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- 1. rn { L t- I I USN 1OMAT31 and hence deduce (07 Marks) (06 Marks) (07 Marks) (06 Marks) (07 Marks) Time: 3 hrs. Third Semester B.E. Degree Examination, June/July 2013 Engineering Mathematics - lll Note: Answer FIVE full questions, selecting at least TWO questions from each part. Max. Mar:ks: 100 Yo >.i 6v :q o." d.9 C: o- i; 9< -..i ..i a z ts A I a. obtain the Fourier series expansion or ft,,r=l '' if 0<x..ln l2r-x. il n<x<2n .1t'llllhat-=.+ .* . *......... 8l'35- b. Find rhe hallrange Fourier sine series of it*l = { *' o.^ o-:* '% [7I-)c tl y)<x<T c. Obtain the constant term and.coefficients of firs! cqsine and sine terms in the expansion of y fro- t!E&1!9-4g 1qllgi . (07 Marks) 2 a. Find the Fourier translorm of p1"y-{"-x'' 1x| <a and hence deduce Isin x - x co' * d* = 1 . |. 0. lxl>a j x 4 PART-A Find the Fourier cosine and sine transform off(x) : xe-u*, where a > 0. Find the inverse Fourier transform of e-" . Maximize Z: x + (1.5)y Subject to the constraints x+ 2y < 160, 3x + 2y <240 and x, y > 0. b. 3 a. Obtain the various possible solutions of one dimensional he4t equation ur : c2 uxx by the method of separation of variables. (07 Marks) b. A tightly stretched string ol length ,t with fixed ends is initially in equilibrium position. It is / ser ro vibrate by giving each point a velociry n rr[t] Find rhe displacement u1x. t). (06 Marks) c. Solve u*,, * uyy:0 given u(x, 0) : 0, u(x, 1) : 0, u(1, y) : 0 and u(0, y) = u6, where u6 is a constant. (07 Marks) oI least square. Ilt a x 1 2 3 4 5 v 0.5 2 4.5 8 12.5 fo ins table: x 0 600 120' 1809 '2400 000 3600 v 7.9 7.2 3.6 0.5-. , 0.9 6.8 7.9 1 of2 (07 Marks)
- 2. 5a. b. 1OMAT31 PART-B Using Newton-Raphson method find a real root of x + logrox - 3.375 near 2.9, corrected to 3-decimal places. (07 Marks) Solve the following system ofequations by relaxation method: l2x+y+z=31, 2x+8y-z=24, 3x+4y+102=58 Find the largest eigen value and corresponding eigen vector of following matrix A by power method (06 Marks) (07 Marks) lzs t 21 a=l r 3 ol. l, o -4] Usex(q : [1, 0, 0]r as the initial eigen vector. 6 a. ln the gi€n table below, the values ofy are consecutive terms ofseries ofwhich 23.6 is the and tenth terms ofthe series. x 3' 4 5 6 7 8 9 v 4.8 8,4 14.5 23.6 36.2 52.8 73.9 an interpolating polynomial for the data 6'h (07 Marks) given below using Newton's divided (07 Marks) Construct c. 7a. b. c. I Evaluate [-j , A* by Weddle's rule taking 7-ordinates and hence find log.2. (06 Marks) jl+x' ''. Solve the wave equation un = 4irxi subject-,to u(0, t) : 0; u(4, t) : 0; u(x, 0) : 0; u(x, 0) : x(4 - x) by takingfri 1, k : 0.5 upto four steps. (07 Marks) du, d-l.I. Solve numerically the equiitibn = =- subject to the conditions u(0, t) = 0 = u(1, t), t > 0 dt dx' and u(x, 0): sin nx,0 < x < 1. Carryout computations for two levels taking h: / and k: ha . (07 Marks) Solve the ell'iirtic equation u** * uyy = 0 for the following square mesh with boundary values as shown'in fig.Q7(c). (06 Marks) Fig.Q7(c) 8a. b. Find the z-transform of i) sinhn0; ii) coshn0. obtain the inverse z-transfo.. of 8" (22-t)(42-1) Solve the following difference equation using z-transforms: !n+zl2!n+t +yn:n with Yo:Yl :0 2 of2 (07 Marks) (07 Marks) (06 Marks)
- 3. 1OME32B/AU32BUSN Third Semester B.E. Degree Examination, June/July 2013 sizes of the hole and shaft and a E ;h Y.) 'o !r zd :e ,i .9. a= 6E ^; a3 9< -i .i o z E Time: 3 hrs. PART - A I a. What is metrology? State the objectives of metrology. b. Briefly explain limits, fits and tolerances. c. Using M1 12 set of slip gauges, build the following dimensions: i) s2.498 ii) 48.327s Explain universal interchangeability and selective assembly. (06 Marks) (06 Marks) (08 Marks) (06 Marks) b. c. c. 1a. b. c. 5a. b. v) 1T7 : l6i vi) 1T6: 10i State the actual maximum minimum clearances. and minimum maximum and (08 Marks) 3 a. What is a comparator? Explain Johnson Mikokartor comparator with a neat sketch. ' (06 Marks) What are the advantages of electrical comparators? Explain the principle of optical compaxator. (07 Marks) Describe with a neat sketch, the construction and working of LVDT. (07 Marks) Derive an expression for the effective diameter ofa screw thread by 3-wire method. Explain with a neat sketch the terminology of screw threads. Explain the principle of autocollimator with a neat sketch. (06 Marks) (06 Marks) (08 Marks) (06 Marks) (10 Marks) (04 Marks). Mechanical Measurements and Metrology Max. Marks:100 Note: Answer FIVEfUII queslions, selecting at leost TWO questions from eoch part. What do you understand by line and end standard? Explain waveiength standard. (06 Marks) Determine the tolerances on the hole and the staff for a precision running fit designated by 50 H7go. Given: i) 50 mm lies between 30-50 mm ii) i (microns) : 0.45(D)r/3 + 0.001D iii) Fundamental deviation for 'H' hole = 0 iv) Fundamental deviation for 'g' shaft : -2.5 D0'34 c. I of 2
- 4. I 1OME32B/AU328 6 a. Explain with a sketch, the principle of: i) piezo-electrictransducer ii) ionization transducer. (08 Marks) -:' b. Explain with a block diagram, the general telemetering system. (06 Marlbj ' .,'},. c. Explain the working of: il"rr; , i) stylus type oscillograPh ' ', - ii) x-y plotter. (06 Marks) ,i Z a:$Splain with a neat sketch, multiple lever platform balance. (06 Marks) b. WMtaie lhe types of dynamometers? Explain with a neat sketctr- hydraulic Ortl*,"#il:I., c. Explaiii{hp operation of Mcleod gage and pirani gage. _.'. , ' (06 Marks) 8 a. What are thQi-ilethods of strain measurement? Explain the qrryprpl. of electrical resistance strain gauge. '' ,-,,. .'...i.. : ' (06 Marks) b. What is a thermoEtlaple? Briefly explaln the laws of themioceiuple. (06 Marks) c. Write notes on: i) Strain gauge fact&,,';', ,l ii) Temperaturecompensation iii) Cross sensitivity iv) Strain gauge bonding materials. (08 Marks) ' 's--i-; **+*+ iL . ,9;- :-, lli -.... l.:,t. l-, 2 of2
- 5. USN lOME/AU/TL33 iv) Fan. iv) Reference temperature; v) Quasistatic Third Semester B.E. Degree Examination, June/July 2013 Basic Thermodynamics Time: 3 hrs. PART.A 1 a. Classifr the following as open/closed/isolated systems: i) Tree; ii) Printer; iii) Baking of bread inanoven, b. Define the following with examples: i) Property; ii) Cycle; iii) Path function; Max. Marks: 100 Note: 1. Answer FIVEfull questions, selecting at ledst TIVO questions from each port. 2. Use of thermodynamic tables permitted. g I 50 Yci aa 32 .gd }H -ao ia AE, 5,Y --3 -i cj o z E (04 Marks) c. process; vi) Thermodynamic equilibriirm; vii) Macroscopic approach; viii) State point. Develop a linear temperature scale'oB'where in ice and normal human body temperature are assumed as two fixed points and assigned the values 0oB and 50oB respectively. If the temperature ofhuman body on Celsius scale is 36.7'C, obtain the relation between 'B' scale and Celsius scale and find out water boiling temperature in 'B' scale. (08 Marks) Define 'work' from thermodynamic point of view and derive an expression for flow work. (06 Marks) Define 'heat' and bring out dissimilarities between heat and work. (06 Marks) 2a. b. c. 3a. b. A gas contained in a cylinder fitted with a pistoq loaded with a small number of weights is at I .3 bar pressure and 0.03mr volume. The gas is heated until the volume increases to 0.1mr. Calculate the work done by the gas in the following processes: i) Pressure remains constant; ii) Temperature remains constant; iii) PVrr : C during the process. Show the processes on P-V diagram. (08 Marks) With a neat sketch, explain the famous 'Joules experiment' to. lhow that energy transfer to an adiabatic system is a function ofend states only. 1 2 (04 Marks) For isotherming nonflow and steady flow processes show that Jndv = - Jvap . (06 Marks) ll Simplify SFEE equation for a case of throttle value. (02 Marks) An ideal gas (y: 1.4) expands reversibly in a turbine from 10 bar to 1 bar. Assume that process law is P : 12-5V, where 'P' is in bar and 'V' is in m3/kg. If the heat loss from the turbine is 200 kJ/kg, calculate the shaft work done. (08 Marks) 4 a. Define Kelvin-Plank statement, Clausius statement of IInd law of thermodynamics and show that they are equivalent. (08 Marks) b. Using Kelvin-Plank statement show that free expansion process is irreversible. (04 Marks) c. A heat pump working on a reversed Carnot cycle takes in energy from a reservoir maintained at 5'C and delivers it to another reservoir where temperature is 77"C. The heat pump derives power for its operation from a reversible heat engine operating with in the c. d.
- 6. lOME/AU/TL33 PART-B 5 a. Derive Clausius inequality for a cycle. (08 Marks) b. Using entropy principle show that mixing of two fluids is an irreversible process. (06 Marks) c. One kg of water at 273K is heated to 373K by first bringing it in contact with reservoir at 323K and then reservoir at 373K. What is the change in entropy ofuniverse? (06 Marks) 6 . a. With neat sketches indicate various parameters on tlpical T-S and H-S diagrams. (06 Mrrks) '..6. With a neat sketch, explain how tluottling calorimeter can be used to measure the dryness . . fraction of wet vapour. (06 Marks) c. Stream at l MPa and 250'C enters a nozzle with a velocity of 60m/s and leaves the nozzle al 'I6kPa. Assuming the flow process to be isentropic and the mass flow rate to be lkg/s deieirnine: i) The exit velocity; ii) The exit diameter of nozzle. (08 Marks) 7 a. Obtain -frrir -max well relations for a simple compressible system in the form /aM /aN l=l =l=1. (08Marks) t dv, ldx/ b. Obtain Clausius cldpey,ron relation involving the saturation temperature and pressure. (06 Marks) c. Determine the enthalpy ofvapourization of water at 200"C using Clapel,ron equation. '. ,, . (06 Marks) 8a. b. c. State and explain Amagal's law. State and explain law of correspondirg-ptates. A mixture of methane with, just eimugh oxygen to permit combustion, is temperatue and pressure of the final mixture are 27oC and 101.3 kPa (06 Marks) (06 Marks) burned. The respectively. (08 Marks) Calculate: i) Mass traction of reactants. ii) The volume traction ofproducts. iii) The partial pressure of water vapour in the products of combustion and iv) Volume of products. 2 of2
- 7. USN IOME/AU/PM/TL34 E ? I .=A ?d -o 9= o- 5_ 6tz (-) < -i .i o z E Third Semester B.E. Degree Examination, June/July 2013 Mechanics of Materials Time: 3 hrs. Max. Marks:100 Note: 1. Answer FIVE full questions, selecting at least TWO questions from each part. 2. Missing data may be suitably assumed wherever necessary. PART-A I a. The tensile test was conducted on a mild steel bar. The following data was obtained from the test: Diameter of steel bar : 16mm Gauge length ofthe bar :80mm Load at proporlionality limit : 72 kN Extension at a load of60 kN = 0.1l5mm Load at failure :80 kN Final gauge length ofbar : l04mm Diameter of the rod at failure : 12mm Determine: i) Young's modulus; ii) Proportionality limit; iii) True breaking stress and iv) Percentage elongation. b. A brass bar having cross-sectional area 300mm2 is subjected to axial forces Fig.Q.l(b). Find the total elongation ofthe bar. E: 84 GPa. sol{N lokN 2a. b. (10 Marks) as shown in (10 Marks) A bar of 20mm diameter is tested in tension. It is observed thdt when a load of 37.7kN is applied, the extension measured over a gauge length of200mm is 0.12mm and contraction in diameter is 0.0036mm. Find Poisson's ratio and elastic constants E, G, K. (08 Marks) A composite bar made up of aluminium and steel is held between two supports as shown in Fig.Q.2(b). The bars are stress free at a temperature of 42'C. What will be the stresses in the two bars with the temperature drops to 24'C. lf i) The supports are unyielding; ii) the supports come nearer to each other by 0.1mm. The cross-sectional area of steel bar is 160mm2 and that of aluminium bar is 240mm2, EA : 0.7 x 105 MPa, Es: 2 x 105 MPa, or- 24 x 104 per oC and cxs = 12 x 10-6 per oC. (12 Mark) w Fig.Q.2(b) Fie.Q.1(b) 1of3
- 8. IOMEiAU/PM/TL34 3 a. Show that the sum of the normal stresses on any two planes at right angles in a general two dimensional stress system is constant. (08 Marks) b. At a cefiain point in a strained material the values of normal stresses across two planes at right angles to each other are 80MPa and 32MPa, both tensile and there is a shear stress of 32MPa clock wise on the plane carrying 80MPa stresses across the planes as shown in Fig.Q.3(b). Determine: i) Maximum and minimum normal stresses and locate their planes. .' il Maximum shear stress and specii, n, gl;it (12 Marks) (10 Marks) (08 Marks) (04 Marks) State Castigliano's theorem. Where do you usp it? (0J Marks) The bar with circular cross-section as shown in Fig.Q.4(b) is subjected to a load of 10kN. Determine the strain energy storedrin it..Take E - 2.1 x 105 N/mm2. (07 Marks) 1O[nr t r/ ffi v 110 le 2oomrD--+.k-- EgO mr, -------r{.. soom,, -+1 [n Fis.Q.4(b) c. A thin cylindrical shdll 1m in diameter and 3m long has.a metal thickness of 10mm. It is subjected to an internal fluid pressure of 3MPa. Determine the change in length. diameter and volume. Also find the maximum shearing stress in the shell. Assume Poison's ratio is 3Zt4Po Fie.Q.3(b) 4a. b. 0.3andE=210GPa. -... 5 a. E5plain the terms: i.0 ' Sagging bending moment. :, : i, Hogging bending moment. 6a. b. PART * B iir) Pointofcontraflexure. (06 Marks) b. What are the different types of loads acting on a beam? Explain with sketches. (06 Marks) c. A simply supporled beam of span 6m is subjected to a concentrated load of 25kN acting at a distance of 2m from the left end. Also subjected to an uniformly distributed load of 10kN/m over the entire span. Draw the bending moment and shear force diagrams indicating the maximum and minimum values. Enumerate the assumptions made in the theory of simple bending. A cantilever of square section 200mm x 200mm, 2m long, just fails in flexure when a load of 12kN is placed at is free end. A beam ofthe same material and having a rectangular cross section 150mm wide and 300mm deep is simply supported over a span of 3m. Calculate the minimum central concentrated load required to break the beam. 2 of3 (08 Marks)
- 9. lOME/AU/PM/TL34 c. A rolled I section of size 50mm x 75mm is used as a bearl with an effective span of 3 meters. The flanges are 5mm thick and web is 3.75mm thick. Calculate the uniformly distributed load the beam can carry if the maximum intensity of shear stress induced is limited to 40N/mm2. ' ,'75 a. Show that for a simply.!/. .ib. - A simply supported steel beam having uniform cross-section is 14m span simply 8 a. A hollow steel shaft has to transmit 60kW at 210 stress does 60MPa. If the ratio of internal to the value of is 84 GPa, furd the fthe shaft and angle of twist in a length of 3m. -{) (10 Marks) calculate the safe load usingl*fl;. and the otherS:nd is free. Taking the factor of safety as 3, , -l-.-r Rankine's formula taking yield and o=-L1600 Euler's formula, taking E: 1.2 x (10 Marks) - i;).r' ***** ji '{, r-1io , .;rt. ,,<1U i",ay' ,l'.,*t)/. /,-/ -r' ' tl'ai[ ce..:l I ' .* 1l -l tre,: lrt ' "' 6' -.:.'.' ' 't' -."1. t '-16a..-- &' J (10 Marks) 3 of3
- 10. USN Time: 3 hrs. PART - B lOME/AU/TL35 (06 Marks) (06 Marks) (08 Marks) Third Semester B.E. Degree Examination, June/July 2013 Manufacturing Process - | Note': Answer FIVE full questions, selecting ot least TWO queslions from each part. o q rk gor ?2 .9 6 -a <): d= ,,i 6.Y 6lo a= o. :i (-, < -.i z E 1a. b. c. d. 2a. b. c. 3a. b. 4a. b. 5a. b. Max. Marks:100 (06 Marks) (05 Marks) (04 Marks) (05 Marks) (06 Marks) (06 Marks) (08 Marks) (10 Marks) (10 Marks) Explain the construction and working ofdirect glectric arc firnace. List the advantages. Explain with neat sketcb,working principle of resistance furnace. List ,n" ,J*ff;:'l disadvantages and applieations. (10 Marks) 6a. b. Define weldi4-g. Gjve classification of welding process. (06 Marks) Exnlain Ine4 Gas Metal Arc welding (MIG) and Atomic hydr;gen welding pro".rfor rn.u.l Explain briefly forward and backward welding methods in gas welding. (06 Marks) Explain the principle of seam welding with neat sketch. (06 Marks) With neat sketch, explain projection welding process. List the advantages of projection welding. (08 Marks) With neat sketch, explain explosive welding process. List the applications. (06 Marks) ta- b. c. 8a. b. Discuss the factors affecting weldability of metals. Explain the parameters affecting Heat Affected Zone (HAZ) briefly. Explain briefly welding defects and its causes. Compare soldering and brazing processes. Mention their advantages and disadvantages. (10 Marks) What is NDT? Explain radiography and Eddy current method of inspection of metals. _ ,:, ,;..1;- (t0 Marks)

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