4th Semester Civil Engineering (2013-December) Question Papers

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Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4Engineering Mathematics - lV

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... . PART_A..

I a. Emplo,y Taylor's series method to obtain the value of y at x: 0.1 and 0.2 for the differential

Time: 3 hrs.

c. Apply Adams-Bashforth method to

y(1. I): 1.233, y(\.2): t.548,:y11.3) :

2 a. Solve t = t * r*. 9- -xy. v(O) =

Runge-Kutta method of fourth order.

equation * =rr+ 3e* . y(0) : 0 considering upto fourth d.gr.. t*rrn.dx

b. Determinethe value of ywhenx:0.1, giventhaty(0):1and y":i +y2using modifiedEuler's lormula. Take h : 0.05. (07 Marks)

. dv )-solve the equatron ---!-;;'1t+y). grven

dx1.979. Evaluate y(1.4).

Q,z(0):1atx:0.3

b. Applying Picard's method to compute y(1.1) from the second approximation to the solutionof the differential equation y" * fy': x'. Given that y(1) : 1, y'(1) : 1. (07 Marks)

by taking h : 0.3. Applying

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coordinate axes in z-plane under the(06 Marks)

points z : l, i, -1 on to the points(07 Marks)

c. Using the Mitni's method obtain an approximate solution at the point x : 0.8 of the problem

*= t-ZV!. give rhat y(0) :0. y'(0) 0. y(0.2) : 0.02. y'(0.2): 0.1996.dx' " dxy(0.41 : 0.0795. y'(0.4) :0.3937.y(0.6) :0.1762.y'(0.6) : 0.5689.

3 a. Derive Cauchy-Riemann equations in Cartesian form.

b. Give tr.-- v (x - yXx2 + 4xy + y2; find the analytic function f(z): u + iv.

4 a. Find the image of the straight lines parallel totransformationw: z2

b. Find the bilinear transformation which maps the

w:0, 1, oo.

c. tf f(z): u * iv is an analyic tunction then prove thrt (* | f(r) l) . [*

| f (r) I) =1f '1ztl)

(07 Marks)

c. Evaluate f---gj-. where c is the circle I zl : 3.r, (z + ll(z + 2)

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(07 Marks)

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PART _ B

5 a. Find the solution of the Laplace equation in cylindrical system leading to Besseis differentialequation.

If cx and B are two distinct roots of J,(x) : 0, then prove

(06 Marks)I

that fx J, (ux) J,, (BX)di = O,o ' r;... """

.lm + n.

c. Eipq*ur (x) : *o - 2*' + l* - 4x + 5 in terms of legendre polynomial.,,

(07 Marks)

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following table:

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6 a. A coiilfufttee consists of 9 students, 2 from first year, 3 from second year and 4 from thirdyear. 3 st'"udepts are to be removed at random. What is the probability that (i) 3 studentsbelongs to different class (ii) 2 belongs to the same class and third belongs to differentclass. (iii) All the 3 belongs to the same class. (06 Marks)

'1""''r "tb. State and prove Ba$Cs theorem. :'::: :::'::"' (07 Marks)

c. The chance that adodtirw^ill diagnose a disease correctly is 600/o. The chance that a patientwill die after correct diagncise is 40Yo and the chanCe bf death after wrong diagnose is 70o/o.

If a patient dies, what is the bhhrpE that diseasdWas conectly diagnosed.

7 a. The probability distribut ion of finite random variable x is siven by thex 0 1 ') J 4 5 6 7

o(x) : 0 Ir 2k 2k 3k k 2k 7k'+kFind k, p(x < 6), p(x > 6), p(3 < x < 6)

b. Obtain the mean and variance of Poisson distribution.

c. The life of an electric bulb is normally distributed wiXh average life of 2000 hours andstandard deviation of 60 hours. Out of 2500 bulbs, find the number of bulbs that are likelyto last between 1900 And 2100 hours. Given that p(0 < z < 1.57) : 0.4525. (07 Marks)

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8 a. Explain the foilbwing terms: ,,':"-"

i) Null hy sis (ii) Type I and Tlpe II error (iiil Confidgnce limits. (06 Marks)

b. The weight of workers in a large factory are normally distributediWith mean 68 kgs, andstarydard deviation 3 kgs. If 80 samples consisting of 35 workers each are chosen, how manyof,80 samples will have the mean between 67 and 68.25 kgs. Given p(0 < z < 2) : 0.4772and p(0 3 z < 0.5): 0.1915.

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Eleven students were given a test in statistics. They were provided additional coaching andthen a second test of equal difficulty- was held at the end of coaching. Marks scored by thenin the two tests are given belo

Do the marks give evidence that the student have benefited by extra coaching? Givent005(10) :2.228. Test the hypothesis at 5Yo level of significance. (07 Marks)

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Fourth Semester B.E. Degree Examination, Dec.2013/Jan.2$t4

Advanced Mathematics - llTime: 3 hrs. Max. Marks:100

Note: Answer any FIVEfull questions.

I a. Prove that sin' cr + sin' B + sin' y = 2. (06 Marks)

b. If 11; ml, n1 and 1.2, mz, fl2 are direction cosines of two lines then pxove that the angle

between,,them is cos 0: l-J-zt m1m2 * nrflz. : ,,ir (07 Marks)

c. Find the equation of the plane through the interaction of the pl4nes'2x + 3y - z : 5 andx-2y -32= - 8, also perpendicularto the plane x +y -z:2. (07Marks)

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2 a. Prove that the equation of the plane in the intercept form is I + {*i=,b. Find the equation of the plane through the points (l; -2,2) (-3, l, -2) and perpendicular to

theplane2x-y-z+6:0"c. Find the angle between the following lines:

x-2:,u-l _r-3 end x+i_>-3_z-1t22*1 0

a' Find the sine of the angle between

b. Find the value of ), if the vectors

are coplanar.c. Prove the following: , '

i) (34 - 26) x 1-la + 2b-; = l4(A + 6)

ii) (2a+ 36) x (a +,::,45) = 5(a + 6)

a. A particle rr,lclVes along the curve i = (t' -4O1+(t2 +at)j+(8t2-.3t3;[. nina the velocityand acceleration at t : 1 and also find their magnitude. ., (06 Marks)

b. nind,ihe unit normal vector to the surface xy3 z2 :4 at the point (- 1 , -1 , 2). :_ (07 Marks)c. Findthedirectionalderivative ofx2yz3 at(1, 1, 1)inthedirectionof i+j+2k (07Marks)

rr {,;a' Find div F and curl F, where F = xti + ytj + zt[ . (06 Marks),,"'lb. Prove that curl grad Q

: 0. (oiiMarks)c. Find the constants a,b, c such that the vectorF =(x* y +az)i+(x+ cy +22)k+(bx+ 2y -r)j

is irrotational. (07 Marks)

a.

b.c.

d.

Find the Laplace transform of the following:sin 4t cos3tcos hat

t e-t sin t1 - cost

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7 Find the inverse Laplace transform of- /s+1\a' '"1r r.,J (06 Marks)

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., t' G+1)G{2X,L:5

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8 a. tr;'@g Laplce transforms, solve the differential equation {furgl. 6y =5e"dt'- dtsubjectEffi-the conditions y(0) : y'(0) :0. , (10 Marks)

b. Solve the siffilppeous equations **r=sint, gy-*x

=9oF$, using Laplace transforms.Lfl./ dt dt ,.ftrI*Given that x : 1, yffiwhen t : 0. (lo Marks)

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Fourth Semester B.E. Degree Examination, Dec. 20l3lJan.2Ol4Goncrete Technology

Time: 3 hrs. Max. Marks:100Note: Answer FIVEfull questions, selecting

atlesst TWO questions from each part.

PART _ A

1 a. What are Boughe's compounds in cement? Explain the role of each compound in strength

gaining and hardening process. (10 Marks)

b. Exp14,,1$he process of "Dry Process" of manufacturing cement with a help of flow,lt"Jlr.u,

What are the physical requirements of good fine and coarse aggre$ates?

Define "Grading of aggregates", what is the importance of.grading of aggregates in the

manufacture of quality concrete.

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3 a. Define water cement ratio, and how this w/c ratio will have influence on workability of fresh

concrete. ::: ,. ,, ,, (10 Marks)

b. What are admixtures? Why ihey..ale used in ttle,,manufacture of concrete? Explain any three

admixtures used in concrete manufacture. ',,,,, '''i (10 Marks)

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tt"'' - "t"'4 a. Write notes oni) Segregationii) Bleeding. (10 Marks)

b. What are the filed tests condtrCted on quality of cement at site of construction. (10 Marks)

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5 a. Define "Tensile "strength of concrete".concrete?

b. Define: . ,',ll'i) Flex$ml'strengthii) Cofuressive strengthiii) : Sptit tensile strength.

PART - B

How is it related with compressive strength of.,,i ,, r (10 Marks)

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6 a., Fxplain the relation between the modulus of elasticity and compressiv th of concrete.

Write shoft notes on :

i) Factors affecting the shrinkageiD Factors affecting creep.

What are the factors contributing to cracks in concrete?

Explain the significance of durability of concrete in itsaffecting the durability of concrete.

8 a. Define nominal mix, and its types, explain the importance of design mix in the RCC designof structural members. (10 Marks)

b. Write step by step procedure for I.S method of mix design (preferably flow chart) (10 Marks)

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Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l4Structural Analysr's - I

Max. Marks:100Note: 7, Answer FIVEfull questions, selecting

ot least TWO questions from each part.2. Assume any missing data suitably.

PART _ AI a.: Distinguish between determinate a.rd indeterminate structures with examples. (06 Marks)

b. Determine the static and kinematic indeterminacy for the structures shown in Fig.Q1(b).

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; Fig.Ql(b)c. Write strain energy expressions fbr 4xrql, shear bending and twisting.

2 a. Determine slope and deflection at the free end for the cantilever beamusing moment area method.

(10 Marks)(04 Marks)

shown in Fig.Q2(a),(10 Marks)

, Fig.Q2(a)Deterftine the slopes of support and deflection underFig.Q2(b), using conjugate beam method.

State and prove Maxwell's reciprocal theorem.

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(06 Marks)Using the method of virtual work determine the horizontal displacement of a point C of theframe shown in Fig.Q3(b). Take E :2x10s N/mm2 and I :4x106 mma. (14 Marks)

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Determine the vertical and horizontal deflections at point C of the truss as shown in Fig.Q4,using unit load method. Area of cross section of all the members is 6x10-a m'.Take E:200 GPa. (20 Marks)

3a. A three hingedloaded points.

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PART _ Bparabolic arch is loaded as shown in Fig.Q5(a). Determine the B.M- at

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b.

6a.

b.

h6" -'l t+u -aw =lFie.Q5(at Fie.e6(a)A flexible suspenSioa cable of weight 0.0075 kN/m hangs between two vertical walls 60 mapart, the left end being attached to the wall at a point 10 m below the right end.A concentrated load of I kN is attached to the cable in such a manner that the point ofattachment of the load is 20 mhorizontal from the left and wall and 5 m below the left handsupport. Show that maximum tension occurs at the right hand support and find its value.

A cantilever beam of constant flexural rigidity is propped at its free end to the level of fixedend. Determine the reaction of the prop when the beam carries udl over the entire span.Hence draw BMD and SFD. Fig.Q6(a). (10 Marks)Determine the fixed end moments or support moments for the beam loaded as shown inFie.Q6(b). (to Marks)

, Fie.Q6(b) Fig.e7(b)a. Derive the generalized Clapeyron's theorem of three moments. , (06 Marks)b. Analyze the continuous beam ABC shown in Fig.Q7(b), using Clapeyron's thoorem of three

rnbments. Hence draw BMD and SFD. Also sketch elastic curve. (14 Marks)

Find the horizontal thrust for the two hinged parabolic arch as shown in Fig.Q8. The moment ofinertia at any section is I. secO, wheie 0 is the slope at section and I. is M.I. at the crown.Neglect the effect of rib shortening. Draw BMD.

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Fourth Semester B.E. Degree Examination, Dec.2013 /Jan.20l4Sunreying - ll

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

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I a. List out the miscellaneous operations that can be performed with a transit tlreodolite and

explain the procedure for setting the horizontal angle which is less than the least count of theinstrument (10 Marks)

b. Explain the procedures for extending a straight line using a transit'when it is in adjustmentand not in adjustment. ''. (10 Marks)

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2 a. What are the fundamental lines of a transit theodolite and state the desired relationshipsbetween them. ,,,,,, (10 Marks)

b. A dumpy level was set up at 'C' exactly midway between 'A' and 'B' which are 100 mapart. The readings on the,'st4Jf when held at the stations 'A" and 'B' were 2.250 and2.025respectively. The instrumeilt,has then moved and set up at 'D' on the line 'BA' producedwhich is at a distance of 20 m from'A'. The respective staff readings on'A'and'B'were1.875 and 1.670. Calculate the coirect staff readings on'A' and'B'to give a horizontal lineof sight and state whether the line oicollimation is inclined upwards or downwards.

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3 a. An instrument was set up at 'P{ alld the angle.,o"f elevation to a vane 4 m above the foot ofthe staff held at 'Q' was 9o30,', The horizontal distance between 'P' and 'Q' was measured tobe 2 km. Determine the RL of the staff station'Q'. given that the back sight reading taken ona bench mark of RL 50.217 m was 0.880 m. Apply the necessary corrections. (06 Marks)

b. Write a note on total station and mention its advantages. - (02 Marks)c. To find the elevatio,ir of the top 'Q' of a hill, a flag staff of 2 m height was erected and

observations were made from two stations 'P' and 'R' 60 rti';-a The horizontal angle

measured at 'R' between the top of the flag staffand 'P' was 68o18'and that measured at 'P'between'R' and the top of the flag staff was 60o30'. The angle of eleVation to the top of theflag ;iaff 'Q' was measured to be 10o12' at'P' and that at 'R' was 10o4$r. Staff readings onthe bench mark when the instrument was at P : 1.965 and that when the inStrument was atR: Z.OSS. Calculate the elevation of the top of the hill if that of bench mark was 250.075 m.

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(tr0 Marks)

Write a note on tacheometric surveying. Derive the standard expression for 1

distance with usual notations.Briefly explain the stadia method and subtense method of tacheometry.Ihe following observations were made using a tacheometer fitted with an ahavins the constant to be 100 and the staff held vertical.

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30030'

75030',

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RL oF0.--s.l150.000 m

Calculate: (i) The horizontal distance AB (ii) RL of AB (iii) Gradient from A to B(08 Marks)

5a.

b.

c.

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PART _ BDefine degree of a curve. Establish the relationship between degree of curve and its radius.

(04 Marks)Explain the method of setting out a simple curve by the offsets from chord produced.

(06 Marks)Tabulate the necessary data to set out a right handed simple circular curve in the field havinga radius of 250 m, connecting two straiglrts which intersect at chainage 1250 m at an angle

150'by Rankine's method. Take peg interval of 20 m and least count of the instrument

,, as 20" ,"(10 Marks)

6a.

b.

7a.

b.

c.

What do you understand by a reverse curve and mention its significance. Derive therelationships between various elements of a reverse curve between the parallel straights.

(10 Marks)Two tangents AB and BC intersect at B. Another line DE intersects AB and BC at D and E

such that Z/ff,E: 150o and IDEC: 140o. The radius of the first eurve is 200m and that ofthe second is 3Q0 rn. Calculate all the data necessary for setting out a compound curve if the

Write a note on traniition curve and list out its advantages. What are the pre-requisites forthe design of a transition curve? (08 Marks)Calculate the length of the iransition culve, when the rate of radial acceleration is 30 cm/s3,allowable speed on curve is 60 kmph and radius of the circular curve is 200 m. (04 Marks)When would you prefer a vertical curve and how are these classified? Explain the role ofchange of gradient in the design of a vortical curve. (08 Marks)

a. A page of the field book of a cross-staff Survey is given in Fig.Q8(a). Plot the required figureand compute the area. (10 Marks)

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Fig.Q8(a)An embankment of width 10 m and side slopes l%:1 is required to be made on a groundwhich is level in a direction transverse to the center line. The central heights at 40 mintervals are as follows:

0.90, 1.25, 2.15, 2.50, 1.85, 1.35 and 0.85Calculate the amount of earthwork according to :

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(i) Trapezoidal formula (10 Marks)

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expression for the depth of hydraulic jump in(08 Nlarks)

Fourth Semester B.E. Degree Examination, Dec.2013 lJan.20l{Hydraulics & Hydraulic Machines

Max. Marks:100Time: 3 hrs.

2a.

b.

Note: Answer FIVEfull questions, selectingat lesst TWO questions from each port,

PART _ A

a.

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State the Buckingham theorem and mention the advantages of dimensional uralysisloo Marks)

Capillary rise h depends on density p, acceleration due to gr,avity g, surface tension oand radius of the tube r. Show by using the Buckingham n-theorem that

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c. In the model of a spillway, the discharge and velocity of the flow over the model were2rilsec and 1.5 m/sec, respictively. Calculate V and Q over the prototype spillway if thescale is 1/36. ' (06 Marks)

Derive an expression for the discharge through an open channel using Chezy's formula.(06 Marks)

A flow of water flows at 150 litres per second in a rectangular channel of width 70 cm anddepth of flow 40 cm. Uniform flow occurs at a certain bed slope with Chezy's C equal to 60.

c. A canal is to have a trapezoidal section with one side vertical and the other sloping at 45'. Ithas to carry 30 m'/sec of water with a mean velocity of 1 m/sec. Compute the dimensions of

Find the bed slope of the channel.

the section which will require the minimum lining.

3 a. What is specific energy curve? Draw specific energy curve and then derive expressions forcritical depth and critical velocity. (06 Marks)

b. Show that the relation between alternate depth )1 and yz in a rectangular channel can be

expressed by

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c. Explain the term hydraulic jump. Derive anterms of the upstream Froude number.

4 a. Find an expression lor the efficiency of a series of moving curved vanes when a jet of waterstrikes the vanes at one of its tips. Prove that maximum efficiency is when u : v and thevalue of maximum efficiency is 50%, (10 Marks)

b. A jet of water coming out of a nozzle of 10 cm diameter with a velocity of 10 m/sec strikesthe flat plate. Find out the force exerted on the plate, work done, power developed andefficiency when (i) plate is stationary (ii) plate is moving with a velocity of 10 m/sectowards the jet (iii) plate is moving with a velocity of 10 misec the jet

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(10 Marks)

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b.

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PART _ B

Prove that the work done per second on a series of moving curved radial vane is

pav, [v*,u, * v*, u, ] (10 Marks)

A jet of water having a velocity of 35 m/sec impinges on a series of vanes moving with a

velocity of 20 m/sec. The jet makes an angle of 30' to the direction of motion of vahes when

entering and leaves at an angle of 120o. Draw the triangles of velocities at inlet and outletand find:(i) The angles of vanes tips so that water enters and leaves without shock.

(ii) The work done per unit weight of water entering the vanes.(iii) The efficiency.

a. Obtain an expr€ssion for the work done per second by water onthe runner of a Pelton wheel.

b. Design a Pelton wheelwith the lollowing data:

Shaft power :735.75 kW ; H : 200 m ;

Cv: 0.98 , $ :0.45. r'

Determine D, d and number ofjets

What are the uses of a draft tube? Describe with neat sketches different types of draft tubes.,: (08 Marks)

A Kaplan turbine working under a head of 20. m develops 11772 kW shaft power. The outletdiameter of the runner is 3.5 m and hub diameter 1.75 m. The guide blade angle at theextreme edge of the runner is 35o. The hydraulic,and overall efficiencies of the turbines are

88% and 84olo respective$irlf the velocity of whirl is zgro at outlet, determine:(D Runner vane angles-at inlet and outlet at the extrerhe edge of the runner and(ii) Speed or,n.,,,,u.O*". (12 Marks)

Define a centfifugal pump. Explain the working of a singld-sthge centrifugal pump withsketches. : (08 Marks)A centrifual pump delivers water against a net head of 14.5 meties and a design speed of1000 qpm. The vanes are curved back to an angle of 30o with the periphery. The impellerdiameter is 300 mm and outlet width 50 mm. Determine the discharge of the pump, if

(10 Marks)

(10 Marks)

N.= 800 rym ; 116 : 0.86 , ? =,0,

manometric efficiency is 95oh.

(10 Marks)

(12 Marks)

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