+ T H t LUSN 1OMAT41

Fourth Semester B.E. Degree Examination, June/July 20L3Engineering Mathematics - lV

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

at least TIV'O questions from each part.2. Use of Statistical tables permittecl.

PART - A1 a. Use modified Euler's method to ,olu. !I=*+y, y(0)=1 at x = 0.1 lbr three iterations

dxtaking h : 0.1. (06 Marks)

e

.!8P.

xi

EB9i

-ao'i -.9'=

oi

AE,

,-o6=

og(r<

;zaEoE

(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-0lakeh: 0.2. (10 Marks)

dvh 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_BF

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

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 isfrom 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 timesiil At least onceiii) 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 thatshower 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'st-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 Total315 101 108 )z 556

of theory which predicts proportion of frequencies

(07 Marks)

x 0 2 3 4 5 6p(x) k 3k 5k 7k 9k l lk l3k

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IISN t0cY42

Fourth Semester B.E. Degree Examination, June/July 2013Goncrete Technology

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

at leqsl TWO questionsfrom each parl2. Use of IS 10262-2009 is permitted.3. Assume any missing dala suitably.

PART-AI 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 thebehavior 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 thefineness 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 - B5 a. Depict the interplay offactors influencing concrete strength, preferably through a simpiifiedflow chart. (08 Marks)

b. Establish the relationship between (i) compressive strength and tensile strength ii) Cubestrength and cylinder strengths. (06 Marks)

c. Strength of a fully matue concrete is 30 MPa. Find the strength of concrete at an age of7 days when curred at an average temperature of 25oC during day (12 hours) and 10oCduring 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.66d

i99:-

Q<-i oi

ozE

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.

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t0cv42

a. Explain the elastic behavior of concrete and the relationship between modulus of elasticityand 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 cementpaste? Explain. (08 Marks)

Design a concrete mix for a concrete of Ma5 grade as per IS I 0262-2009 guidelines. Withfollowing 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 mmd) Minimum cement content : 360 kg/m3

e) Maximum water cement ratio : 0.45f) Workability : 125 mm (slump)g) Exposure condition: Severe (for RCC)h) Method of concrete placing : Pumping.j ) Degree olsupervision : Goodkt 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 MATERIALSMaterial Sp. Gr. Water

absorptionFree (surf) moisture

CEMENT 3.1 5 TYPEI N IS38360% 40%zoNE-r(rs383)

COARSEAGGREGATE

2.70 0.5 NIL (also absorbsmoisture)

FINE AGGREGATE 2.60 1.0 NILSuperplasticiser 1.145

COARSE AGGREGATEI.S.SieveIruN

Analysis ofcoarse aggregate

Percentage o I di llerent ltactions Remarks

I II Ieo IIro Combined 100

20 t00 100 60 40 100 Conlorming toTable 2of I3383

10 0 71.20 0 28.50 28.s04.75 9.40 3.70 3.70

2.36 0

FINE AGGREGATE: Conforming to grading ZONEJ of Table 4 of IS383. (20 Marks)

2 of3

CHAPT -.ThBLit0cY42

[.0

€E

2

oT:

IE

.l

hE

o

50.0

40.0

A: 319-lB. !6'8-tC ! (1.7-r

0: t5.6-5g .51.5.5F:564-G

3'0.N/.rrrly'7 Nl mrrli6 lllffirl'5 N/mm2i 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 lK9./ c rn2)

K9 /cm2)K9./cn2)

t\E.

o\c\ SB\

---ra-_-

\

:----

30.0

20.0

00.10

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,tivccooditic.s, cxclpt for ..b.icf priod of crPoturc tooormal wcrficr cmdiumr durinS .o(nrcuon

MODERATE - shcltcR/ f.orn hc.vy winditivcnraifl rnd againl frcczjng vhcn s:tunlcd witl ertliboricd cctrcclc i. soil: rnd. cc.tcr!!. entinuodtly undct

SEVERE * crpos.i to rc. *rr.r. rltcm.rc welti!8 inddrying; frcczirie ,hil. wdt rubjccr to h.rrycondcnr: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

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, selectingot 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

:q5'!

:3Qr-

U<-..1 c.i

oz

eE

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, forthe 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 inenergy 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'

USN t0cY44

(10 Marks)

hence obtain the(10 Marks)

Fourth Semester B.E. Degree Examination, June/July 2013

oe

I

.= cr

utr

-o;

9'=*q

atr

$o6=

9<-i c.i

z

E

la.

b.

2a.

b.

3a.

b.

4 a. Derive the tacheometric equation lor horizontal line of sight andtacheometric equation for inclined line ofsight.

Surveying - IlMax. Marks: 100

Note: Answer FIVE full questions, selectingat 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 theerors that are eliminated by repetition method? (10 Marks)

What are the fundarnental lines of a theodolite? State the desired relationships betweenthem. (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 usingtrigonometric levelling. When the base in inaccessible and the instrument stations are in thesame 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 twostations A and B, 50m apart. Angle BAC : 60" and angle ABC : 50', Angle of elevationfrom A to top of spire : 3.0-1; Angte of elevation from B to top of spire = 29', Staff readingfrom 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 ofline AB. Tacheometric constant 100 and 0.3.

Instrumentstation

Sraffstation

Bearing Vertical angle Staff intercept Axialhair 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 methodwith a sketch. (10 Marks)

b. Two tangents intersect a chainage 1192m, the deflection angle being 50o30'. Calculate thedata for setting out a curve of 300m radius to connect two tangents by Rankine's method.Take peg interval of20m.

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(10 Marks)

10cv44

6 a. With a sketch, explain the various elements of a compound curve. Derive the relations forcalculating the chainages oftangent points. (10 Marks)

b. Two parallel railway lines are to be connected by a reverse curve, each section having thesame radius. If the lines are 12m apart and the maximum distance between tangent pointsmeasured parallel to the straights is 48rn, find the maximum allowable radius. Calculaqlfuchainage 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 aion curve. t t (lo Marks)

b. A'rlp$rvhich deflects 80o is to be designed for a maximum speed of 10Q kmph. maximumcentif@{ ratio is l/4 and maximum rite of change ol radiai accelCflsion is 0.3 m/s2. Thecu*i eo-Ba$ -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. ,$t"\Yiir) I.enethofi@Gurve. ,4\'iri Chatage oft''@cpt points and junction pointsj{goihiof intersection is 42862m.t(ro" L&$ (loMarks)

ii) Length €lrfnsition curve.

ii,l Lenethoft@f,urve.

*rA8 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 at40m interval are as follows: O.S/(lX).tS, 2.50, 1.85, 1.35 and 0.85rq calculate thevolume 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

,;q\e f./)t\" 1.,{ ",1-! / ^\{J ,J

d.,\) \rt\ ){$ '-,\

1-$r ! {./ '\.j

"-\ - '1,]"'.:,.

'+*"-.' ": ^-f

2 of2

USN 10cv45

Fourth Semester B.E. Degree Examination, June/July 2013Hydraulics and Hydraulic Machines

Time; 3 hrs. Marks: 100

Note: Answer FIVE full queslions, selectingat 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 overthe spillway model and model discharge. Ifmodel experiences a force of7500N, determineforce 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. Drawdepth 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 rectangularchannel. (06 Marks)

c. A sluice. gate discharges water into a horizontal rectangular channel with a velocity of5ml.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 ofthejet 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 smoothplate. 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 jetwhen the plate is moving. (10 Marks)

1of2

10cv45

PART-B

a. Derive an expression for the force exerted by a jet of water on a moving semi-circular platein 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 velocityof20 m/s. The jet makes an angle of30' with the direction of motion ofthe vane at the inletand leaves at 90o to the direction of motion ofthe vane at the outlet. Determine vane anglesat 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. Thespeed 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 speedof 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 backat an angle of 30' with the periphiry at the outlEt loru, : 0.92 find discharge. (06 Marks)

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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: l0oNotc: ,{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.

lltl

a. Plan'at sill levslb, Frorrt Elcvationc. Se{:tion rtlong A - Ad,,$oheduleofopenings,

-g

!'l3.!

Etfc'c

?b

t=5.. qYargUEE

c{;.1

7it

(?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 \ryithBBM 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=Nr.Ers.?

[,{,

(t\(,.

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 thetruss. l'rovije Qussst plates at jullctiofls of the truss mumbcrs. Assume slsnde.fd aecessoriesrBqoiftd 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 datui) Shdents capacity at cgrtccn (seating) - 100 Nos,ii) Food countcr - 16 sqmiii) Eitchen - ?0 sqm -

iv) Wash - I (r sclnv) 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 primarylrealth centre, l'he rtquirements ere as follorvs;i) RsDsptior/Rcgistrfltlon couDter ii) Consuiting Docror's room - 2 Nos.iii) Laboretoryv) Mcdical storevii)'l'oilcts.

iv) Minor opcration thcatrcvi) OfI-x

(20 Mrrks)

The lint: diagrom ofa residenrial building ls shown in Fig.es. preparc watcr supply, ganitaryand e'lectrical loyout plan. Drsw ro s scal€ ol l:50. (20 M{rlaB)

I Ot ,/-

Fig:Qs