n€fnnq S€il-E fcb(,s) HAY ?tts'.- i.u'" svB:nil -g sfitr

QP Code I 3451

,c) If the tangent of the angle made by the y:*Eression of y on x is 0.6

and o, - 2c*. Find the correlation coefficigElb-etween x and y'

e. 2. a) The means oftwo random suoS{gr\of size 9 and 7 are t96.42 and 198.82u, L, a) lIIv 1lrvalr vr vYvv rs^vvru "*?sr -' "'

respectively. The sum of the squarep$,t'lie deviation &om the means is 26'94 and

Rev Course -O(3 hows) [ Total Marks: 100

,RSl.Ql is ccq,:lsq' *qY?- Sohrc ao,vtkaeqrtoftheremaining from Q2to Q' 6' fN3. Frgrrms m rte dght hand side indioate marks. -:y4. Liscofml*icalubles is allowed. , (}

Q.i. a) A continuous random variable with P.D.F. {x): k x(l-x), *=+s.Find K and detsrnine a uumber b such that P(x< b),.= p(x > b)'_{)- 5

b) If A:[1 3 tl, ,*uthe characteristic roots of A and

"d- s' [r z zJ (,

c) By using Green's theorem Show that the area bound@ffi a simple closed

cury" c is given av *!-ar - ydx +r+-

r L 5,b .$

d

rg5ptrutrvEl)! . LLLS Dl"Lllr t,r ullv rYusrvPtsge uv Y ^Br

18.73 respectively. Can the sample)'Jconsidered to have been drawn from the

same population? ,^.tb) If the vector field F is irr@*nal, find the oonstants a,b,c where

F = t1.x ;2y * az)t + fp$ 3y - z)I u{(4x * cy + Zz)E Show that F

.un U. .*pr.rrrd "r

th**ldient of a scalar function. Then find the work done in

mor,ing a particle ig@-netd from (1,2,-4)to (1,3,2) along the sfraight iine

i:ining '*re pointry*v 6

c; Using.*. [qprtTucker conditions solve the following N.L.P.P. Maximize

Z=xl *xl,pi'bjected toxl* xz- 4 < 0 ondZxl* x2 -5 S 0, x1,x2 7-0' 8

;S' [Turn over

N\l--\.\

JP-f,on. 9209'{ 5.n\

Gv-S'6\./r.\

tnN..,',.,',,'..,.,,,,.,..,,',',,..",'.,,**-Jd;f

i

z QP Gode :3451

Q3. a)Seven dice are thrown 729 times. How many times do 1'ou expect at least

four dice to show three or five? 6 a;"-.}-

b) Evaluate by using Stokes theorern, Jxydx + xy2dy , c is t&e square Ln ry"- plunt6f

with vertices (1,0),(0,1), (-1,0)and fr, ;) {dc) kr a laboratory experiment two samples gave the foUos'ing resultt' !td'.9Requality of sample variances at 5oA leve1 of signilicance. c

size mean

1 tr0 15-i9o r ,.

2 13 t4 108

*\',fi.

JR*;". e2oe-{5.

o$"Y

[Turn over

1

Sample

Q. 4. a)can ir be concluded that the average life span q$uaan is more than 70

y**r, if a random sample of 100 Indians has an urybg. life span of 71.8 years

6with the Standard cleviation of 7.8 years ^Jt

1-b) use Gauss,s divergence theorem *" .rrrgiqil.reijr.Fas , F=(4xT -zy'I +

\r'

zzk,andSistheregionbounded"r{f =4,2=A,z=3' 6

c) Using Lagrange's method of muli,ipl#rs solve the lriLPP, Optimize Z:4x1*Bxz - x? - xl subjected to *5fE'= 4,x1,xs 7 0 8

Q.s. a) show that the *,fqjr. -!r +]

,. ciiagr:nalizable. Find the

ttransrorming marrix Sg airj"3* ;fl". = 6

6) Catculate Ae l{4aTd"arson's coefficient of correlation for the following data.

x 28 4s" 40 38 35 33 40 7) 36 JJ

23\ Tq 33 34 30 26 28 31 36 35

t\

QP Gode : 345{

c) The frll:'"'..:.: -:-: glves the number of accidents in a city during a week. Findwhe'.he: -. :::.:-::s are uniformly distributed over a weelg using Tztest. 8

d-(gd

t a6'

.,r-,r, l2 1l

: .:: nontiCl' salary in a big organization is normally distrihlXd with:i;.:, F.s. -1000, and standard deviation ofRs. 250.Whatdrbrdta be the:--:-r'r:r salary of a worker in the organization so thpt tldprobability that.-.: ::-l-ss ic top 5Yo workers. ".Ot-

: -,'s:--i' Eeen's Theorem in the plane for where F$+

y2)dx + x2dy

: is -;ne closed curye of the region UounAeQ$d = x and y: x2

r?x{.

6

'{

*f^sJr

PN-{P-.;Eon.

9209-{5.n\

Gt/\-n'

..QoNs

,t^,. !Ion Tues Wed Thurs Fri Sat Totali5 9 1t L2 10 14 84i

-S

I

i 5 E fcrw) svlry-fcua{9u9:9urR{t

(3 Hours)

N.B. (l) aocstim m- I is coryulsory-(2) Aocryt-ytfFc fromtheremaining questions'

fl) es*qmFfu node should be clearly stated

[4i EEEI. b fre riglt indicate full marks'

MAY 2OI5

z,lfl{QP Code :3452

[Total Marks : 80

Stn

RL(m)

HI(m)

co-ordinadlistatid)"

StaffStn

Beaing VerticalAngles

StaffReading

Lat{ }DepR

S

1020.60

t02t.2L1.50

1.53

80Q- 1800

tr zsooxY

15014'

34001 8

+809'

+203'

1.10,1,85,2.60

r.32, 1.91,2.50

10

10

10

10

3. (a) Explain in brieltS$rocedure for setting out a simple circular curve by the

method of o.f$elfrom chord produced.

O) In making($rkey for a new road, the inJersection point oftwo straights

was fountXo be inaccessible. Fourpoints P, Q, R, S were therefore se-

lectelfro on each straight, and the distance between Q and R was found to

Ue$)iZOm. If the angle PQR w as 169047'40" and angle QRS 148022'20";

.F;, up a table of deflection angles and chainages for setting out a 200m

jSAirr curve by pegs driven at every 20m chain . Chainage of Q:( I 40 +90)

=\*t chains.

,A t

[TURN ovER

.s,t\-

ea JP-Gon. : 9984-15.Ns

: -{:rmryt ry rmo questionsi; F*lplain in detail the field procedure for setting out the curve by Rankine's

:.; --.--; :i deflection angles' \: : :,.:.:.;r n derail the procedure along with neat sketch the tachometric-ra-dial

:::-,::';:ng rroject aiong with method employed for plotting the co,ntburs.

- :,::..1r r'i) Principle of EDM (ii) Principle of tache'r'metry

'

. l-i1e:eniiaiebenveen1 Stadiasystemandtangentialsystemoftachecrietry: r ) Fixed hair method and moveable hair q,ethod of stadia

tacheometory .--:--: - : :;:errnine the distance between two points X.1l-$'Y and their elevations'

: :1.:r,,.ing observations were recorded upon vediLally held staves from nvo

:ravers stations R and S. The tacheometer waifitted with an anallatic lens

.nd instrument constantwas 100. Comp,EIqtlie distance XY gradient from

X to Y and bearing of XY d --. *'

,^*)

a

I

I

I

rI

10

10

4. (u)

(b)

5. (a)'

QP Gode :3452

Define setting out of works and explain in briefthe detailed procedure for

setting out of bridge

What is Total station. Mentionthe advantages oftotal station over level and

theodolite along with the uses of total station. Mention the features of Total

station

What is transition curve? What are the requirements of an ideal transition

cul've. Enlistthe objectives ofprovidingtansition curve andmentionthe {-differentypes oftransion curves. aYdifferentypes oftransion curves. a)A3%vising gradient me els a2Yodown gradiants the vartical curve 200{toilgis to be used. the pegs are to be field at20m interval . Calculate the,elQyltion

of the curve points by tangent correction methsd and calculate thp.ffiread-ings required given that the height of collimation is 350m, RL q}hd apex is

350.0m and its chainges is 1000.0 m "^" r\y

What is cPS? What are te advantages of space b*.o r.dfi; system and

enlist the various application of GPS in surveging

Explain inbrief:-(i) Auto level(ii) objectives and advantages of GIft

.VS"

10

10

10

(b)

6. (a)

(b)

tc:ea1,\ry.c*'

:i?.-s

\L,Su\,.4\.V(\

dzV\l

q*\,os-i\\

rF'*r

^Y4t'11\4^v,t

'O\J

1*x\

. + JP-Con. :9984'15.\,i'"

2

5€fctvtA seu$;cons) n,q1 ?-al)

Su{), 9/)''f- ql:/{QP Code: 3455

(3 l{ours) ffotal Marks: 80

N.B. (1) Question No.l is compulsory.

(2) Attempt any three questions out of remaining fir'e questions.

(3) Assume suitable data wherever required and state it clearly'.

I. Attempt any four of the following:

(a) In three hinged parabolic arch subjected to IIDL or er entire span, show' that 05

bending moment &rudial shear at any section is zero.

(b) Find the strain energy stored due to bending in cantilever beam subjected to Upt-i 0S

of intensity w kN/m over entire span. 't .. "

(c) Define influence line diagrarn and give its application in civil engrneeiid Draw 05

ILD for Reaction, S.F and B.M for Simply supported beam. , ; _*-,,.'(d) A symmetrical cable of span 50 m and centrdl dip of 5 m subjaeted to ldl of 05

intensity 20kN/m. Find the maximum and minirnum tension ifi-ih. cable.

(e) Using Macaulay's method determine maximum deflectioiuand slope at suoports

for the beam loaded as shorryn in fig.

/^ 29 KN/rl okN

L.strl

,(.4Y,

..tC,.-\An unsymmetrieal three hinged 4fubohc arch is 1oaded as

Determine: Support reactiorq ,jffii and RSF at 5 m from left

find maxinrum bending *orrreHo left part and right part.\J

2+ kn/fitr- @

- (b$S" and explain Maxwell's Reciprocal theorem and Betti's theorem.

;ib State Moment Area I't and IInd theorem.

amII*j

2. (a) shown io fig.

: support. Also

13

@

04

03

ITURN OVER

. A,'

{ld- JP-Gon. {o963-'t5.\\t$

0

@

t

@

2 8P Gode : 3456

(a) Draw neat sketch of cable and suspension bridge. Show all the components of

suspension bridge and explain r,vhat type of rnternal forces developed in each

component. Also explaih different types of cable supports-

(b) Draw AFD, SFD and BMD for the frame loaded as shown in frg.

OKN

rskN\r.rt

.I.H.= aobrnaJ

@tot,,-[ *dI -,Fsrn "()-.;I

@ 5m

TI

I

ZrnI

06(b)

4. (a)

locate principai axes.

+yl\r( ILI

"*Sn 6o,\\

l

rF* I#'l-b"\ |,Yt

x\-"\{! !

{;V\-J

-i i JP-Gon' f 0963'{ 5.

",f**I-

[ruRN OVER

*-*+6rr)

I-t6 ann

t.

A simply supported girder of span 50 m is traversqffi a series of of wheel loads

160 kN, 200 kNI, 180 lil{ and 140 }}{ spacq#at distances 2 m, 1.5 m arid\]-

1 m respectively. The lodd system move_ryp.dt'n left to right with 140 kl.l load

leading. Find the location and magnitu@.4?absolute maximum bending moment

J

F-,

3 QP Gode:3456(c) Draw I.L.D for members 4, 5 and 6 of the truss as shown in fig. Assume that

load moves along the bottom chord.

ll

,r\

3,srn/\-/t2\/\

-l* \#rrn97T r"' 7- >tr) l- >rrl -7VfV-

5. (a) Find the maximurn and minimum stresses developed at the base of a cq]i$n 01

loaded as shown in fig. Also draw stress distribution. Take E: Z * f Offi'z

- //rt.tl , . f-fl-^{ l5okN .'r,-l*

]Tll,',,F a9" '\y

D=3oo

'1* | r-J rl -j l* -If06(b)

,... , , =--=-_\ ffi ' 4st-T t= 26rnfi

516l "

o@

(c) Using @Sut. Beam Method find the vertical deflection at D and slope at A 07

for6{S.S. beam loaded as shown in fig. in terms of EI.r,Y

\!Y'TP-'

+- CE^\-*l-lfzl/t\

Art l- zt I :- "P

r'=-,1 . '

-\, I I I I [ruRNovER

o {t IA 6

@-T-

sin* ,tn 9tll@- t-

e,J

t'ilil-l

lt'ci{'- secrroN x-x-\\r

tt

rE'ti .lp-Gon. {0963-15.s

Iii

'"****.*_;i

06

l'-L-

r

QP Gode: 34565. (a) Artempt any OI{E ofthe following

ffi Find the vertical deflection in the frame as shown in fig. by Unit Load

Method or any other Energy Method at point C. (EI: constant)

@ @*a"rx ,e

4r^ I \ L/ IJ-erchnor^{ds-l-l \l/ J" ,S]: i

zr>-- {^Sfn r\l' '{f- 5 ,rl ---:!i+-#5 r' ' *\*/Using Unit Load Method or Castigliano's second theorem, for;Siaid4)a 08

frame as shown in fig Find horizontal displacement of roller supp:O-

Take E =210 x i03 N/mm2,I:2, 108 mma .k,to lqj/CI .{+?'--rr- 1E,ffi"19i -vtl.ry1 ,l"d

t2-n1 .i,ok* I I #r 3 l.'#8m

+(b) Explain Concept of Shear Centre i

Determine shear center for a C as shown in fig.

06

iy***

%m{t\

(c)

f-,

,.. "j out the bending stess at each of the comer points of the cross section..tA1

n\/' \,/

^J1.4-.,.

{l;w JP-Gon. 10963-{5.-t

\--\

E

20rn14

al

$nr 'h:'Gtt'^trt

Question Nc. I is comPulsor,"-

Amempt any three cut of the remairiing five que'stiot'ts

Fig.lre tc the right indicates i'ull rnarks

Assurne any suitable data and clearly state the sarrlc'

wit\ the tbllo*ing area requirements-

Dmuing Hall :20 ,i-il;; s.Jnoo,',',:20 m2, Children's Bed Rooryl

15 m2, 6uest Room: 15 m2, I(itciren anci Dining P'ooli: : 20 nr' 'a'\U

Se*ffi ('oq \,- 9rl4l rfSub l- BDD -U

NOTE:.

v)vi)vii)viii)

)*be

QPIRE\/lsED coultsEl

(4 Hours)

Gode : 3459

fTotalmarks: 80]

,({o;

Q.l h is proposed to construct a RCC Framed structure Br'rngalow (single storey)

Fr\.t,-'.i'-^\.\/i'tr \C*<y'\

{ t-vt\.2rs

Pruvicie veratlciair, passftge Sanitiirv unils etc. tls !]t'l' -i'1'e laws' dYi) Drawthe FloorPlan ,O*ii) Drarv the Front elevation ""

. {r,::ot!.,$Y of builclingQ.l A) Draw the cross seotion passing througil staircase' 1

drawn in Q. no.01 LJB)Drawthesir;elayor-rtplanforbuilclingclravvnin(l.nqf Ql clearlyindicating

vario,-is sen'ices, operr spaces etc. . f:*"\*

e.3 A) Draw the foundatiori plan with dimensir:,',s f$;b b,rilaing drau'u in Q no'

- .. .A,lso clraw tlte section olorle tiloting

14

06

15

0-5

ts.r Suggest the type oi'pitcheti roof tbr afa,:.i,tty o1 sizc fi mx l0 sr' I)rarv tiie

.iun *a section of tU. same shou,ing alf-d&ails with climensiot'ts.

,*t tQ r A) Enlist the 'principles of ptaq,fuS" used in plarrning of a lesidential

brri1ding.Explainwithsketc]res+:.,}t*oindetail.B) Expiain the zoning regutatrp,frJC Btiilclingt bye lalvs in:detail.

t:J,l r A) Cornpale the Loaci beql:l.r{vrith framed ItCC strttcture.

gj Ora* i5e pIag, elegrhn ancl section of the half paneled and half glazed

1:',r: i:::l:,i:: lr"id::l I,3ti 1l.'x'C i hrr",l:rin carnelaE:t. brriit uu ;Lr'clr :lllil FSi'

"'i*Q 6

Y'[:.il?ii,:.Prtr:*:lli::::''-],\:\,1::",",. (circL ration) diagram rri)

Functionaf*fia,rning o1' a residenrial building. ir'). SLrn shading der iccs.

v). Seffilk distance' rr!'"r

t' '

u{"\\+*\/\.n"\

fi],*i,' :

^. "J

10

1L)

10

10

07

0'7

[.ro

20

Od- JP-Gon. 11763-15.

Ns

n\. _/

'2_d -r-S Enr\

*ffi,rii"r'rftig,n is-O.lg (tq* tlre graph), Refer the various tables givin at the'end.

t,

.(QsS

(0s'M)

, (os [e.(05 M)

Page; I of 3

pv\J\i (

:.3.Writ.qingtebonthefo1loryig}....,.'''.':,.'' .....r' ' /. I- :': ' ixedCorr"rg$U.. . ' '., b)iC,ringofConcrete,

"' "

.

',' -,ia)'ReadyMi

J'' al#*'*"*a*dieiorljsrlr

. -\iH-l ..':: -:..:...'.:4: a) $q+Irgqhg gFes3fac^l in cggret? Wlat'are the factors affecting,bteeding? If the rate of: lt..i.. .trr_

aee gv.apomtio& what -h?ppens.to:.the

c'oncrete? I , . , (05 M). -ble{iqS)egsthanthatof.srirfacbevapomtiorywhathappensto:.thec'on.r.# '.,, ' ",' ' --(0S.1\,[

ffiscussthefactorsaffectingcreep&shrinkageofconcrete.r n\' .B{For major.concreting works, you would recommend weigh batching or volume batching? Discuss

-,W . --. - tI.-' , .. : .. {05 M)

,.''(

9, , :- JP-Gon. {2396-{5.

:__--------,f

*l

QP Gode .3462; 'i-het is the effect of maximum size of aggregate on concrete sftength?

5. ar Choose & write the correct option:

i) The most commonly used admixture which prolongs the setting & hardening time is

a) Glpsum b) Calcium chloride c) Sodium silicate d) A1l of the above

f mm nominal ma:r. size of aggregates)

Exnosu$' Reinforced ConcreteMin. cement content (kglm' Max. free water-cement ratio Min. concrete grade

MildP' 300 0.ss M20

I4ohlate 300 0.50 M25

Eeiere 324 0.45 M30

'Very Severe 344 0.4s M35

Exteme 360 0.40 M40

Maximum cement content: restricted to 450

2(0s Iv$

(4Xt=04M)

{

toii) If 3S0 ml (or grams) of water is required to have a cement paste of 1880 grams

"f 2WSconsistency, the percentage of water is: ,(Y

a) 26.67% b)20.2tYo a)25.33% d)1qfli,rr*.

iii) Wp and Wf are the weights of a cylinder containhg partially compacted *9 @ compacted

concrete. If the compaction factor (WpAMfl is 0.95, the workability of concrete fot{

a) Extremely low b) Very low c) Low ,i;?

urn*

iv) The target mean strength (MPa) for M25 grade'&ncrete with rislqYactor : 1.65 & standard

deviation: 4, is: _ O"

a) 18.4 b) 45.25 c) 31.6 ' lJ d) none ofthese

b) Write a detailed note on High Perforrnance Concret.$d (0s M)

c) Write a detailed note on Light Weight Concrete. 5)- (08 1\[)

.\)

6. Write notes onthe folowing. ,Oq*r\ (20 M)

a) Retarders in concrete -$ b) Self Compacting Concrete

c) creep of concrete

*d#Y

d) shrinkage of concrete

.F-n"t1$poncrete Mix Design from Indian Standard Code [Q. 1 (a)]

Table 1: frrfinimurr(Qdent content, maximum water-cement ratio & minimum concrete grade (20

JP-Gon. { 2395-15. Page: 2 of 3

/"\r\a\.J

z':\./.s\I

r

::;lled Ok*,{4t.v

'lteble 3: Comections to the values given in Table2,to be applied for con!ffis other than those given\.--r"rr- -:: :enarks colum:r of Table 2.

S Etvl g

S4B r-

Cc,gai)

CT3

&.\4Y 2a l_r

rlslrrQP Gode :€462

.({3

-olF

\J

*dCf rable 4:,

Table 2: Approximate sand & water content pet m3 of concrete+

r--".i-rJ - { - E \ominal size ofaggregate (mm)

Water content inm3 of concrete

fts)

Sand as o/o ofaggregate by

absolute volume

Remarls

10 208 40 Sand zone II, I

water-cemenq=1}ratio:0.6#-:'

l-.,\uompac{0sFacto.n4*ry;g

:1-l 186 35

-U t63 . 30

10 200 28

20 i80 25

- ::-: '. a-ues appl1' to the conditions given in the remarks column. For other

, :: :: :::lled as per Table 3.

Change in conditions other than those

siven in Table 2Correction foF"

,water contmt/

Correction for sand contentin total aggregates (o/o)

Sand confonning to zoneI,III or fV*-/

h.*t'H-Y

+1.5 for zone I,

- 1'5 for zone III,* 3.0 for ione tV

lncrease or decrease in compacting factorvalue bv 0.1 (for workabilitY) q\*=* 0

Each 0.05 increase or decrease in water-cement ratio

;-0 +1%

For rounded aggregates (gravel) ,.\ / - 15 ks/m' -7%

Table 4: Approximate Air Content

Entrapped air

Ja'nY

\J/{\/\/\\n\q7-I-.^Q JP-Gon. { 2396'{ 5.

,\1\YY

Page: 3 of 3

rrL

U

Mry[m r,ffirrtaggregate

-F 10 3%

\i 20 7%

40 t%

'S-f C.,v,t) S6r-a- [csEsJ *"u,i FH.

(3 Hours)

11) QuestionNo.l is comPulsory

(2) Solve my three questions of the remaining questions .

(3) Assume snitable data if required.

(a) Drawneatfigures.

,] . Answer any Four

Total Marks :80

{

20

aa,l Deive Dupit's Equation '': -!

r \ dr - -{--1 d-- ar- --^L^- ^.C-^--l^ f^--^,,:-..* &^-----t--A-V--c

10

r0

g.II-

b) Show that the diameter of nozzle for ma:rimum transmis@vof power is

givenbyd:{FJ'o ^fL:kng& ofthe pipe andy' friction Co-efficien$b} Diameter of the pipe.

c) Write a note on water hammer md contol q$il1e.

O Derive an equation for stagnation temper4SC and stagnation Density

e) Define mach mrmber and state its siryifieance in compressible fluid flow.

0 Explain Hydro dynamically Smo@.aid Rough Boundaries.

Q 2) a) The difference of watbr levelraN'do reservoirs is 8 m .They are connected by

40 m long pipe. For tht EgPt(m

length the diameter of pipe is 120 mm and

for the rernaining len$i fre diameter is 200 mrn , the change in diarneter

being sudden. FinA@iarge into loyer reservoir .Take.if: 0.008.Draw HGL

and TEL also, t'b) tte '*ater,$ul in the t$o rsserrroirs A and B are 104.5 m and 100 m

t"tp."tit{Pabove the datum. A pipe joins each to a common point D,where

presq$is 98.1 kN/u.*'gauge and height is 83.5 m above datum .Another pipe

$$.tr D to another tank C. What will be the height of water level in C...)Ssuming the same value of 'f ' for a1l pipes,

-rf [ruRN ovER]sA\A\

^ry'

"O JP-Gon. 12676-15.

\\iat

20 t_s

-c,a*t t tzlelt5

QP Code 3465

n

QP Gode : 3465

Take friction co-efficient:0.0075.The diameter of the pipes ADBD and CD

. are 300 mm ,450 mm,600 mm respectively and their lengths we 240 m,270 m

and 300 m respectively.

a) Power is to be transmitted hydraulically to an accumulator at a dlstance of 8

km by means of nurnber of 100 mm pipes laid horizontalty for which the co-

effrcient of &iction may be taken as 0.03.The presswe at the accumulatot is

maintained constant at 6524kT{l#.Determine the minimr:m number of pipes

L

10Q3)

required to ensure an efficiency of at leasl92 oZ ,when the power delivered.fY\-

162 kW. Also determine the maximum power that can be transmitt.Ttscase. cf

b) Calculate the discharge in each pipe of the netrvork shown y&*low by 10

Hardy Cross Method.Take n:2.0 CY

C,

L

5

10

QP Gode : 3465

Calculate the pressure, temperature and density of air at stagnation point on '

the nose of the plane Take k:1"4

{l --' a) Derive Hagen Poiseuille law for flow of viscous fluid in circular pipes. 10

b) Two parallel plates kept 100 mm apart have laminar flow of oil between them 10

with a maximum velocity of 1.5 m/s. Calculate:

(|The discharge per meter width .(ii) The shear stress at plates.(iii) The -$. "-N

Q6) a)

difference in pressure between two points 20 m apart.(l$ ffre tetoc(9'-gradient at the plates,and (v) The velocity at 20 mm from the pfate. a@viscosity of oil to be24.5 poise. d ,

Explain Prandfl's mixing length theory. Der:rve expression Qg, velccit-v 10

distribution for turbulent flow in smooth piflps. VIn a pipe of diameter 300 mm the cente line velocity ?"Sh'; velocity at a 10

point 100 mm from the centre ,as measured by pitot fi{d#" 2.4 mtsand 2.0

3

Ib)

m/s respectively. Assuning the flow in the pipe to U$JsrU"ient ,find:

(i) Discharge through the pipe. .Y(ii) Co-efficient of Friction. *

"$sss/\\

c+'Sd-JP€on. izBTG-ls.

=t9

d

'J"

fl

9f - errti]-l:"-'*\

l-,:r', i",1'i,tt_-I /

D-J irt:-") f ---\

..,r, r'\ :

,,1t \*/ ./

(3 F[our*)

4755

ITotal &farlis I 80

N.B,: (l) Questiorr No. I is compulsory.

_lll-a \/ n - 1s'i v- eL/N\LCH/

/ \1.\

q.r. Code:

i{Joslrr

(2) Attempt any tlrree questions oui ol rcmaining five queslions.

I (a) lind the Lmlace trarsform cf 1e{ cosh2t

(b) Find the lixed points of w * iz*-"I . Aiso express it in the normalz-l

Il* =;; + ]' rvhere i is a conttanl and o is the fixed pr:int. ir this

transformation parabolic?

lrrI(c) Evaluate ) (x1-it )dz along the parh i) ,v*r, ii) y*f

0

(d) Prove that :1,("x)=1, l.(x):x, fr(x): ry are c*hogonal over (-1,i)

Fiad inverse Laplace rransion.:r -l +t .s +4

Find the image of the i.riangular :*gion whose yertices are i, l+i, l-j underlhe transformation w : z+4-2i. i_rraw the sketch.

Obiain fourier expansion cl ;(x) * lcosxi in {-n, :r).

Obtain complex lbrm oi lourier series for f(x)-cosh 2r + 5inlg;; in (-2,2).

Using Carnk-Nirhclscn simplilieci formuia solve $* * = O c.ir.nc)i- ct

u{O,t) *i.u(4. tl * 0. u(x, oi - } 0 s-rrl fird uij fnr i=0, I.2,1.4 and j:0, 1,2J-

Solve the equatir:n 1, +. .l i:dt : l-e",

lorm J

1

3.

(a)

(b)

(c)

(a)

(b)

6

6

8

6

6

(c)

JF-Con. &S3S-'{5. lTt;IiI'0\r&R

?.1

/

5

Q.P. C*de : 475l$

3 J_rJ5ur\J

(b) Find half-:ange cosine series fcr f(r):r{, 0<x<1 5

,

idU6A l^\ F,,-l,,^r- | _.--t (., tr I (1rsi:rrv 1 -i 5+3sin0

(c; Obrain two distinct Laurenr's series lor ftzl = # in powers of 8L -"1L ^)

(z-4) indioating the regions of c<xvergelce.

t2". - du5. (a) Solve a* -2A = 0 by Bender - Schmidt method, given r,(0, r) = 0, 6

u(a, t) * 0, r.i(x,0)=. x(4-x). rlssume h:1 and find tlie value; olu upto I = 5

(b) Find the Laplace !.ans i,rrm of e" Jusin3u,lu 60

r z*3(c) rvaluate J;.rr-, dztl'here Cisthe cilcl,:

u'rt b,:;I by using convolution lheorem.

(b) Find an a$algic lunction i1z) = u*iv where u+v*f (cosy + 5;1y;

(c) Solve the equation "l = o $1 for rhe conducrion of heat along a rod ofii r,i"x-

length / subject to following condirions

(i) u is not inffnitl' for t-)co

,u(ii) ^ = 0 lor x:0 and x=1 lor rnr, lime r' cii

fiii) u=lr-x2 for t=0 berq,een x - 0 and x--l

i) lzi - 1, ii) lz+1-il=2 I

6. (a)

JP"Gon. &$3S-'l$.

6

6