This document appears to be an examination paper for a third semester engineering degree. It contains multiple choice and numerical questions on topics related to engineering mathematics, manufacturing processes, basic thermodynamics, and materials science. Some key questions assess understanding of metal casting processes, welding techniques, thermodynamic equilibrium, intensive/extensive properties, and the Joule paddle wheel experiment.

1. 'IAT31
Third Semesaer B.E. Degree Eraminrtion, D
Engineering Mathematlcs
ExPand r(x)=Jr-cNx
1rl
Note. A svo a ! t:l vE fiU qu$tiots, set ctiae
al.al TwO tttestiohs lroh eacl wr,
-l
=.
;a
aa
4,2
,.
lc
!
r I 1.5 5.7
f_iM rhe lulf-Enee snE sries .l lh) : e' in (0. I).
Iu a machine rhe JinlaEin.ni v.li el
0
v 11
tind tlre constant remand the nrst nvo hamonics in Fourier se.ies expaolion oll.
Find fourier aaDslorm ol c and hen
rnrd Fou,ier sine rtustbmrol r(r)=
c. Solvcthe i'nej:nlcquahon
Find yarious po$ible soluiion of one-diinensional bear equaho.
A ieaargular platc {ith insulnied surlice ,s locn ride and so
thar n mry be coNide.ed infiDire in lereth i,ithout inttuduc,ng
rempcrantre ofdre nroft cdpc y= 0 n siven bv
1't,
= l0 (10 r).5<x<10
a.d
'he
Bo long.dges = 0, x= 10 aswcllasrhe orlEr shor cdgc arc kepl al0"C F drhe
tenrncrrure u(x. y) (10M,rk,
i l r!u Lent clom)=Jer brrenJL:
9 t2
v lo 15 | l
long conpared to its $idth
an rpprecilble eror llthc
Use gnphical melhod lo sohe
Nlnrimi2. z= 20xL - lox:
2x, + 2,:20:
3r :r. > l.1i

2. IOMAT3I
c. Sohc the lbllovin.c LPP by dsina sitoplcx nethod:
Mlritoize Z= 3xr + 2x: -5x.
Subjcct to r +2ar+xr <4r0
27x+6y z=lJ5i 6x-15y=2,=72; x+)+512=1ll) C ryout 3 itcrarlo.s by taking
the iniiial app.oxinration to ,re solurion as (2, l- 2). Considcr aou decimal places at each
b I sinp ric v or-tupt.o' n.'lod. find rl-c rcal _oor o_'tp "qlb,
ro = n.cBrlour lbr krar 06l in radn6)
c Fiird the largcst cigcn laluc and the conespondine eigen vectororthe matrir
l1 t r
A r 1 I rr n"*. ."r"a ,,.. ,,1..
". ".'"', "'- p r..r ' r.,,.,.
l, , .l l.l
(07rr,rL)
fomula and 1i4.99) by uslng NcMo.t
(071u!rks)
Use lne Gau* seidal nerativc mcthod to solvc the svsren orlinear edutio.
2 l
(') .8 212
b. Flnd tu interpolating poLlmoniial (x) b, nsing Ncwron s dilided differcnc. ,neijohrn,n
fornuh lion the data: (06Nt&rks)
x0 2 5
r]r ll 59
Fnrd (01) by usins Ne$ont
backward iniem.lail.n fornn'li
cqual sub inte^ak. comlare rhe resultu$ng Ieoorc s ruG. rrKrn!
*,*$- = 0 in t[e bllowins squarc nesh. Can! out t"! iretaho.s.
I
v give. bel.lv rvnh u = 0 o. rho
(06lY'rkr)
-;-+-,'2 ofl

3. lagei,/*7 ir '."
(6t it )EI't !' '/"r//
*r" , 4 = o4 o*t, r':.|,/ru,2.,
l0MAmr
.t, ,rJ
8 a. tiod hc I ratuiomol i) - I - - ir) l_cos-.
I /./ r.l
b, Siate md prcve innial value lheoEm in Z-tmstums.
c. Solve ihc difleEnc€ equadon
u..r -2u,.' + u, = 2'j q =2,u = l.
= 0,,1r, o =0,
fli',or=0,.r*,0)=*1s *).

4. tuf}
rrsN
a findrh.D'iderivaiiveorc'r co5tbx- c).
b lfy= aco(logr)- bsln(los ) prore rb arni-r - (2n +
c C.tupurc lbe nrrdcrivaries ofsiD x sin 2x sii l.
d. Wrh u(u:lnuknons pr.ethar
MATDIP3OI
Third Semester B.E. Degree Examination,Dec.20l4lJan.2015
Advanced Mathematics - |
2a
2a
=:
".,
,:
a!
a
met Ahstzr tht FIYEfi qEsbns.
- Li - illl-llrLpre$
-ntlretonn
r
-idrt-moor . hroJ p.rroeojrhe!onpc^ )rrbp. -losu. r"ru.
lf (lx 2iy)(2 + i)r = l0(l + r, rhen fDd rhe values of x dnd y.
PDeturtos0r +isin€r)(cos 0r - i sin e, = cos(e, - il, + i sin{or + €r.
l)y,,:0.
b Proc rhar rhe .urves .uh ri = ,
c lxpand log(l - u x)in porves ofx byVaclaurin s theoreto uD ro the tcmB conraininE rr
(07 nxrr,
au iu JL
, ntuve rhx
-+
+ =lr+v+21cx at, az
;a Ar ,,
:a r' ,l7
,,i,, - find r =
11!L-l |=l!11ande,nl =l..(,,I ) i(u,,
J=7t l1 ,,0 i
,odr..on formla ro,
Jsiri'r dx
6:
lJ c ) -,rzdJd
dd f
Definc Gdmnu tundlon Prcvcthatr(n- t) =rl_(r.
wirrr Nuar norarion rrovc rhar, pr.", =ffi#
r-,"
'u
p(.,i)= r,. ,p1.,.1.

5. MATDIP3OI
Solre : s*: xtanydx+ se':ytdxd, =0.
sorve:
q=r+-I+l-IJ:
di x l/
sotue:!I+,-t'=**
.Solve:
(x'?+y)dx+(yr + x)dy = o.
" sor,er* r4+r9 oy=0.
L dx' dr'
b. solre : /^- 6/ + 9y = e'+ 3".
" 5o1". Qlly=,'z+,inl*.d'
,j;
.i-
i,'
-
);

6. -x
l" t
x4;U/I P/I M/M,d/PM35
a
.!
E!
1!
a;
2
Third SemcsterB.E.D.grecE{amirltion, Dcc.2014/Jrn.20r5
lllanufacturing Process . I
IiDe:3 hrs. Max. Marks:100
ot t /7ns$et aq F|VE f l qtuslions, teledntg alleast TWO qaestio-s lrotu ea.h tad
!L8.L-1
B.elly dxplam th. {.pi n,lolred ir meulcasrhgprocess.$ith a neat nory diaEram.
, hat are $e desimble pbpenies olmolldmE sand?
b [plxin briefiv $e diflernt raringdelects durine caslingFroce$
c alh a near skcth. explan rhe $orking principle oljoli & SqGeze
r nh a ncar sketch. erplain $c ncps involed in rhell moulding
b !hat c the neps mroh,ed ir investmenr casinsl Extlrr in bnel
Li$ lne typcs olD!11ems drd explain anvl olthein. sirh.eal skelches.
fr.l" ., 'a!' i'.,o i.Bor.oree.. -J-,r'ol r ' e
!3BL.A
Skethandctla IlC qeldirsproccsand nsapplMton
Erplah ilh a next keich, d,e subDrereed A! w.ldnr! lSAw)proce$
r,rh a neal skelch. erph $cOy a.erylene e6 $eldins proces.
Eflain rhe consrtuction md! ingprinc,pleoI CUPOLA tirmncc. wirh .car skerch.
Skctch hJ explain rheThemir y.lding poccss xid rnenrion dre adlseges. dnadwrages
anti appli.ali.ns 00N&rk,
Wnh d near skelch, explri' rhe Laser Beam $eldine pocc$ ind .ridon ns advotages,
dndJvrnrages and applicarions.
.. Rcsidudl stesses li rYelding
b. Elec1tud. usi'rg iD tretding.
a. Dilltrcnriare Soldcnngand BDzing
b whar are rhe dlftlLenr od De$rudive Te$lig NDT) nrelhods and erpianr
skcthcs ollvrrgneric Panicle Inspedion md RadioEapni. InspetioD nenlod.

7. sslcsrerB'E Dcgtec E{!
i i:l 1o!r/nurr.-r4
i tfrt
.lil
f/"ttf,. oc' :o r'r' t'r'rut <
uaierlals
r rr--I ll
i Lll-L i
,,...
I]SN
il-lr
* ", :;::::;iL"i):,# i::;:i::;;::i "'"
i' ; {*"::l::ii";;J1*:'iL'"*'T'fl:li:::"*;;'xl;'u':Ylil'il"'fillrlli:
: :ll
.]:i:,:1;iillll l1l" ,'"
i ,Jlli.ilii,:'::::,',,,'' "'"'
*, :r;[::'1.'ilt]]r;'i:1lP
: I,iii:.;,'rlr':rr "".' '""':1'r.
., i.'rl,r'iri,,,;:,. ;,:,1,r:::':.'1',i:' -j:,:r"'""'"":;""'

8. t-l
6n
ir! fu, n! +r,$ .Uduurd
rb$ trdF I6id l'i!1!' rt;;
10 {ill/At7 tr_34
i";"il11[Blii'::'J[1Hil ;]Ti;:i]l ;l'"l i'i:
( ,. ' , "r, r-';;:d:'.:"::.l1ll."i;;, ;:::, 1 ;)j, ,** ;'"
'',::,',1; 1;i:;;l')1,i:,,': .1.i'",:,1i:: " ;;:-''"''' l';,.1i
! It1 _ B
Ii.... .f.. ."'',g "'l:";' " ' " t"'
;i'''"':
;.' .." " *,,,, .. ''' ::9u.' 'n"'"n''o'"'i;1i.,,.,
'r..", ' ' ".. '"a'* '
-,ratr*'' l
' !1-:'- 4 =-r*:.;i .l-I -. ' ; rL.J
il.::il:'.'&i::'ilH;;;;,;;;"'p !€iqcdr r'o..ng sh$ md Edi$'rctrd.,.a n,"1. .iflpb ftdY orhetulinsl

9. i.i"o",,l
tsN loMF,/Alrr[:ll
Third Semester B.E. Degrce Exalnination, Dec.201,l/Jan.2015
Basic Thermodynamics
=
:i
:.
,a
ax
12
?
zz
Noiet t. A s*et ah|' Ft rE fuq questit ts, relectine
ai.ast TwO qrcstious froh each part,
2. Use ofthemodtaamic .lata hatubook is p.nfline.l.
PAR'I'A
i. Erpla wbat do you unde$tand by rhemodynainic eqnilibrium. (06ILrk,
b Namc a iew neasuEments or quantities that can be conlenlenlly uscd as th$mometic
proPenies in order to quantiii the renperarure (0.rrrrrk,
c. ,har a,. inrensile md extensile propenl.sl Oils exlnples foi each (04 rrrrk,
d In 1709. Sn ksac Newron proposed a.e* renrperBture scale. On rbn scale. nre temperarurc
*as x hnear nnrction on Cehnr scxle. lhe readine on rh6 at ic. ponn {0'C) d nomal
hunran bodr renfcratuc (17'C) sere 0'N and 12.N. rcspccrively Obtxin drc rclarion
beNccn dENe*1on scaleand rhecelsius scale. (06 tu'rt,
a Sho* that heai and worh are padr turctioD andnorpropdlr.s olihestsren. (06yarrn
b Specilythe nro$iridelyLsed sgn convention lor workard hear ireracrion. (0rlrk.)
c list thediaicrcnceber$eenrorkandhear. {0r 1rr!,
d The pistonofan oilenglne, ofarca() 0ot5m: nolesdorneards 75mm. dmuing .)(]l](]28nl
olliesh a[ non the atmosphdre The pEsur€ in tie cylinder n unifomdtrdns rhe procesr
at 80kl%. while lhe ahrosplreric prcsntre is l0l.l75 kPa. rhe ditle.eo.e berg dud to the
Iov rcsistan.e m the inducnon pipe and tne inlet lalle. E$imxre rhe disnla.cnrcri work
donc byrhe air. (06 Nr,rkt
r. Describc the clasic paddle he.l eapcriment pedbrmed by Joule. whar conclLsio. $as
d[wD based on the experimenral observationsl ooNhrrn
b A turbo .omFresor derivers r l3 mrt at 0.276 MPa, 43oC $hich is heared ar ris presue
to,1l0'C and linally expanded in a rutunre which dclilns i860kw Dunng lhe expansion,
tlrere is r heat mnsfer of0.09 'lj,s ro ire suroDndi..s. Calcula.e ihe turbirc exhNst
tenp..at(c il changcs ln kincric and potenrial eneryy arc nceligible A$une a.r atr
a wlat is rhennalcncrsy rcserloirl trplain source ard sink. (0lMlrkt
b Establah equivalence olKehin Ph* rd C lan s ius $atene.6. (06 nark,
c Two rcrcsibl. hcar cngin.s A ! B de amnged ir series, A reJe.hn! heat d;e.dy to B
LDginc A receiles 200kJ ar a iemFeralLE or.J2l'C lion a hot sou.e, whilc cnginc B is in
conrmuDi.ati.n wnh a cold siDk !t a tcmpemrure of,1.4.C. ilrhe work ourpur ofA n hyice
P =0:S7 [ kgK cf: ] n05 r lrE I
,) The intcmediare rcmpctururc berween A and B
ii) The efficic.cy .feach e.Ene..
iii) Thchcar djecred ro the cold sink.

10. !l
what n mcant by a purc $rbstance? Can we lrear atas apue ibstarce?
Name tlEwidely used ihermodlmmic diaCrams tbr a ture sub$ance.
The lollo$nrg observlrions rvere recorded in anexpeimcnr wirh a combined
Presure in the $eam mi. l5bar.
Nlas ofwaterdrained nom the separator0.55kg.
Mass of$ean condensdd dfter thidde lalve4.2ke,
PEssuE and tempenlue ailer tltrortlins I bar. l20qc.
Evaluate the drynes n0dion ofdre sean in ihe m,in.
Shorvlhatthe intemalcnereyof a. ideal gas isa functionoltemperdurconly. (08ltarkg
A gas ol nas 1.5k9 undergoes a quasisratic expansnrn which follo$s I rchrionship
P: a + bv, whcrc a and b are comtants The innial and iinal presuEs are l000kPa a.d
200kPa Espectilely ard thc coftsponding v.lumes € O.2rnr a.d 1.2tri. The srecln.
irrr "z c'crs' o-reBas'. -'.e1b, rereldr... I l. P d. .g,.ter P s 5.t f ,
"ndr..nn tp
'rl,uld'"',. tr'h.J'r.i "'J... , 1a . lere-rt,irt ..
artained dnring cxpanslon.
a. Explain: i) Dalton's las ofparrialprcsuc:
olcorespordiq:states
b. ErFlai. general,zed coftpresibility chart.
c. A balloon ofspheical shape 6m in diamerer is filled
bar abs and 20'C. At a hrer hme, rhe prcsuG olrhe
(r? rrrirk,
ii) Anagat la{oraddlicohrnrsr iii) L^!
(06Mrrk,
(Gnr!rk,
Nin lydrogen gas at a pBsuE of l
gas is 94% ofits originol pre$ure at
,) whBt m$ ofde ortnral sas mu$ halc cscaped ifric dimens,ons.fdE brlloo. is
ii) FiDd thc amounl olhcat rcmoved to cause thc sane ntur in presure.r con{anr
volume. Takec,lorlynDseDas 10400j/kg K. (r0ttr!rt,

11. ;x*'.);.,
VE'/, nr, a rrn,o,,i2 A/,r r l2/rr.:12
Third Semester B.E.
Material
Degree Examinatiotr, Dec.20r4lJan.201s
Science and Metallurgy
1?
5:
'+4
i)
..1
FlYEfi qu.st tns, s.l.dnu!
qucstions ton eo.h pan.
PART-A
a. Classlly ir detail the d,ricrc.t r]'I]es olcrysral nnperlecrions. Explaln i!ilh a neat
luy"'e ic/d) nJern,l I on-readJ nre d'rtu o0
1
Stcclgear. having carbon conle.t or0 29,o is ro be EBs carburized to achlc!. carh!r co.r.nt
.f0 90!ro ar dre surfacc rnd 0 4"1, at 0 5ftnr depth fton the surrir.e lrthe p.occss is ro b.
ca ed o ar 9?7'C. tind the tinrc rcquicd lor carbunzarion Take diltusion co-eJticienr of
!nbuo rn gtrei eeel= I li . lt, nf sec atren darrl
Denc.dr,p-' "L'.' .."'csol.o eJr Jp-'o. .. ro'r.r ln.rr tre.
O6 Merlo
b. Eiablish ihe Elatiorship bct$een engi.eeri'i{ sr.css and true sres also slDs r[.
iehiiorhip ofcDgnredi.S stmin rDd ruc srrai.. (06 rrirk,
c Consider a rensle sperLoEn of 5nnn dranrerer ard 2smm eluec lcngdr Ilrts dianrern n
reduced to ,1m1 tltrough fla{ic defoflnarion what s ir lengrh rr rlns stasel, Also tlnd
engrleen.a stEss. tre $rcss. cngiirfing srainard rrue stmi. wherc loadapplicd h s00N.
103llarks)
Illustde rhcsraees nl the cuf anlcone liacnrc{lthsunablesketche!. (08}rrrk,
Dcfine (ies relaxalon. Deire thecorcspoDdirg cxpre$ron. (06urrk,
A latigrc tc$ n tuade fith nrean stEss,6- = l2oMPa,nd nre$ aorPLitude 6" = 165!lPa
find ori.6-",6..,,." x.d 6.",
" (n6Nt!rk,
Expla,n thc nrechanhm olsoliditimrnr.
wh.r ita solidsolurlonl Vcnrionr]t trpes.rsdlidn ution AhocDunuatc
rles govcrning rhe ibnmuon ol solid solurion
i - li'6..c. r .loI' 1 n.,Li. o, ro.d'T ir',c r.'I wn!
i) TheNu.ns remFralure
li) Thesoliditicari..tenrpentuE
rii) llcsupohcat
iv) Tac..oling raie,jLEr beaore s.lidili.aiion begins
!l The nhl .liditicrti.n rlme
!n The l..rlr.lid ti.aii.n ii'n.

12. I O{E32A/AI J:I2A/MT32/TI,]2
+iqtaA) _
Fig e.,1(c)
PART B
Dra* the Iron-Carbon eqnilibrium diaemm and label ft Sho* the ,nurianr poinrs on ir.
$iire the reactions occuring ar lhese polnts irdrcar g rlre temperaturc rnd composiriotr ol
edch phase. (r0Nrrrkt
Iwo metak A and B havc then mching poinh al900'C and 800"C rcspectivcly Thc alloy
pan fortos an eutectic at 600"C of conposnion 60% B. They have u.linlired hquid
solubilities The solid solubility ofA in B is l0% x.d ihar olB i11 A is 59; ar eured.
re$peralure and retuaft consran' rill0'C Dra( the phasc diogram rnd label ,ll rhe ficlds.
rindrheamountof liquidandsolidphases inrnslLy.l:10% Brr 650'C. (l0rr,rkt
TTT dlagrab for entecroid seel and explai. rhe diflcEnr
thc lypes of heat trcatnrent proccscs. EplaiD wirh a
a. Eplainthe $rucrue. .omposnion a.d propenies dfstuv cast non
b. Bricfly crplair rh. elecr olalloy,ng elesehrs onpDpenies ol$ccl
. Write a $.n note on the c.pper and ih alloys.
micro strucntres obraired
mrerial. Cire the cla$incaion based on matrlx. geonEry or
.o.itucti.n Aho extldin brcfly rhe produ.rion ol tilanen! winding
sker.h. o0Nrirkt
skerch tne pnltruionprcces and mentlon its applicarions. (,0]turk,
I u12

13. 1 0l F"/A I t32 BU5
Mechanical Measurements and Metrology
!
€i
i2t.
iz
?6
5!
z
or..1. Anlwd dt)'FIvEIttt q atiots, ple.tit,g
aleast TwO qucstions Irom each pan.
PART A
Dell.e merruloey Sra.e and explain the objectiv.s ofnrcrology. (06rlrrkn
Sketchand explairr: l) lnternationalprotoqDe rnerei ri) lmpe.ial staDdard yard. (l0Nrlrrt
Wine the slip gruge c.mb ation to build the follo{lne diftnsians using M 87 sliF Sauge
ser: i)49 3825nn: ii)S7lllsm @rrrrrkt
tr) rr, = 25i
vi) Ftrndancntal dcliarion = 0.
b. wnha.ealsketch, explanrthe differentqles of fitsyirhexrmplcs.
x. List lhe.haracterNtns olcompamtor
b. Erplain wnh a neat skerch. rhc oNtncrio. a.d
. Detehrinethe dimcnsioDs oltheshifrrDd hole aor.
i) i(micron) l= 0.45 Dr'+0.l]()lD.
li) Upper devialion lnr 'd shan- l6Dil
lii) 30nh falls in the diamcrcr stcps oflS-lonnn.
x. wllh a nert sketch, cxpLanrrbcNo nE
b. wite sho( Doles on rhe folloxine:'i)
courlei iY ) S ondnrr natcria ls
rirl0HrJ rnd sle(h rhe tir gien
$ork g.lI rhn! 4,kfuId tr.nd {a1c
a. Erplar with a diaaEr the ne rod ro measuE ninor dlaneter ol i.temal scres rlEad
us g taper parallels a.d 6lle6 ('0nhrk,
b. Dcrile aD exprcssion aorbe$ size wne, (06 rkdO
c whal areranous t}!es oferoN on scre$ theads and explaiD the reasons lbr the same?
(01}I!rb
PARI'B
a. with a neat block diaeram, cxplai. rhc rhre srages ofg..edlized ntasurment system.
withanexanple 0orsrk,
b Explah wiih neal skethcapacitive tansducers ofchanging aier and cnaneine dklancc
(10r$k,
c. Listthe 0dlantasesanddisaduntalesof opn.al comparator.
a. rith a ncrt block dug6h. explair the worki ng princ ip lc olcanDde
b what!rcX-Y plotdsl wiiha block diaernm, cxplaid ns worknrg.
a. Explai. Prony bnke dynamonrter$ih neat sketch
b. wllha nelr sketch, explain i'lo Leod -sauge
principlcolopti.alttro.rtcr. (,0Nllrks)
Cauge racror; n) BondinE nethodsi iii) Themo
(r0M,rr,

14. tisN l0tllo/AlI35R
Third Sem€ster B.E. Degree Ex,t mination! De..2 014/Jan.2015
Fluid Mechanics
'!!
!:
i.
:i
ai
a
Z
ore. r,Ahs et FIVE ful .t uesnons, selectihA
at least IWO quesnons to,n .ach part,
2, Missn,e data can b. asio .d titabl.r.
Dc&re the follo$ing fllid properies:
i) Densiry iil Specific rclutre
iii) vlscosir] r) Specificeravity (06t!hrkt
Deltue sudic. tensio.. Prove rhat the rcldlon bc61€en suriae rension and presu€ inside a
i) Th. d)umic liscosnyoltlr oilinpoNe.
ii) The kinemaric !iscosity ofrhc oil in strokes,frhe specitic graliiy oltbe oil is l] q5.
(03 rLrl.,
a. StateandFrole rhelascah Ia$. (06 vsrkt
b. An inleircdU tube man merer is connecied ro tm Lonzo$alpipes A and B rhroueh vhi.h
rater isflowing Thelerricaldisranccbetq€entheaxesoldresepipesisl0cm.whenaDoil
olspecific gra ny 0 3 r used rs a satrge nuid. Tlr refiical hcight olwarer colums in ihc
tM hrbs of the invertcd Unube na.onrter aE lbund ro be srrne Md eduat i. i5 .rr
Dcrrmine rhc diileren!e orpNur beneen
'he
pipe
c A rectangular surrace is 2nr vide and 3m dccp n Iies in vcdicd phne i. *arer Dste.nN
tu totalpresse ard posnion oaccnreFre$u.e oo the pl.ne surfaue whcn ns uppei edge is
horlzonra!and (i)coincid.svirh wlrersuface. (ii)l.5 n betorvr* O* **.t *,*".
r,.u.,
a Ddn. rlt luhas equdion ofDotio. aLong a $ream ltne Also derire Bernoulti e.luarion
tion Eulcr's eq!.rion of motioa nnd lisr th. Asumptions made for derninE Be;ou[it
droplet orliquid h cxces orouNde presure n siren by p=+.
Thc iJace betrcen dro n t parallel plates is nlEd wirh oil !ach side
The lirknesofrhc oil liln is 12.5 mm. Thcupperrlare wlrich moves
lbrce of!3 I to minain the speed Delemine dre lo11o ing:
a Deire dre contihun],equaioD in Cafiesn. coordnrates.
b, A block olwood olspecific graliryl].7 floats in waier Deteminethe
the block ifits lizc is2ml lm:0 3n
c. Defin. n1e folbwnrg rEnN:
i) M.ra centre and tudra cenric heilhr
n) Buor€ncyardcenneoabuolanc)
A pipc line cauying .il ofspecific gralny0.8?. changes indiameEnoo2(]l]
.'.o.'i.i c ..500 r,' ob.- .d po.tror B r .L . i- rr tisnd
|.'..ue 1' B m oo I' d.d .s8. N!n c,oereh "i. ne
:L.l'r .(. Dc,-',1. .e o..o.i.d.odd1- i, L not

15. W;,
1O}IE/AU36B
i) Discharge orthoo,l.
ii) Iresure difcrcncc between rhe enfuan.e secnon and rhc thro secrion. txk. ihe
coeflicie.t ofmctcr as 0.98 andsFe.ificeryitrofmcrcu!" L 13 6 (t0rrrrln
c. Srare Bnckinghamt r tneorem (0r irirk,
Derive an expresion aordncharge $roughv-notch (06rrarkn
A l0 cn x 15 cm lenturimclff n provrded in a vetic,l pipe line cari.g orl.tspccinc
grlvity 0.9. Ile now belng uCrdrds The differcn.o ir1 eleyation ofrlF th.oat sedioi and
entBnce sectlon ol.he rentuitoeter n 30 cm. the ltiffercnrial U tube oercuv rnaooDreter
shorsa gauSedenedion of25 cnr Cal.ulalethe:
c A tlpc line 300 mnin diameter and 1200 nr long is used to pump nF t0 kg/s oran oil 1rose
dmsityis950k-s/in'and*hosekincmaricvhcosnvx2lslokesThecenrcolarepipelioe
at rhe upper end is 40 m. aborerhan rhar rhe lo*er end Tbedis.hdrge I the upper end h
arnDsphcric. Find lheFrcssurc ar rhe loer end and dm$ rhc hldrauicgFdtent lirc and r
total energy line? (ro]b n
for vncous tlow is equalro
a pipe ofdl.neter r00 nr.l
a DeriteCbezy s equation lorlossofacaddue!o iiiction r.p1pes.
b. Denne lne lollo*ing temN:
i) Hydmulic gmdient hre
ii) Totalencrsyli.e
Prort that the maiimum lelocity in a cEularpipe
alerage vclo.iry oithe ilor.
An oil orspccific srayitr,0.? is nowing rlyough
flo! 500ln^. FiDd the folloni.g:
i) Head lo$ dueto liiction
ii) Powerrequned to nmi.tain the low.
i) PEsu€ drag and tictiondrae
ii) Shean bodr and blufbody
Denne Mach number and derile the samc.
A nar plare 1.5 m: 1.5 m noves ar 50 kmltr i. $ationarr air oldensny
.o"l',eflodi,carol.,r0l.droO ' ' .p*'r.lt oec rr-
iv) Power requ tcd to keep rhe plare inm.tio.