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- 1. + T H t LUSN 1OMAT41 Fourth Semester B.E. Degree Examination, June/July 20L3 Engineering Mathematics - lV Time: 3 hrs. Max. Marks:100 Note: 1. Answer FIVE full questions, selecting at least TIV'O questions from each part. 2. Use of Statistical tables permittecl. PART - A 1 a. Use modified Euler's method to ,olu. !I=*+y, y(0)=1 at x = 0.1 lbr three iterations dx taking h : 0.1. (06 Marks) e .! 8P. xi EB 9i -ao'i -. 9'= oi AE, ,-o 6= og (r< ; z a E o E (07 Marks) x -0.1 0 0.1 n, v 0.908783 1.0000 1.1 I 145 1.25253 2 a. Approximate y and z at x = 0.2 using Picard's method for the solution of I = r. dx !=*'ty*rt rrith 1{0): l. z(0): l/2. perform two sreps lyt-yz-zt-zz). (t0Marks) dx $. Using Runge-Kutta method solve y": x(y')2 -y2 atx=0.2 with xo:0, y0 =1,ztt-0lake h: 0.2. (10 Marks) dv h Solve iL=x*Y.x=0, y=1 at x:0.2 using Runge-Kutta method. Take h= 0.2. "dx c. Using Milne's predictor-corrector method find y(0.3) conect to three decimal, U,rJll '"'u"' 3 a. If (z) = u + iv is analy.tic prove that Cauchy-Reimann equations ux : v). u) : -vx are true. (06 Marks) b. Il'* = zt find dwldz. (07 Marks) c. Il'thepotential functionir 4=toglf,=f . Find the stream funclion. (0? Marks) 4a. b. c. 5a. b. c. Find the bilinear transformation which maps the points z:1,i, -1onto the points w: j, o, -i. (06 Marks) Discuss the conformal transformation w: e'. Any horizontal strip of height 2n in z-plane (07 Marks) (07 Marks) (06 Marks) (07 Marks) (07 Marks) will map what portion of w-plane. State and prove Cauchy's integral formula. PART_B F Prove that Jl'] :.,/: r;n*. linx State and prove Rodrigues formula for Legendre's polynomials. Express (x) : xa + 3x3 - x2 + 5x - 2 in terms oflegendre polynomial. I of2
- 2. 6a. b. c. 1OMAT41 The probabilities of four persons A, B, C, D hitting targets are respectively l12, 113,114, 115. What is the probability that target is hit by atleast one person if all hit simultaneously? (06 Marks) i) State addition law ofprobability for any two events A and B. ii) Two different digits fiom 1 to 9 are selected. What is the probability that the sum of the two selected digits is odd if '2' one of the digits selected. (07 Marks) Three machine A, B, C produce 50%, 30%, 20oh of the items. The percentage of defective items are 3, 4, 5 respectively. Ifthe item selected is defective what is the probability that it is from machine A? Also find the total probability that an item is defective. (07 Marks) 7 a. The p.d.f of x is Find k. Also find p(x > 5), p(3 < x < 6). 6. A die is thrown 8 times. Find the probability that '3' falls, i) Exactly 2 times iil At least once iii) At the most 7limes. What is null hypothesis, alternative hypothesis significance level? c. In a certain town the duration of shower has mean 5 minutes. What is the probability that shower will last lor i) 10 minutes or more; ii) less than lOminutes; iii) between 10 and 12 minutes. (06 Marks) (07 Marks) (07 Marks) (06 Marks)8a. b. The nine items of a sample have the following values: 45, 47, 50, 52, 48, 47, 49, 53, 51. Does the mean ofthese differ significantly from the assumed mean of47.5. Apply student's t-distribution at 5% level ofsignificance. (toos for 8df:2.31). (07 Marks) c. In experiments on a pea bl'eading, the following frequencies of seeds were obtained: Round-yellow Wrinkled yellow Round green Wrinkled green Total 315 101 108 )z 556 of theory which predicts proportion of frequencies (07 Marks) x 0 2 3 4 5 6 p(x) k 3k 5k 7k 9k l lk l3k 2 of2
- 3. IISN t0cY42 Fourth Semester B.E. Degree Examination, June/July 2013 Goncrete Technology Time: 3 hrs. Max. Marks:100 Note: 1. Answer FIVE full questions, selecting at leqsl TWO questionsfrom each parl 2. Use of IS 10262-2009 is permitted. 3. Assume any missing dala suitably. PART-A I a. What are the constituents of cement? Explain the role of constituents in controlling the prope(ies ofcement. (08 Marks) b. Define the terms: i) Standard consistency ii) Fineness and iii) Soundness. Explain their significance. (06 Marks) c. Distinguish between i) False set and Flash set ii) Dry process and wet process iii) Hydraulic cements and non-hydraulic cements. (06 Marks) 2 a. How do you classify aggregates? Describe the characteristics of aggregate influencing the behavior ofconcrete. (t0 Marks) b. Explain the significance of Bulking of Fine aggregates and Gap grading. (04 Marks) c. In a sieve analysis of 1000 gms of sand, the weights (gm) retained on different I.S. sieves are: 10mm : 0, 4.75mm : 20, 2.36mm: 100, 1.18mm : 100, 600 Microns : 190, 300 microns:350, 150 Microns: 170 and passing 150 microns : 70. Determine the fineness modulus ofsand. (06 Marks) 3 a. Explain the lactors affecting consistency and cohesiveness of liesh concrere mixl.ures" Suggest ways to improve. (08 Marks) b. Explain any two methods, equipments and advantages of handling and placing concrete. (06 Marks) (06 Marks) (08 Marks) use of any (06 Marks) (06 Marks) PART - B 5 a. Depict the interplay offactors influencing concrete strength, preferably through a simpiified flow chart. (08 Marks) b. Establish the relationship between (i) compressive strength and tensile strength ii) Cube strength and cylinder strengths. (06 Marks) c. Strength of a fully matue concrete is 30 MPa. Find the strength of concrete at an age of 7 days when curred at an average temperature of 25oC during day (12 hours) and 10oC during night (12 hours). Use the relation for strength at maturity as percentage of strength at full maturity, express as A + B logr0 Mft;;ry , when A:21 and B :61 corresponding to strength at full maturity. (06 Marks) 9 t9 -oo I ?,- 9+ !'= o.6 6d i99:- Q< -i oi o z E E c. Explain the significance ofsetting time ofconcrete 4 a. Explain the role of mineral admixture and chemical admixtures. b. What are supplementary cementitious materials? Explain the characteristios and two. c. Discuss the composition and usefulness of rice husk ash and GGBs. 1of3
- 4. t0cv42 a. Explain the elastic behavior of concrete and the relationship between modulus of elasticity and strength. (10 Marks) b. Distinguish between: (i) Creep and shrinkage (ii) Plastic shrinkage and drying slrinkage. (06 Marks) c. If the volume ofpaste is 40% ofthe total volume and Eo and E" are 2,00,000 and 3,20,000 kg/cm2. What is the modulus of elasticity of concrete? (04 Marks) a. Define durability. Explain how concrete is made durable against (i) sulphate attack (ii) freezing and thawing (iii) corrosion ofsteel. (12 Marks) b. $fhy is the permeability of mortar or concrete is higher than the corresponding cement paste? Explain. (08 Marks) Design a concrete mix for a concrete of Ma5 grade as per IS I 0262-2009 guidelines. With following stipulations and test data for materials. A- 1 stipulations for PROPORTIONING: a) Grade Designation : ivl+s b) Type ofcement OPC 53 conforming to 1512269-1987. c) Maximum nominal size of aggregate : 20 mm d) Minimum cement content : 360 kg/m3 e) Maximum water cement ratio : 0.45 f) Workability : 125 mm (slump) g) Exposure condition: Severe (for RCC) h) Method of concrete placing : Pumping. j ) Degree olsupervision : Good kt Type ofaggregate : Sub angular aggre.gate 1.1 Maximum cemenl content :450 kg/m' m) Chemical admixture bpe : Superplasticiser (Capable ofreducing water content upto 20% max.) A-2 TEST DATA FOR MATERIALS Material Sp. Gr. Water absorption Free (surf) moisture CEMENT 3.1 5 TYPE I N IS383 60% 40% zoNE-r(rs383) COARSE AGGREGATE 2.70 0.5 NIL (also absorbs moisture) FINE AGGREGATE 2.60 1.0 NIL Superplasticiser 1.145 COARSE AGGREGATE I.S.Sieve IruN Analysis of coarse aggregate Percentage o I di llerent ltactions Remarks I II Ieo IIro Combined 100 20 t00 100 60 40 100 Conlorming to Table 2 of I3383 10 0 71.20 0 28.50 28.s0 4.75 9.40 3.70 3.70 2.36 0 FINE AGGREGATE: Conforming to grading ZONEJ of Table 4 of IS383. (20 Marks) 2 of3
- 5. CHAPT -.ThBLi t0cY42 [.0 € E 2 o T: I E .l h E o 50.0 40.0 A: 319-l B. !6'8-t C ! (1.7-r 0: t5.6-5 g .51.5.5 F:564-G 3'0.N/.rrrly '7 Nl mrrl i6 lllffirl '5 N/mm2 i 4 N/mm: '3 l,l/ mm2 ( 325 - 375 1375 - 42! Itzs-1n (t7s-525 ( 525 - srs ( 575 -6?5 Kg,. c ni) Kg./cm2) Kqlcr l K9./ c rn2) K9 /cm2) K9./cn2) t E. o c SB ---ra-_- :---- 30.0 20.0 0 0.10 rig ! Rcbrua bctwten frcc 0.4 0.45 050 o 55 Water - cerneflt ralio v.<tter-cca.Rl rdtio a.dd coacret. ttrcdgrh or 28 days for dilJcrcnl ccakn drc,'gtfu T*BLE-T. Erpoiurt Rciafarccd coaaerc Ifaar,olq-ee,ranl urnanl ,atio. conlanl, by wziqttt kgt,n' rutio, bt wcitrt 4l^' MILD - coplct ly prolcct d .Srirst wclhcr, or .88rc,tivc cooditic.s, cxclpt for ..b.icf priod of crPoturc to oormal wcrficr cmdiumr durinS .o(nrcuon MODERATE - shcltcR/ f.orn hc.vy winditivcn raifl rnd againl frcczjng vhcn s:tunlcd witl ertli boricd cctrcclc i. soil: rnd. cc.tcr!!. entinuodtly undct SEVERE * crpos.i to rc. *rr.r. rltcm.rc welti!8 ind drying; frcczirie ,hil. wdt rubjccr to h.rry condcnr:tion or ccrrosivc fumer 0.45 250 160 0.55250 310 0.60 0.50 Jorc:; IS:(56-1978. /'ror.r: (, $rhal lhc ruxihum wrtcr-ccmcit nrio c.n bc ttrictly coflliot cd, the tlrncnt co.ucnl h fdbL l mry bc rcduc'i by,lo Ptcdll' fii) Minimum ccmcnr @nrsu t brtzd.n Zg-mrn rggrcirrct for 4tl.om i,grcg,c. rcducc ir by l0 pcrccd. rnd for 12.5'mm rgSrcgatc' incrtrs. i by l0 pcrccnt- ***+* 3 of3
- 6. USN 10cv43 (08 Marks) (08 Marks) Fig.Q.3(b), using strain (12 Marks) Fourth Semester B.E. Degree Examination, June/July 2013 Structural Analysis - I Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting ot least TWO questions from each part. PART_A a. Explain with examples statistically determinate and indeterminate strudtures. (05 Marks) b. Find degree of indeterminacy of following structures: (05 Marks) o E 39. .= c.r gii =2 :q 5'! :3 Qr- U< -..1 c.i o z e E c. Derive an expression for strain energy stored due to bending. (10 Marks) 2 a. Using conjugate beam method, find slope at "A", maximum deflection and its location, for the beam shown. (12 Marks) Fig.Q.2(a) Determine slope and deflection at the free end of the cantilever beam shown in Fig.Q.2(b). Using moment area method. A 3a. b. Fig.Q.2(b) Derive Clarke-Maxwell's theorem of reciprocal deflection. Find the horizontal deflection at point C for the frame shown in energy method. Take E:2 x 105 N/mm2 and I:2 x 10E mma. 24Y.N !, z?D .-jr.: ,4.. ' t! [-i; ,, ii: l ' cB 4ro '2.1'
- 7. USN t0cY44 (10 Marks) hence obtain the (10 Marks) Fourth Semester B.E. Degree Examination, June/July 2013 o e I .= cr utr -o; 9'= *q atr $o 6= 9< -i c.i z E la. b. 2a. b. 3a. b. 4 a. Derive the tacheometric equation lor horizontal line of sight and tacheometric equation for inclined line ofsight. Surveying - Il Max. Marks: 100 Note: Answer FIVE full questions, selecting at least TWO questions from each part. PART-A Explain the following terms with reference to a theodolite: i) Transiting; ii) Swinging; iii) Line of collimation; iv) Centering; v) Vertical axis. (t0 Marks) Describe the method of measuring horizontal angle by repetition method. What are the erors that are eliminated by repetition method? (10 Marks) What are the fundarnental lines of a theodolite? State the desired relationships between them. (10 Marks) Explain with a sketch " two peg method" adoptq{ in the permanent adjustments ofa level. :,, '" (10 Marks) Explain the method of deterririning the distance and elevation of an object using trigonometric levelling. When the base in inaccessible and the instrument stations are in the same plane as that ofthe object. Derive the required equations. (I0 Marks) Find the reduced level ofa Church spire 'C' fiom the following observations taken from two stations A and B, 50m apart. Angle BAC : 60" and angle ABC : 50', Angle of elevation from A to top of spire : 3.0-1; Angte of elevation from B to top of spire = 29', Staff reading from A on BM of RL 20tir = 2.50m, Staffreading from B-to same BM = 0.50m. b. The following are the observations taken from a tacheometric station. Find the gradient of line AB. Tacheometric constant 100 and 0.3. Instrument station Sraff station Bearing Vertical angle Staff intercept Axial hair reading P A 400 35', -40 24', 2.t75 1.965 P R 11,7. 05', -5' 12', 1.985 1.86s (10 Marks) PART - B a. Explain the method of setting out of simple curve by offsets from Chords produced method with a sketch. (10 Marks) b. Two tangents intersect a chainage 1192m, the deflection angle being 50o30'. Calculate the data for setting out a curve of 300m radius to connect two tangents by Rankine's method. Take peg interval of20m. 1 of2 (10 Marks)
- 8. 10cv44 6 a. With a sketch, explain the various elements of a compound curve. Derive the relations for calculating the chainages oftangent points. (10 Marks) b. Two parallel railway lines are to be connected by a reverse curve, each section having the same radius. If the lines are 12m apart and the maximum distance between tangent points measured parallel to the straights is 48rn, find the maximum allowable radius. Calculaqlfu chainage of point of reverse curvature and point of Tangency. if the chainage of Tr {l!}r. flg Marks) _,1/iiur is a transition curve? Enumerate the functions and conditions to br]fiftf,bd by a ion curve. t t (lo Marks) b. A'rlp$rvhich deflects 80o is to be designed for a maximum speed of 10Q kmph. maximum centif@{ ratio is l/4 and maximum rite of change ol radiai accelCflsion is 0.3 m/s2. The cu*i eo-Ba$ -of circular arc combined with two cubic spirals. Catqffiet6: i) nadi/#(the circular arc. "6$Ji) Radirf${{he circular arc. q)"ii) Lenglh'@nsition curve. ,$t"Y iir) I.enethofi@Gurve. ,4' iri Chatage oft''@cpt points and junction pointsj{goihiof intersection is 42862m. t(ro" L&$ (loMarks) ii) Length €lrfnsition curve. ii,l Lenethoft@f,urve. *rA 8 a. The following offsets *"i/$<"n from a .qfifri,. to an irregular boundary line at an interval of l0m. Compute the d9$Py^trape4{6t and Simpson's rule. Offsets: 0, 2.5,3.5, 5.0,4.6, 3.20-apffirn. (10 Marks) b. An embankment of width lOm an$-($fope lV:1.5H is required. The central heights at 40m interval are as follows: O.S/(lX).tS, 2.50, 1.85, 1.35 and 0.85rq calculate the volume of earth work by trapezoffi,kf,nd ffiiwnoidal rule. (10 Marks) ! {t- {} '^ * f-. x+, ^qt' ,r"^q' * * 't * * 1- ,v "d-r' .x(f' -). (}- "-'1; . cl.- '/,'t ,;qe f./)t" 1.,{ ",1-! / ^{J ,J d.,) r t ) {$ '-,1-$r ! {./ ' .j "- - '1,]"'.:, . '+*"-.' ": ^-f 2 of2
- 9. USN 10cv45 Fourth Semester B.E. Degree Examination, June/July 2013 Hydraulics and Hydraulic Machines Time; 3 hrs. Marks: 100 Note: Answer FIVE full queslions, selecting at least T/l/0 questions from each part. PART_A 1 a. Define the dimensional homogeneity. Give an example. -", '. (06 Marks) b. State and explain Bukingham's theorem. (06 Marks) c. A7.2mhigh and 15m tong spillway discharges 94 m3;/sec of water under a head of 2m. If a 1:9 scale model of this spillway is to be constructed, determine model dimensions, head over the spillway model and model discharge. Ifmodel experiences a force of7500N, determine force on the prototlpe. (08 Marks) :l] 2 a. Bring out the difference between flow thLrough pipes and flow through open channel. (06 Marks) f. Derive the conditions for the most economical trapezoidal channel section. (06 Marks) s. A rectangular charmel carries water at the rate of400 litres/sec when bed slope is I in 2000. Find the most economicaldimensions of the chanriel if C : 50. (08 Marks) 3 a. Define specific energy. Draw depth and critical velocity. specific energy curve, and then derive expressions lor critical b. Derive the expression for sequent depths of , (06 Marks) hydraulic jump occurring in a rectangular channel. (06 Marks) c. A sluice. gate discharges water into a horizontal rectangular channel with a velocity of 5ml.sec and depth of flow is 0.4m. The width of the channel is 6m. Determine whether a hydraulic jump will occur, and if so find its height and loss ofenergy per kg of water. Also . determine the power lost in the hydraulic jump. (08 Marks) 4a. b. c. Max. .= r.r I qa 66 U< -i ..i z to State impulse momentum equation. (02 Marks) Show that the force exerted by ajet of water on an inclined fixed plate in the direction ofthe jet is given by Fx - p a I sin2e. (08 Marks) A jet of water 75mm diameter having a velocity of 20 m/sec strikes normally a flat smooth plate. Determine the thrust on the plate. i) Ifthe plate is at rest. ii) If the plate is moving in the same direciotn as the jet with a velocity of 5 m/sec. Also find the workdone per second on the plate in each case and the efficiency of the jet when the plate is moving. (10 Marks) 1of2
- 10. 10cv45 PART-B a. Derive an expression for the force exerted by a jet of water on a moving semi-circular plate in the direction ofthe jet when the jet strikes at the cenffe of semicircular plate. (08 Marks) b. A jet of water with a velocity of 40 m/se strikes a curved vane which moves with a velocity of20 m/s. The jet makes an angle of30' with the direction of motion ofthe vane at the inlet and leaves at 90o to the direction of motion ofthe vane at the outlet. Determine vane angles at the inlet and outlet if water enters and leaves without shock. Also determine eff&jency. 6 i. .,'Draw a neat sketch of an hydroelectric power plant. Mention the funclbis of each -component. (06 Marks) b. How'riill you classifr the turbines? (06 Marks) c. Desig{?ielton wheel with the following data, shaft power : 735.75 kN H : 200m, N : 800 rpm r1o:O:86 D/d: l0 C, = 0.98 0 : 0.45. Determine D, d anddrlnber ofjets. (08 Marks) ,a:.] :_, 7 a. Draw the neat *etch of Kaplan turbine and mention the partq.. '' (08 Marks) b. A Kalpan turbine ii:llqer is to be designed to develop 10000 kW. The net head is 6.0m. The speed ratio = 2.09. flow ratio = 0.68. overall efficiency is 80% and diameter of the loss is 1/3 the diameter of the ruriirer:.Find the diameter of the r,niiner, its speed and the specific speed of the turbine. (12 Marks) 8 a. Derive an expression for the miniiium starting.speed for a centrifugal pump. (10 Marks) b. What is priming of a centrifugal pump and how is it done? (04 Marks) c. A centrifugal pump runs at 1000 rpm-!6d-.delivers water against a head of 15m. The impeller diameter and width at the outlet ar-e O-3niand 0.05m respectively. The vanes are curved back at an angle of 30' with the periphiry at the outlEt loru, : 0.92 find discharge. (06 Marks) 2of2
- 11. FRrlt't : 17 ,iFr. lA12 lrl:4sPtj F1 USIN 10cv46 $'ourth Semester I3.8. Degree Examinntion, Junel.Iuly 2013 Building Plaftnirtg and Drasrang Time: 4 hrs. Max- M arks: l0o Notc: ,{fisrser SECrIOA'-I conpsl!;Gty &7rr1 sn$wer anp TVYD fr .l qaestiow J'ro,rt SECTfON-ff SECTI0N - I (Compul:Er:y) 1 'l'lrc linc diagram of ir resklcniial buildirrg is sh,rrvn in Fig.Q ! . Diaw to rr scale of i ;100. ll tl a. Plan'at sill levsl b, Frorrt Elcvation c. Se{:tion rtlong A - A d,,$oheduleofopenings, -g !'l 3.! Etf c'c ?b t=5.. q Yar gU EE c{ ;.1 7 it (?i Mnrkc] (15 MlrkE) (tS M.irkr) (05 Mnrksj Note: Take all lond lrearing walls of 210 ltrn thigk arld ps|tition rvrlls I l5 ixm thick. built ryith BBM irr CM I:6. Foundatio is of SSM jn CM l:6. Height olthe ruoi3.15m from pliurh leve!. Liniel level is at 2.1 In above plhrrh level. Width of foundation I rn. Deprh of fbundation I.Z m, Plintl lcvi:] 0,6 m above ground level. x|rqH=N r.Ers.? [,{, (t(,.
- 12. FRDI'I : FAX t.D, : 17 Apr. 2812 lE I 4r5Pl"l 1llcv46 SECTION _--tI Draw d steEl truss for tho span uf a itrilushhl truilding 20 m. Assumo suilablc scctiorts for the truss. l'rovije Qussst plates at jullctiofls of the truss mumbcrs. Assume slsnde.fd aecessories rBqoiftd for the truss, The truss has to suppon A.C. shcct rooting. (20 rvlx.k!) De'vclop r plan tilr a college cAflteen with the following datu i) Shdents capacity at cgrtccn (seating) - 100 Nos, ii) Food countcr - 16 sqm iii) Eitchen - ?0 sqm - iv) Wash - I (r scln v) Store - I (i sqn: yi) 'l oilets each separutc lor girl$ and boys 12 sqm. Assumo suitohlo dirnensions lor thc sitc. (20 Mirks) Prepare a bubble diagrarn (crrnnectivity diagr*rn) and davelop a line diagram for a primary lrealth centre, l'he rtquirements ere as follorvs; i) RsDsptior/Rcgistrfltlon couDter ii) Consuiting Docror's room - 2 Nos. iii) Laboretory v) Mcdical store vii)'l'oilcts. iv) Minor opcration thcatrc vi) OfI-x (20 Mrrks) The lint: diagrom ofa residenrial building ls shown in Fig.es. preparc watcr supply, ganitary and e'lectrical loyout plan. Drsw ro s scal€ ol l:50. (20 M{rlaB) I Ot ,/- Fig:Qs

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