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- 1. 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 Tl'yO questions from each part. 0) o o PART _ A L a I a. Using the Taylor's 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 .= a'l using the Milne's predictor-corrector method. Apply the corrector formula twice. (07 Marks) :bo E() -O 2a. Employing the Picard's method, obtain the second order approximate solution of the following problem at x: 0.2. Ep dv I!-=x1-yz, dz dxJ'dx =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 d'y , 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 Milne's method, obtain an approximate solution at the point x : 0.4 of the 3o '-^ 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) : 1'873' 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 = ;r'1zl' . 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& r'00' 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)
- 2. t 1OMAT4l PART _ B 5A. Express the polynomial 2x3 -x' -3x+2 in terms of Legendre polynomials. (06 Marks) b. Obtain the series solution of Bessel's 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 Rodrique's formula P.(*) = . 2.r! d*l 6 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*{<{<*
- 3. 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 Taylor's series method. (06 Marks) if {y - y-*,y(0): ! bor b. UsingEuler'smodifiedmethod, solveforyatx:0.1 l,carryoutthree dx v+x s- 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 ox gdi y(1.4) by Adams - Bash forth method. (07 Marks) oE eO =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, -i oc) and hence find the image lrl.t. (07 Marks) 50c 3 a. Using the Cauchy's 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 Laurent's series for the function f (z) = ." the regions i) z <lzl<l sQ. Fg o.. =' z- +52+6 -in ii) lrlrt. (07 Marks) ed Z, C.- c. Determine the poles of and the residues at (07 Marks) h12 t.2 (, -1)' (z + 2) fa( X9 c50 'sa/ /s o= tr> 4 a. prove that e%ex'= it'J,(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 Legendre's 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
- 4. 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 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 day'i output ,ho*r'the 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 d'f') 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, .,9'o /, 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<
- 5. ( / usNilT-1 l0M 842 B/A U42B/tlM42rI'L4: "_il_ Fsrunth ,$emrster" II.E. Ilegree liraminationn l]*c*mb*r 2012 fllle*hanicat Mea$ursment and MetroloEy 'l'itrrrl: .1 hrs. s Max" M*rlis: l0{) : : ,{n.rwcr r N*te r:r1y .l?Ffi.firf/ ryrres/rdns, se/rclirrg g#rns/ T'lr'{) questir;xs -{iorrr rw'y'r ;rnr/" 7 { l,^g'1" { $ir rl. l.:xpl*in inlclnitri*rral prolitt,vpe nlctcr. rvith skctch, €3 {{}6 l{arks} {}-.r b' Wfral arc Air3'paints'l Wlrtre ure th* rirv poinls loc*tur.l9n 6{.}0rnr1 l;ar'J {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 ${*rks} it. ll:xplain lndiln Srirr:dard {lSglg l9{r3} itbng rvith 1hq cr}nccpi ol'lilriit" sizc and t*lerancc. €* rvith tire n*lrt rli*gran"t. {05 Marks) aJ lr. ( ,)lllI;tlr' llrc lull,,rrirrr: !., i) lJLriiri i-t11 t{)lcr$ncr iincl {'orrrpr:uiitl lolcr.arre r: ii) lntcrchlrrgcabilitl xn(j sclcclir* ,: c, ils$crnbIy, {05 Murkr} {]. State the "l';tyk:r's prirrciple arrd dtsign tlrc gaugcs t$ 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 .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 "l'olerance gr*de iirr l"l'4 and I't^lt is "'ji" rncl ..15i". *.6 't: Wrilctlrelype *l'I'lt lbr5{i}:+15enci cxprcssthcvalucirunilalcraliiirlsrrsion. {tt}t}Iarks} f*r :1. [xpiain thr r,r,urling r;l'a signra eompil.iilor. r.vi{h a skeleh. {t{} x*rks} ?J' h. 'ith * neat diagr"alr. expllin thc principlc ol'u.*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{cctir'u: 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' 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} ; ( I"{ll'l'* $ 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 ol'hcLrrdun pt*ssurr galrgir as lrr rramg:le . {{}fl Mrrk*} j t). Lxplrrr, &ll llrrcc s'$tL:ill r{s}l{}ilsd r:haraclcri.sli".:. {{}s i{arks) C. (.I*ssily- i:nd ruh clirssit'r .rrilrs. l-:rplirirr liriclll.circh lype ol'!trr.)r" witl:,-rrrrrrr;.lic;rrrd lrou, i1 tar: i:e reduucd. {{}$ 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 uI'h1.,draulic rlr,il;rrnorllcli:r. {{)$ }t*r$s} Iol l {o #/ r.{{* a
- 6. t0M A{2 I}/A U 42 B/P M ,t2lT L42 c. Write a nolecnX *Y ploters. (0ll illarks) a. Explain the inherent problcm prescnt in mechanical inrcrmeeli;rre rrroclilying systems. b. Hxplain the rvr:rking rl"'Carhoel* I{ay Oscilloscope". ff H:Xl Wlal ixe electronic amplifiers? With a neat sketch, expl*in chcppcr amplifir3r. (88 Marks) c. litate *nd explain the [au,s ol'thermocouple. (06 Mnrks] h. Explain th* principlc and u'nrking o{"unhonclcrl an<J horrrled elcctrical slrain ga1rges. (06 Mnrks) c. Wri{e noies on &ny two o{'the li:llowing : i) Gauge tactur unel cross sensitivity. iil l**p*r*ture compsns:rrion in resistan*e type strain g{}uges. iiii Calibration r:rf srrai:'r g$uges. iv) Wheal str:ne briclge arrongement fbr strain rne{isur"e$.}ent" {0S Marhs} 2 of? _ !q' *# I '. t:*- ..'"'---..- .*:*b%,: ,: , ,f} _.-q 'r1
- 7. ( / 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)
- 8. lOME/AU43 / PART _ B 5 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 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 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 ,)
- 9. -:,.-- / USN IOME/AU|PMITL44 Fourth Semester B.E. Degree Examination, December 2012 Kinematics of Maehines Time: 3 hrs. Max. Marks:100 Note: 1. Answer FIVEfull questions, selecting at least TWO questions from each part. () (.) 2. Gruphical solution moy be obtained either o on graph sheet or on the unswer book itself, 0. PART _ A C) I a. Differentiate between: () i) Degree of freedom and mobility of mechanism' ox ii) Kinematic chain and kinematic pair. (08 Marks) b. Explain with a neat sketch, the single slider mechanism and its three inversions. (12 Marks) )ll 2 a. Define 'Exact straight line motion'. Prove that a point on the Peaucellier's mechanism traces =A an exact straight line. (10 Marks) .! cr b. Define 'Quick return motion' in a mechanism and using a neat sketch explain the drag link :bo (10 Marks) E6) mechanism. e0 EE o3 3 In the mechanism shown in Fig.Q3, the slider 'C' is moving to the right with a velocity of o= .=o 1 m/sec and an accelerationof 2.5 m/sec2. The dimension of the various links are AB :3 m, AP inclined at 45o with the vertical and BC : 1.5 m inclined at 45" with the horizontal. Determine oc) 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. (20 Marks) OE 50tr -o ft ,6 -4() OE o-a ;o o= ai l--k; rZ l"Sr-r GE !o D +-- >'3 C j8g{- a0- Fig.Q3 tr oL) o= o. ;i tr> o. 4 a. State and prove 'Kennedy's theorem'. (06 Marks) U< b. Explain the analysis of velocity and acceleration of a piston in a single slider mechanism C'] using Klein's construction. (06 Marks) : - c. For a pin jointed four bar mechanism having the following dimensions. Fixed link AD 4rn, o o : : Driving link AB 1.5m, Driven link CD :2.5m, connecting rod BC 3m and angle BAD Z is 60'. Link AB rotates at25 rpm. Determine using instantaneous centre method i) Angular L o velocity of link 'CD' and ii) Angular velocity of link BC. (08 Marks) a I of2
- 10. IOME/AUIPNIITL44 PART _ B The crank of an engine is 200 mm long and the ratio of connecting rod length to crank radius is 4. Determine the acceleration of the piston when the crank has turned through 45" from the inner 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 each side of pitch point has half the maximum possible length. Determine the addendum height for 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 rotates independently 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. All gears have the same module. The number of teeth on gears C, D, E and F are 28, 26, 18 and 18 respectively. 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 cam is 30 mm and the axis of the follower is offset to the right by a distance of 5 mm. The follower completes 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
- 11. USN lOME/AU46B Fourth Semester B.E. Degree Examination, Decemb er 2Ol2 Fluid Mechanics Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting d at least TWO questions from each part. o o k 9. PART _ A 1 a. Distinguish between the following and mention their units: i) Specific weight and mass density. C) ii) Surface tension and capillarity. L o iii) Dynamic viscosity and kinematic viscosity. (09 Marks) oX (g= b. Obtain an expression for capillarity rise. (03 Marks) c. In a 50mm long journal bearing arrangement, the clearance between the two at concentric ;n condition is 0.lmm. The shaft is 2.0mm in diameter and rotates at 3000 rpm. The dynamic ;l viscosity of the lubricant used is 0.01 pas and the velocity variation in the lubricant is linear. troo .=N cd+ Considering the lubricant to be Newtonian, calculate the frictional torque the journal has to X o.) overcome and the corresponding power loss. (08 Marks) (.)tr FO o> 2 a. Obtain an expression for the force exerted and centre of pressure for a completely o2 submerged inclined plane surface. (10 Marks) a= b. A cylindrical roller gate 3m in diameter is placed on the dam is such a way that water is just oO going to spill. If the length of the gate is 6m, calculate the_;ngggltrr{e and direction of the resultant force due to water acting on it. 4fXN (r0 Marks) o0i -o -6 6- 3 a' s 'r'*L:-ry,,t:ffi';,"ru,", ,ifil ,:;$li X E(6 J?a) ii) Metacentre r"- o /-i '6) OE iii) Metacentric height. iff ;/(04 Marks) o. 6- b. A solid cylinder of diameter 4m has a height of 3m. Fi ric height of the o.j cylinder when it is floating in water with its axis vertical. Take specific gravity of the o= cylinder as 0.6. (08 Marks) i, fE c. Explain the different types of fluid flows. (08 Marks) !o >(ts 4 a. Obtain an expression for Bernoulli's equation from Euler's equation of motion and also boo c50 mention the assumptions made. (10 Marks) o= 90 b. A pipe 300m long has a slope of 1 in 100 and tapers from lm diameter at the high end to tr> 0.5m at the low end. Quantity of water flowing is 5400 litres per minute. If the pressure at =o 5L (r< the high end is 70 kPa, find the pressure at the low end. (10 Marks) *Ol o PART -B o z 5a. Derive an expression for discharge through venturimeter. (10 Marks) b. The resisting force 'F' of a supersonic plane dunning flight can be considered as dependent L o o. upon the length of aircraft '/', velocity 'v' , ak viscosity 'v' , atr density 'p' and bulk modulus of air 'K'. Express the functional relationship between these variables and the resisting force. (10 Marks) 1
- 12. t- lOME/AU46B (10 Marks) a. Derive Darcy-Weisbach equation for loss of head in a pipe due to friction. 8m' then expands _ and rum b. A 5pm diameter pipe takes off abruptly from a large tank directly in to open air with a abruptly to 10cm diameter and runs 43m, and next discharge above the point velocity of 1.5 m/s. Compute the necessary height of water surface 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' are kept at a b. en oi-l of viscosity 10 poise flow between two paral lel fixed plates which 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' trrtaitr number, mach cone and mach angle' (10 Marks) iiO r of a parachute while is ^ b. A man descends to the ground from an aeioplane with the help homispherical having a diameter of 4m againsf the resistance of air with a uniform velocity is 9.81 N. Take Ct : 0'6 of 25 m/s. Find the ri.iglrt of the man if the weight of the parachute (10 Marks) and density of air: t.ZSkglm3. I nf )