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USN C- 1OMAT31

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

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Find the Fourier cosine and sine transform of(x) : xe-ul, where a > 0.

constant.

4 a. Using method of leastol least souare. rt a

x I 2 3 4 5

v 0.5 2 4.5 8 t2.5b.

[/!-^,-rr

c. Obtain the constant term and coefficients of first.cosine and sine terms in the expansion ofy

Ix, if 0<x<flb.FindthehalfrangeFouriersineserieso[f1x1=] if f <x<r

lollowinp. table:

x 0 60" 120' 180: 240" 3000 3600

v '7.9 7.2 3.6 0.5 ''- 0r9 6.8 7.9

2 a. Find the Fourier transform of r(*l={u'-x'' lxl <a and hence deduce| 0. lxl> a

b.

c.

3a.

b.

Find the inverse Fourier transform of e-s" .

Obtain the various possible solutions of one dimensional heat equation ut : c2 u,* by the

method of separation of variables. (07 Marks)

A tightly stretched string of length .[ with fixed ends is initially in equilibrium position. It is/\

set ro vibrate by giving each point a velocity U. talIf .,J

. Find the displacement u(x. 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) = u0, where u0 isa(07 Marks)

(07 Marks) .

(06 Marks)

(07 Marks)

Time: 3 hrs. Max. Marks:100Notel Answer FIVE full questions' selecting

ot least TlltO questions from each part.

PART - AI x. if 0<x<n

I a. Obtain the Fourier series expansion ol i(x)={^ "' and hence deduce[2r-x. il n<x<Ztr

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x+y>4, x+3y>6

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PART - BUsing Newton-Raphson method find a real root of x + logrox : 3.375 near 2.9, corrected to3-decimal places. (07 Marks)Solve the following system ofequations by relaxation method:12x+y +z--31, 2x+8y-z=24, 3x+4y+102=58 (07 Marks)

Find the largest eigen value and corresponding eigen vector of following matrix A by powermethod

A

us;x.01: tl,....

a. In the giG;i*o- teffn- Imd,

lzs t 21

=l , 3 o I

l, o -4]0, 0]r as the initial eigen vector. (06 Marks)

below, the values ofy are conseirst and tenth terms ofthe series.

x 5 '4 5 6 7 8 9

v 4.8 8.4 t4.5 23.6 36.2 52.8 73.9an interpolating polynomial for the dataConstruct

difference formula.

consecutive terms ofseries of which 23.6 is theieries. .,.. .' :. . (07 Marks)-fs] i:',-

given below using Newton's divided(07 Marks)

I

c. Evaluate [. j

. a* by Weddte's rule taking 7-ordinates and hence find log.2. (06 Marks)jl+x'or, ^

7 a. Solve the wave equation utt =.'{ux, subject.tq u(0, t) : 0; u(4, t) : 0; u(x, 0) : 0;u(x, 0) : x(4 - x) by taking h i.l, k: 0.5 uptofour steps. (07 Marks)

^^)b. Solve numerically the equation +=+ subjecttotheconditionsu(0,0:0:u(1,1),t>0dl dx'

and u(x. 0) = sin nx.0 S x < l. Carryout compulations for two levels taking h - /, *dk : /to . (07 Marks)

c. Solve the ellibtic eouation u*. + u,., = 0 for the followins souare mesh with houndarv vahresSolve the elliltic equation u*, + uyy = 0 for the following square mesh with boundary valuesas showt,!!r'Fig.Q7(c). (06 Marks)

' u 5oo looo 5oo uf-T t- r- l,"""1 l', l.u 1,, 1,"^"

,*J--P]-lrf,o.,o Fig'Q7(c)

(07 Marks)

(07 Marks)

(06 Marks)

8 a. Find the z-transform of: i) sinhn0; ii) coshn0.

b. Obtain the inverse z-transform of 8z'(22-1)(42-1)

c. Solve the following difference equation using z-transforms:yn+zl2yn+t + yn: n with ye: yr :0

2 of2

USN

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

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and shear stresses on an oblique plane are given by on - o cos2 0 and o,

0 : Angle made by oblique plane with the normal cross section of the bar.

Strength of MaterialsTime: 3 hrs. Max. Marks:100

Notez Answer FIVEfull questions, selectingot leost TWO questions from each porl

PART _ AI a. Brielly explain the behaviour ofductile material under gradually increasing tensile load.

(05 Marks)b. Derive the relationship between modulus of rigidity and modulus of elasticity. (05 Marks)c. A member ABCD is subjected to point loads Pr, Pz, P: and P4 as shown in Fig.Q1(c).

Calculate the force P2 necessary for equilibrium, if Pr : 45 kN, P3 : 450 kN andP+ : 130 kN.-Determine the total elongation of the member, assuming the modulus ofelasticity to be 2.1 x 10s N/mm2. (10 Marks)

Fig.Ql(c)

Define: i) Modular ratio, ii) Volumetric strain. (04 Marks)

c.

A load of 2 MN is applied on a column 500 mm x 500 mm. The column is reinforced withlbur steel bars of l0 mm diameter. one in each comer. Find the stresses in the concrete andsteel bars. Take "E" for steel as 2. I x 105 N/mm2 and ftir concrete as 1 .4 x 104 N/mrn2.

(08 Marks)A steel rod of 20 mm diameter passes centrally through a copper tube of 50 mm externaldiameter and 40 mm internal diameter. The tube is closed at each end by rigid plates ofnegligible thickness. The nuts are tightened lightly home on the protecting pans ofthe rod.It the temperature oI the assembly is raised by 50"C. calculate rhe srresses developed incopper and steel. Take E lbr steel and copper as 200 GN/m2 and 100 N/m2 and a for steeland copper as 12 x 10-6/nC and 18 x 10-6fC. (08 Marks)

Define: i) Principal planes, ii) Principal stresses. (04 Marks)A rectangular bar is subjected to a direct stress (o) in one plane only. Prove that the normal

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(06 Marks)

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c. Two wooden pieces 100 mm x 100 mm in cross section are glued together along line AB as

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4a.b.

Define: i) Shear force, ii) Bending moment.Tluough sketch list the imporlant tlpe of beams.

Fig.Q4(c) shown the shear force diagram for a simply supporled beam.

pattem and also draw the bending moment diagram.t

Fig.Qa(c)

PART _ BDefine: i) Neutral axis, ii) Section modulus, iii) Moment of resistance.

beam.

Define: Torsional rigidity, ii) Polar moment of inertia.

10cv/EV33

(04 Marks)(05 Marks)

Obtain the loading(l I Marks)

(06 Marks)

(06 Marks)

(0,1 Marks)

5a.b.

c.

6a.b.

c.

Calculate the maximum bending stress induced in a cast iron pipe of external diameter40 mm, internal diameter 20 mm and of length 4 metre when the pipe is simply supported at

its ends and carries a point load of80 N at its centre. (06 Marks)

A beam is simply supported and carries a uniformly distributed load of 40 kN/m over the

entire span. The section ofthe beam is rectangular- having depth as 500 mm. Ifthe maximumstress in the material of the beam is 120 N/mm2 and moment of inertia of the section is

7 x 108 mma, find the span of the beam. (08 Marks)

Define: i) Deflection, ii) Elastic curve. (04 Marks)

Derive an expression for the slope and deflection of a simply supported beam carrying a

point load at the centre. (10 Marks)

A beam 3m long, simply supported at its ends, is canying a point load "W" at the centre. Ifthe slope at the €nds ofthe beam should not exceed 1o, find the deflection at the centre ofthe

7a.b. For: a circular shaft subjected to torsion, derive the relationship between the torque

transmitted and shear stress induced in the shaft. (06 Marks)

A hollow circular shaft is to transmit 300 kW power at 80 rpm. If the shear stress is not toexceed 60 N/mm2 and the intemal diameter is 0.6 of the external diameter, find the external

and internal diameter assuming that the maximum torque is 1.4 times the mean. (10 Marks)

a.

b.

Differentiate between long and short columns.Using Euler's theory, derive an equation for the crippling load of a long column pinned at

(04 Marks)

both ends. (06 Marks)

c. A simply supported beam of length 4 metre is subjected to a uniformly distributed load of30 kN/mt over the whole span and deflects 15 mm at the centre. Determine the cripplingload when this beam is used as a column with both the ends hinged.

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(10 Marks)

USN 10cv/xv34

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

fTime: 3 hrs. Max. Ma.ks:16b'Note: l. .4asw er FI VE ful I q uesti on s, sel ectin g:-

E I 2. Assume missing data suitably. ii.._9

-E PART - Arn < F r : ,.fii r'- rAl( I - AI a. Explaini[e.classification of surr"y.- (0E Marks)b. Explain theifrsic principles of surveying. . r,.il (06 Marks)

^ II,L^. :- D- ':,r- :! o r , .) ) "E9 c. What is Ran'gi$? Explain indirect method of ranging ^ '.

' (06 Marks)8=E 3 2 a. List the different tapo corrections. Explain and give expressions for tape corrections.-sXe- , (10 Marks)H? b. A 30 m chain was tesied;before measurement of $!..1day's work and fbund to be correct.

E A. A^fter measuring 3000 m. the chain, was found to be 5 cm loo long. At the end ofday's work

f g after measuring. _5400

rn the chain was four{ lo be I 0 cm too long. What was the truei.C distance chained? (06 Marks)

i i c. A rectangular plot was measured with a 20 m chain which was 12 cm too long. The areag E obrained was I 17600 m'z. Find the .1q&6da of plot. (04 Marks);EE f' 3 a. With neat sketches. explain obstacles in chainihg. (08 Markslb d J a. wlth neat sketches, explain obrtbtles in chai4iiiil. (08 Marks)

E S b. Witl a near diagram" .*plain tt" *ort ing oiun iprUf ,qu*.. (07 Marks)

E" I c. A chain line ABC crosses a river. B and C being on_the near and distant banks respectively.

; E The respecrive bearings ofc and A taken at o. I p"iri+l rnrn.;r;;;'; right angres to AB€ € from B are 300o and 210". The tength of AB is 24 m. Find rhe width of the river. (os wru.r,g->ii6'!q

i; 4 a. Define the terms true bearing. magnetic bearing, whole ci(le bearing and quadrantal

F F bearurg. (04 Marks)

I ; b. The -lo !!sw lnL-inq bearings were observal with a gompass. Calculate the intrior angles.?, i D. rne rox{wmg Dearmgs were observal wrth a gompass. Calculate the inbrior angles.

.f E lline I es lffi '/=gE

= i \/

(t o Marks)1: c. On an old map" a line was drawn to a masnetic hearinq nf 'l?oo?o, rvhen tha .la.'Ji.,ti^. .,,."3 E (tu rylarks)

aF" c. O^n an old map. a line was drawn to a magnetic bearing of 320"30' when the deo{ination was

E -g 3"30' w. Find the present bearing of the line if rhe declination is 4" I5, E. ioo nrrarrrs;

F; PART- BI ; PAR'I: > LN_P /-A'7-\- ^r,\6 € 5 a. What is meant by local anraction? How is it detected? i::7

'.r :-' (06: > LN_P /-A'7-\- ^r,\6 € 5 a. What is meant by local attraction? How is it detected? f -*7 '.. io (06 Mar6-j .\i b. Explain dependant and independenr coordinates. lii[ ".

, , 'i .j iol ur.L.i.3 c. Following are the observed bearings ofa closed traverse:Z lti^^l Dn I nn I M-----T-----;;-----

folk&ing bearings were observal with a compass. CalculateLiie" AB BC CD DE EA

,Frire bearing 60" 30' 122'0' 460 0' 2050 30' 300" 0,

are the obseryed ofa closedLine PQ QR RS SPF.B 124'30' 680 15', 3100 30' 200'15'B.B 304'30' 2460 0' 1350 I 5' 170 45',

At what station local attraction was suspected. Determine the correct bearings ofthe lines.(10 Marks)

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6a.b.

Define the terms: level surface, bench mark, reduced level, back sight.Explain the temporary adjustments of dumpy level.

10cv/Ev34

(04 Marks)(06 Marks)

..'-l (08 Marks)'-L

'" wo rYrar lrs,,

Efpfih;he characteristics of contours. * t* '' (07 Marks)

*"ffi10, orientation? Explain any one method of orientatio.o. (05 Marks)

'td -Write short nb(/spgany roun: .*Tt\"Traversing

"- \ {,/

anote on profile leveling and cross sectioning.- +L^ ^L^-^^+^*:-+:^- ^f ^^-+^,,--he characteristics of contours.

a.

b.

c.d.e.

f

'rd zWrite short nl(/spgany rOUR: .,.rt\"Traversing Ll() .-\ {,/Grade con-tour ucr"

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Curvature and,refractlo?4- t+,Classification of maps andtfuir numberingPrecision and accuracy tll* d]Profile leveling. "oa{:.

#- (20Marks)

L'/d-\uiot{'1p *,*'x *

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2 of2

USN r0cv35

Max. Marks:100

Third Semester B.E. Degree Examination, June/July 2013Fluid Mechanics

Time: 3 hrs.

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Note: 1. Answer FIVE full questions, selectingat leost TWO questions from each part.

2. Assume missing data if any.

PART-AWrite units of i)Surface tension; ii) Dynamic viscosity; iii) Power; iv.) Momentum andv) Pressure. (05 Marks)Illustrate capillary rise and drop with appropriate sketches clearly indicating the fluidsinvolved in each case. (05 Marks)A thin plate is placed between two flat surfaces 'h' cm apart such that the viscosity of theliquids on the top and bottom ofthe plate are pl and p2 respectively. Determine the positionof the thin plate such that'the viscous resistanse to uniform motion of the thin plate isminimum. Assume 'h' to be very small. (10 Marks)

Derive equation for hydrostatic law of.pressure variation. (08 Marks)If mercury barometer reads 700mm and Bourdon gauge at a point in a flow system reads500 kN/m2, what is the absolute pressure al the poini? (04 Marks)Fig.Q.2(c) shows a glass funnel fitted to a U tube-manometer. The manometer reading is0.25m when the tunnel is empty what is the manometer reading when the tLrnnel iscompletely fitted with water? Take funnel height = 2lir. (08 Marks)

Fig.e.2rcr

Prove that for a plate submerged in horizontal position in water the centre of pressure issame as centroid ofthe plate. (10 Marks)Fig.Q.3(b) shows a rectangular flash board AB which is 4.5m high and is pivoted at C. Whatmust be the maximum height ofc above B so that the flash board will be on the verge oftipping when water surface is at A? Also determine if the pivot of the flash board is at aheight h : 1.5m, the reactions at B and C when the water surface is 4m above B. (10 Marks)

1of3

4

5

10cv35

' . ,,,, l1g.Q.J(b)

a. In a ffoy..!!e velocity vector is given by V = 3x i +4y j-72k. Determine the equation ofthe streainliiie passing though a point M(1, 4, 5). ^ (10 Marks)

b. The velocity p&ltial Q for a two dimensional flow is givert'ttiii'z- y) + 3xy. Calcuiate:

i) the stream fuidtlo! V *a ii) the flow rate passing between the stream lines through ( 1 ,

(10 Marks)l)and(1.2).

..., PART_Ba. Fig.Q.5(a) shows nozzle at itielgnd of a pipe 1in'6 discharging oil fiom a tank to atmosphere.

Estimate the discharge from thqiiozzle when'&e head 'H' in the tank is 4m. The loss in thepipe can be taken as 20 y2l2g, where 1V' is thrj velocity in the pipe. The loss of energy in therozzle canbe assumed to be zero. Alsd, determine the pressure at the base ofthe nozzle.

(10 Marks)1

25 mm Dia

f, .-

I'

Fig.Q.s(a)b. 250 LPS of,$'ater is flowing in a pipe having a diameter of 300mm. If the pipe is bent by

135". Fiff{'the magnitude and direction ofthe resultant force on the bend. The pressure ofthe wriiiili flowing is 400 kN/m2. Take specific weight of water as 9.81 kN/m3. Refer

" .... (10 Marks)FigQ.s(b). v1

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Fig.Q.5(b)

Fie.Q.3(b)

o='l.s)l I ,oo ,, o" p,p".

i._1.

2 of3

6a.

10cv3s

The following data were collected for a stream at a gauging station. compute the discharge

s. A pitot tube is mounted on an airplane to indicate the speed of the plane relative to theprevailing wind. What differential pressure intensity in kPa will the instrument register whenthe plane is traveling at a speed of 200km/hr in a wind of 60 km/hr blowing against thedirection of the plane? eui. : 1.2 kg/m3. (06 Marks)

7 a. A pipe line of 600mm diametet is I .5 km long. To increase the discharge another line of thesame diameter is introduced parallel to the first in the second half ofthe length (Fig.e.7(a).If the friction factor is 0.04 and the head at the inlet is 0.3m, calculate ihe lncrease in

tlllougtr the stream. Rating equation of current meter V : 0.3N + 0.05, N = revolutions persecond. Marks)V : velocitv in m/s. l0

Distance from oneend of water surface (m)

Water depth 'd' (m) Curent meter immersion at0.6 d 0.2.d 0.8 d

Rev. S Rev. S Rev. S3 1.4 12 506 3.3 38 52 23 559 5.0 40 58 30 5412 9.0 48 60 34 5815 5.4 34 52 30 5018 3.8 35 52 30 5421 1.8 l8 50

b. Compare manual and self recording depth gauges. (04 Marks)

discharge. (10 MarLs)

b.r4-'an'Iel-v'uu

The velocity of water in a 60cm diameter and 15mm thick cast irqn pipe (E : 1.04 x 10rr pa)is changed from 3 m/s to zero in 1.25 s by closure ofa valve i) ifthe pipe length is g0bmwhat will be the water hammer pressure at the valve? what will be the coirespondirgpressure rise ifthe closure takes place in; ii) 2 s and iii) 0.gs respectively? Bulk module of

8 a. It is required to establish the thoat diameter of a venturimeter in an installation of 100mmdiameter pipe conveying water. The maximum range available in mercury-water differentialmanometer gauge is 50cm of mercury deflection. Find the maximum throat diameter whichwill indicate the fill gauge deflection when the flow rate is 20 LPs assuming coefficient of

elasticity of water is 2.11 x 10e N/m2. (10 Marks)

venturimeter as 0.984. (10 Marks)b. A discharge of 0.06 ml/s was measured over a right angled notch. while measuring the head

over the notch an error of 1.5mm was made. Determine the eror in discharge ifthe coefficient ofdischarge for the notch is 0.6. '.iu t L-: r}.i :r.

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3 of3

(10 Marks)

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Time: 3 hrs.

10cv36

of mineralogy,

(08 Marks)(06 Marks)

note on contact(06 Marks)

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

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

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Applied Engineering Geology

Note: Answer FIVE full questions, selectingatleasl TWO questions from each part

Max. Marks:100

PART-AI a. Briefly describe the zonal structure of the earth and add a note on its density and

composition. (06 Marks)b. Describe the property ofcleavage and hardness in minerals. (06 Marks)c. With the aid of physical properties, chemistry and uses, distigusih between

i) Quartz and calcite ii) Chalcopyrite and orthoclase. (0E Marks)

2 a. What are Igneous rocks? How are they classified? Give a brief accounttexture and mode of occurrence ofthe fi2llowing igneous rocks

. i) Dunire ii) pegmatire iii) Basah.D. Write short notes on corrent bedding.c. What is metamorphism? Mention the types of metamorphism and add a

metamorph ism.

-a what is wreathering? write a note on mechanical wearhering by thermal effect. (06 Marks)b. what are rivers? Describe the geological action of rivers and add a note on meandering oi

rivers. (oE Marks)c. What is a soil and soil profile? Describe the various methods ofconservarion ofsoil erosion.

What are earthquakes? Descrite tectonic course of earthquakes.Write a note on causes of land slides.

PART-B

c. Write a brief note on costal land forms.

5 a. What are Auits? How are they distinguished from joints and give.a brief account ofnormaland reverse faults?

b. Write ihort notes on recumbent and isoclinal fold. ,, ,r:., . [;:ffi:[]

6 Explain:a. Tunneling a cross lolded rocks.b. Dam tundations

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(o? Marks)

c. Siltingofreservoir. rueurueKs'

ffiil::I3a. What is a water fable? And add a note on parched water table.b. What are aquifers? Write a note on confined aquifer.c. Explain the electrical resistivity method for exploration of ground water.

Write a short notes on following :

a. Application ofremote sensing in civil engineeringb. Impact of mining on environmentc. GPSd. GIS. (20 Marks)