USN

Time: 3 hrs.

4 a. Find the bilinear transformation that maps the points 1, i, -1respectively.

b. Discuss the transformation'W: e'.

1OMAT41

Max. Marks:100

(06 Marks)

onto the points i, 0, -i(06 Marks)(07 Marks)

(07 Marks)

Fourth Semester B.E. Degree Examination, Decemb er 2Ol2

Engineering Mathematics - lV

Note: Answer FIVE full questions, selectingat least TWO questionsfrom each port.

doo!no.

()

()!

3s!,-6e

-.ocol=oo(c+gdotr-E o)

a=

oo)

>d

!d3a

o{=

o-A

oj,;oo=6E!o=-Eo.i>,too"cooo=sotr>=o5L

lr<-NooZ

Ho

PART _ A

I a' Using the Taylor's series method, solve the initial value probt.* !I - x'y - 1, y(0) : I atrtox

(06 Marks)

at the points

(07 Marks)

c. Given 9= *, + y', y(0) : 1, y(0.1) : I .1169,y(0.2) : 7.2773,y(0.3) : I.5049.Find y(0.4)dx

using the Milne's predictor-corrector method. Apply the corrector formula twice. (07 Marks)

2 a. Employing the Picard's method, obtain the second order approximate solution of thefollowing problem at x : 0.2.

dy =x+YZ dz

dx , , *=V+zx, y(0):1, z(0):-1.

b. Using the Runge-Kutta method, find the solution at x : 0.1 of the differential equationd'y , d'1 ', -x'

*! -2xy =1 under the conditions y(0): 1, y'(0):0. Take step lengthh:0.1.dx' dx

(07 Marks)c. Using the Milne's method, obtain an approximate solution at the point x : 0.4 of the

problem +.:*9-6y=0. y(0): l.y'(0):0.1. Given that y(0.1): 1.03995.' dx' dx -J

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.(07 Marks)

3 a. lf f(z): u * iv is an analytic tunction, then prove that (+l rtr) ll .Pt rtr) ll =lr,1rsl' .

\dx / \ry )(06 Marks)

b. Find an analytic function whose imaginary part is v = e* {(x' - y')cosy -2xy sin y} .

(07 Marks)c. If (z) : u(r, 0) + iv(r, 0) is an analytic function, show that u and v satisfy the equation

A'a 16o lA2a^2

+---+-i^J=U. (OTtVtarks)or t or r- oa-

the point x:0.1

b. Employ the fourth order Runge-Kutta method to solve q.t =tl-"'r, y(0) : 1

dx v- +x-x:0.2 and x :0.4. Take h :0.2.

c. Evaluate ItT n',,l,"ot11'oz

, where C is the circle lzl:3.! tr-t)'(z-2)

5 a. Express the polynomial 2x3 -x' -3x+2 in terms of Legendre polynomials. (06 Marks)

b. Obtain the series solution of Bessel's differential equation *'*+ *++ (x'-r')y = 0 indx' dx

PART * B

the form y: AJ,(x) + BJ-"(x).

Derive Rodrique's formula h(x) = r, #(x'-1)'.

State the axioms of probability. For any two events A and B, prove thatP(A u B) = P(A) + P(B) - P(A n B) .

1OMAT41

(07 Marks)

(07 Marks)

(06 Marks)

c.

6a.

b. A bag contains 10 white balls and 3 red balls while another bag contains 3 white balls and

5 red balls. 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 whiteball? (07 Marks)

c. In a bolt factory there are four machines A, B, C, D manufacturing respectively 20Yo,l5o/o,25% 40% of the total production. Out of these 50 , 40 , 3o/o and 2Yo 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. The probability distributio! gle i1119 r@m variable X is given by the following table:

Determine the value of k and find the mean, variance and standard deviation. (06 Marks)

b. The probability that apen manufactured by a company will be defective is 0.i. If 12 such

pens are selected, find the probability that (i) exactly 2 will be defective, (ii) at least 2 willbe 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, giventhat A(0.5):0.19 and A(1 .4):0.42, where A(z) is the area

under the standard normal curve from 0 to z >0. (07 Marks)

8 a. A biased coin is tossed 500 times and head turns up 120 times. Find the 95o/o confrdence

limits for the proportion of heads turning up in infinitely many tosses. (Given that z": 1.96)(06 Marks)

b. A certain stimulus administered to each of 12 patients resulted in the following change inblood pressure:

5, 2, 8, -1, 3, 0, 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(11):2.201. (07 Marks)

c. A die is thrown 60 times and the frequency distribution for the number appearing on the face

x N glven followins tablethe followins table:

x I 2 J 4 5 6

Frequency 15 6 4 7 1l t7Test the hypothesis that the die is unbiased.

(Given that yf;or(5) = 1 1.07 and X3o, (5) = 15.09 )

Xi 1 -1 0 1 2aJ

p(xi) 0.1 k 0.2 2k 0.3 k

(07 Marks)

/

USN

4a.b.

5a.b.

c.

t0cY42

(10 Marks)(10 Marks)

(10 Marks)(10 Marks)

(06 Marks)(06 Marks)(08 Marks)

(14 Marks)(06 Marks)

Fourth Semester B.E. Degree Examination, December 2Ol2Goncrete Technology

Time: 3 hrs. Max. Marks:100Note: 7. Answer uny FIVEfull questions, selecting

atleust TWO questions from each part .

2. Use of IS - 10262 - 2009 is permitted.

PART _ A

I a. What are the chemical compositions of cement? How the cement is manufactured give flow

oooLaE

4)(!(.)

oX

-*lltroo

6$-ilgc)ogeO

o>

a:

oo)

botr$(d

E(oJ?()OE

oAo_i/ioo=a'i!o5 .:?>'=bo"trbQo=

=dgotr>o

\-, <* a.l

ooZ

oE

2 a. Explain the importance of size shape and texture of aggregate. (10 Marks)

b. Explain the role of admixture in concrete making. Write briefly about the accelerators andretardors. (10 Marks)

3 a. What is meant by workability of concrete? What are the factors affecting the workability of

chart.b. Explain the terms normal consistence initial and final setting time.

the concrete.b. Explain briefly the suggrigation and bleeding of concrete.

6a.b.

c.

7a.

b.

8

Why curing is necessary. Explain briefly the different types of curing. (10 Marks)What are the processes of manufacturing of the cement concrete? Explain briefly. (10 Marks)

PART _ BExplain the influence of water/cement ratio on the strength of the concrete. (08 Marks)

Explain how the compressive and tensile strength of the concrete is determined. (08 Marks)What do you mean by non - destructive testing of concrete? Explain any one of them.

(04 Marks)

What are the factors that influence the strength of concrete?Explain the different types of shrinkage that take place in concrete.Write a note on creep of concrete.

What is meant by concrete - mix - designs? Write the steps involved in the method of mix -

a.

b.

c.d.

design (lS - 10262 -2009)What are the factors reducing the durability of the concrete.

Write short notes :

Light weight concreteMineral - admixturesFibre - reinforced concreteCompaction of concrete. (20 Marks)

USN 10cv43

Fourth Semester B.E. Degree Examination, December 2Ol2Structural Analysis - I

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

atleast TI,I/O questions from each parl

PART _ A

I a. Distinguish between static and kinematic indeterminate structures, with example. (04 Marks)b. Derive an expression for the strain energy stored in a member due to bending. (06 Marks)c. A cantilevers truss is loaded as shown in Fig. Q1(c). The cross sectional area of the members

is as indicated in the figure. Find the strain energy stored due to loading. Take E :72 GPa.(10 Marks)

1u ku

Fig. Q1(c)

2 a. A cantilever of length 4 m is loaded as shown in Fig. Q2(a). Taking EI constant for thewhole length of the beam, calculate the deflection at the free end by moment - atea method.

(08 Marks)

0'?r\T

,rr[

(J()(.)

i:a

0)

()

Eq

;6-*t-oa.= C.l

gil6JC

-C(l)

o>3sa:

oO(60

botr

-6!d

oi=

x9tro.orwoj

a=ao4 t'=

LO

5 .:r>':bo-E50o=o.Btr>=ov!o

\r<*NooZ

Lo

A {{k'lnA :t rrr'-.*', T)Lkn-v

),r"-Li!5Fig. Q2(a)

b.

3a.

Determine the slope at A and deflection at C in the beam loaded as shown in Fig. Q2(b), byconjugate beam method. Take EI constant. (12 Marks)

Find the deflection under concentrated load for the beam shown in Fig. Q3(a), usingCastigliano's first theorem. Take E:2 x 108 kN/# and I : 14 x 10-6 ma (10 Marks)

p=,5okH

b.Fig. Q3(a)

Find the vertical deflection at C for themethod. Take EI constant.

Fig. Q3(b)shown in Fig. Q3(b). Using strain energy

(10 Marks)

/nlrl"tI

Fig. Q2(b)

10cv43

Find the vertical deflection at F for the pin jointed truss shown in Fig. Q4, using unit loadmethod. Assume cross sectional area of each member as 1000 mm2 and E : 200 GPa.

(20 Marks)

PART - B

5 a. A three hinged parabolic arch hinged at the supports and at the crown has a span of 24 mand a central rise of 4m. It carries a conc6ntrated load of 50 kN at I 8 m from the left supportand a udl of 30 kN/m over the left half portion. Determine the bonding moment, normalthrust and radial shear at a section 6 m from left support. (12 Marks)

b. A suspension cable having supports at same level has a span of 40 m and maximum dip of4 m. The cable is loaded with udl of 10 kN/m through its length. Calculate the maximumand minimum tension in the cable. Also find the length of the cable. (08 Marks)

6 a. Draw BMD for the propped cantilever loaded as shown in Fig. Q6(a), by consistentdeformation method. The supports at A and B remain at the same level after the load.

(10 Marks)

{YH

3rt &r{Fig. Q6(a)

A fixed beam is loaded as shown in Fig. Q6(b). Draw BMD.Fig. Q6(b)

l0l+r

Fig. 4

Kh

Enks

(10 Marks)

moments.(20 Marks)

Analyse the continuous beam shown in Fig. Q7 by Clayperon's theorem of threeDraw BMD, SFD and elastic curve. EI constant throughout

ftk*,,to

ktlrt

Itr

Fig. Q7

A parabolic arch hinged at the ends has a span of 30 m and rise of 5 m. A concentrated loadof 12 kN acts at 10 m from the left hinge. The second moment of area varies as the secant ofthe slope of the rib axis. Calculate the horizontal thrust and the reactions at the hinges. Alsocalculate maximum bending moment anywhere on the arch.

golttr

{<{<**x<

(20 Marks)

USN t0cY44

Max. Marks:100

(06 Marks)(04 Marks)

(10 Marks)

(06 Marks)(02 Marks)

(12 Marks)

(06 Marks)

Fourth Semester B.E. Degree Examination, December 2Ol2Surveying - Il

b.

c.

dooIa

()

()!

oX

= r.)

oo ll

troo.=NcS*hboY()(JC_co

?1, ^

a=

o()

50cE:,6!6=-o(B-+ooi=

o-atra.o-l

9i;aoatE

!o

b0ocb0o=o.Btr>:oo

Lr<aOl

ooZ

!oo.

2 a. What are the fundamental lines of a theodolite state the desired relationship between them.(10 Marks)

b. A dumpy level was kept midway between two points A & B 100m apart. The readings onstaff held at A & B were 2.340 m and 1.795 m. The instrument was then kept at C, 20 mfrom A along BA produced. The readings on the staff held at A & B were 1.985 m and1.435 m respectively. Calculate the correct readings at A & B with the instrument at C.Is the line of collimation inclined upward or downward? (10 Marks)

3 a. A theodolite was set up at a distance of 150 m from tower. The angle of elevation to the topof the tower was 10o8' while the angle of depression to the foot of the tower was 3o12'. Thestaff reading on the B.M. of R.L. 50.217m with the telescope horizontal was 0.880 m. Find

Time: 3 hrs.Note: l. Answer FIVEfull questions, selecting

at least TWO questionsfrom each part.2. Assume any missing data suitably.

PART _ A1 a. Describe the procedure of measuring horizontal angle with a transit.

b. State what errors are eliminated by repetition method.c. Explain the prolongation of a straight line using theodolite:

i) Which is in adjustment ii) Which is in poor adjustment.

the height of the tower and the R.L. of the top of the parapet.What are the applications of total station?

the horizontal distance P from B and the R.L. of P.

Differentiate between fixed hair method and movable hair method.

To find the elevation of the top(P) of a hill, a flag staff of height 1 .5m was erected and thefollowing observations were made from two stations A & B at considerably differentelevations 156m apart. The angle of elevation from A to the top 6f the flag staff was 38"24'and that from B to the same point 2612' . A vane 1.2m above the foot of a staff held on Awas sighted fromB andthe angle of elevationwas observedto be 9'54'. The height of theinstrument axis at A was 1.494 and the R.L. of the instrument axis at B was 45.00m. Find

Following observations were taken with a tacheometer fitted with an anallactic lens having avalue of constant to be 100 and staff held vertical.

Inst. Station Staff station R.B. Vertical angle Staff readines.0 P N37"W 4 12', 0.910, 1.510, 2.110

a N 23'E 5" 42', 1.855, 2.705,3.555Determine the gradient between points P & Q. (10 Marks)Two vertical angles to vanes fixed at 1m and 3m above the foot of the staffheld vertically at

if R.L. of instrument axis is 235.665 m above the datum.

c.

I of2

5a.

b.

6a.b.

C.

7a.b.

c.

8a.

A curve has a radius of 400m and a deflection angle of 40o. The chainage of point ofintersection 1804.25 m. Compute the necessary data to setout simple curve by offsets fromchords produced. Take Peg interval as 20 m. (08 Marks)

c. Two straight lines with a total deflection angle of 72o30' are to be connected by a compound

curve of two branches of equal length. The radius of the first arc is 350 m and that of the

second arc is 500m and chainage of vertex is 1525m. Find the chainages of two tangent

PART _ BDerive the expressions for the following elements of a simple curve.

, External distance ii) Mid ordinate

points and that of point of compound curvature.

Explain with neat sketches the different triangulation systems.

Define the following :

i) Satellite station ii) Reduction to centre.

t0cY44

(04 Marks)

(08 Marks)

(06 Marks)

(04 Marks)

From an eccentric station 'S' 9m to the west of the main station B, the following angles were

measured ZBSC : 33"15'40 and ZASC : 67o56'2C,. The stations S and C are to the

opposite sides of the line AB. Calculate,the correct angle ABC if the lengths AB & BC are

3,896.8 m and 4,470.72 m respectively. (10 Marks)

What is super elevation? Derive an expression for the amount of super elevation. (06 Marks)

With the help of neat sketches, explain types of vertical curves. (06 Marks)

A circular curve of radius 300m on a railway line gauge 1.5m is to be provided withtransition curves at both ends. The super elevation is to be restricted to 15 cm. The design

should be such that the rate of change of radial acceleration is 0.3 m/sec3. Calculate the

length of the transition curve and design speed of vehicles if no lateral pressure is to be

exerted on the rails. Also calculate the shift and spiral angle of the transition curve.(08 Marks)

Plot the cross staff survey of a field ABCDFE from the field book measurements given inFig.Q8(a) below and determine the area of the field. (10 Marks)

F 16o kl9b

I oso l4o D

e 150 HUN

Gtoo tzd,

ob*

Fig.Q8(a)

b. A road embankment is 30m wide at the top with side slopes of 2 to 1. The ground levels at

100 m intervals along a line AB are as under:

A 170.3, 169.1, 168.5, 168.1 166.5 BThe formation level at A is 178.7m with a uniform falling gradient of 1 in 50 from A to B.

Determine the volume of earthwork by prismoidal rule. Assume the ground to be level in

**{<{<*

2 of2

Lbtofr

cross-section. (10 Marks)

/USN 06cv45

Fourth Semester B.E. Degree Examination, January 2013Hydraulics and Hydraulic Machines

Time: 3 hrs. Max. Marks:100

Note: Answer FIVEfull questions, selectingat leust TLI/O questions from each part.

PART _ A

a. Define the following:D Most economical channelii) Hydraulic depthiii) Rapidly varied flow. (06 Marks)

b. Show that for most economical triangular channel section the crest angle is 90o. (06 Marks)c. Determine the dimensions of an economicaltrapezoidal section of an open channel with side

slope 2H:1V laid at a slope of 1 in 1600 to carry a discharge of 36 m3/s. Take C : 50.(08 Marks)

3a.b.

C'oo

a)(n(JL

E9d=

s/, 2de

=n-^tle€

.=N.g <-- ol)ts()otrFO

3so=

oo

boc.s c3

-o>66-

-4o6rrob1o..oiv1 -Yo=a,=€i!o6.">\ (k

tro!o=o- Ai

=o5!

\J<-i Gi

ooz

o

a. Distinguishbetween:i) Specific energy and total energyii) Sequent depths and alternate depthsiii) Gradual closure and sudden closure of value.

Kwater :2.1 GPa.

What is meant by dimensional homogeneity? Give example.

b. A stream carrying discharge of 2.4 cumec/m has velocity of 6 m/s is discharged from toe ofa dam on a horizontal bed. What will be the height of jump? Also calculate energy loss inmeters of water. (08 Marks)

c. What is the maximum pressure rise due to sudden closure of a valve in a pipe of 300mmdiameter conveying water at 1.8 m/s? The pipe wall thickness is 18mm, Epipe: 210 GPa,

(06 Marks)

(06 Marks)

(06 Marks)

(08 Marks)

Fluid of density p, viscosity p flows at an average velocity V through a pipe of diameter D.Show that the shear stress of pipe wall is

,r=Or'f[f]c' In 1:40 scaled spillway model, the velocity and discharge are 2m/s and, 2.5m31s. Calculate

the corresponding velocity and discharge in the prototype. (06 Marks)

4 a. Show that the efficiency of a jet striking normally on series of flat plates mounted on theperiphery of wheel is 50%. (10 Marks)

b. A 75mm diameter jet moving with 30 m/s strikes a flat plate with its normal at an angle 45oto the axis of the jet. Determine the normal force on the plate, if the plate is stationary. Alsofind hydraulic efficiency of the jet if the plate is moving with 15 m/s in the direction ofjet.

(10 Marks)

7 of2

06cv4s

PART _ B

5 a. A jet of water 5cm diameter strikes on a curved vane with 20 m/s. The vane being moving at

10 m/s in the direction of the jet. The jet leaves the vane at an angle of 60o to the direction ofmotion of vane at outlet. Determine:

i) The force exerted on the vane in the direction of motion.

ii) Work done Per second bY the jet.

b. A pelton wheel has to develop 13230 kW power under a net head of 800m while running at

600 rpm. If c,: 0.97, speed ratio : 0.46, jet ratio : 1/16, determine: i) pitch circle diameter;

ii) th; diameter ofjeti iily ttre quantity of water supplied to the wheel; iv) the number ofjets

(10 Marks)

(10 Marks)

(08 Marks)

(12 Marks)

(06 Marks)(06 Marks)

(06 Marks)(06 Marks)

6a.b.

7a.b.c.

A Francis turbine has to be designed for an overall output of375 kW under a head of 80m

with 700 rpm. Determine the main dimensions of the runner, runner vane angles. Take

hydraulic losses : l0o/o, flow ratio =

0.15, ratio of inner to outer diameter:0.5, ratio of

width to diameter at outlet : 0.1, no: 0.82, area blocked by thickness of runner vanes : 5o/o,

required. Overall effrciency : 85oh.

with a neat sketch, explain the functioning of a Kaplan turbine.

speed ratio : 0.6.

Define draft tube. What are its functions?

Derive expression for specific speed of a turbine'

A turbine is to operate at ahead of 25m under 200 rpm. The discharge is 10 cumec. If the

efficiency isgOoh,determine the performance of turbine under a head of 20m. (08 Marks)

8 a. Differentiate between :

i) Pump and turbine.ii) Suction head and delivery head.

iil) Single stage pump and multistage pump'

What is primary of a pump? How it is done?b.

c. A centrifugal pump^tas to work against a manometric head of 25rn, rotating at 850 rpm and

discharginf O.)S m3ls. Velocity o? flo* and vane angle at outlet are 2.5 m/s and 40". IfTlman: 95Yo, calutlate: i) diameter of impeller ; ii) width at'outlet. (08 Marks)

***rr*

2 of2

/

USN 10cv46

Fourth Semester B.E. Degree Examination, Decemb er 2Ol2Building Planning and Drawing

Time: 4 hrs. Max. Marks:100

Note: 1. Part - A is compulsory2. Answer any TWOfull questionsfrom Part - B.

PART _ A

I Draw the plan, elevation and sectional elevation for the line diagram of the building shown inFig. Q1. Also write the schedule of openings

(.)oo!

6)

C)

(JX

cge-.oo0 I

t*

o ::J

(.)tr-o=ts

d=

o()6O

botrd6

,d

-?oOE

o- 6.tro.o.'o ..i

o=

a tii

!o5EY.^:bo-caoo=o. :jtr>o

t/<-i ..ioo

Loo.

a. Plan of the buildingb. Elevationc. Section @ A- Ad. Schedule of openings.

(25 Marks)(15 Marks)(15 Marks)(05 Marks)

(05 Marks)(10 Marks)(05 Marks)

PART _ B

A sequence RCC column 400 mm x 400 mm is resting on a flat RCC square footing. Thecolumn consists of 6 bars of 16 mm dia, with 2 legged 8 mm dia stirrups @ 200 mm c/c andthe footing reinforcement consists of 12 mm dia bars @ 150 mm c/c both ways. The size andthickness of the footing are 1200 x 1200 mm and 750 mm respectively. Draw to a suitablescale the following views,Plan of the footingVertical section of the column with footingsCross - section of the column.

b. Calculate carpet area, plinth area for the drawing shown in Fig. Q3(b).

a.

b.

c.

3 a' Drawto ascale of I : l0the elevationof fullypaneled doorforanopening of 1.2 m x 2.1 m.(15 Marks)(05 Marks)

Prepare a bubble diagram and develop a single line diagram of a office building to a scale of1 : 100 with the following requirement.

D AEE roomii) Technical staff roomiii) Clerical staff roomiv) Accountant and related staff roomv) Storekeeper and related staffroomvi) Manager roomvii) Drafting roomviii) Toilet block for men and women (separately). (20 Marks)

p\

10cv46sanitary layout and

(20 Marks)6

diagram of residential building is shown in Fig. Q5. PrepareI layout plans with usual notations.

The lineelectrica

T

/:lo.l6

l^,

T

I| 2-'o r''\

l

_t.-q_

Fie. Q3(b)

=-{

BG> Q- ooi+1

--A,)t'=.s'

\I

t<. r r- a-H e.;l5.O?\=- g1

r.-\ '.4 9.\ -2 -il-2-

B q.r-+l

2-+ x1r.G

r-'r v t N qHqLT-

4-3* 11.-o

5\ er<-- -

r.qxl.?5 11-.D \5'1-

t-?xa.3

\

BEP \

\3. o 1 -='ft\

$t F{

\ {v}

V. rs Ctre O{

.4.=:A?BepB.s iA_3

D...D

)-\ \, I D'.I'h

5-\ox6'.o

rt^

Fr-i t 6tqB A$ r-t a.r-r-c

^'aa\'gA t$ *< +.1

tB+$..{ q-s L

1 -a rl l.q

.g I'l- t5 orB-3 x 9--

J '-J)

BE$

3' s?r3