs Sg S- cp OC bar m/ks kYke kJ/ke kJ/keK kJ/keK kJ/keK -20 1.509 0.1 088 17.8 178.61 0.073 0.7082 40 9.607 74.53 203.05 0.2716 0.683 0.747 (10 Marks)8 a. With a neat schematic diagram, explain the working of winter air conditioning system. Represent the processes on psychrometric chart. (10 Marks) b. For a hall to be air conditioned, the following conditions are given: Out door condition:40oC DBT, 20"C WBT Required comfort condition :20oC DBT, 60% RH : Seating capacity of the hall 1500 : Amount oioutdoor air supplied 0.3 m3/min/person If the required condition is achieved first by adiabatic humidification and then by cooling, estimate: i) capacity of the cooling coil in TOR, ii) capacity of the humidifier in kg/h, iii) condition of air after adiabatic humidification. (10 Marks) F ,< * ,F ,1. a ,)