\'IAT31

Third Semesaer B.E. Degree Eraminrtion, DEngineering Mathematlcs

ExPand r(x)=Jr-cNx1rl

Note. A svo a ! t:l vE fiU qu$tiots, set ctiaeal.al TwO tttestiohs lroh eacl wr,

-l

=.

;aaa

4,2

,.lc

!

r I 1.5 5.7f_iM rhe lulf-Enee snE sries .l lh) : e' in (0. I).Iu a machine rhe Ji\nlaEin.ni v.li el

0

v 11tind 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 sothar n mry be coNide.ed infiDire in lereth i,ithout inttuduc,ngrempcrantre ofdre nroft cdpc y= 0 n siven bv

1't,

= l0 (10 r).5<x<10a.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 $idthan rpprecilble eror llthc

Use gnphical melhod lo soheNlnrimi2. z= 20xL - lox:

2x, + 2\,:20:3r :r. > l.1i

IOMAT3Ic. 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 takingthe 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 matrirl1 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,nfornuh lion the data: (06Nt&rks)

x0 2 5r]\r ll 59

Fnrd (01) by usins Ne$ontbackward 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

lagei\,/*7 ir \'."\(6t it )EI't\ !' '/"r//*r" , 4 = o4 o*t, r':.|,/ru ,2.,

l0MAmr

.t, ,rJ8 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 *).

tuf}rrsN

a findrh.D'iderivaiiveorc'r co5tbx- c).b lfy= aco(logr)- bsln(los \) prore rb arni-r - (2n +

c C.tupurc lbe nrrdcrivari\es ofsiD x sin 2x sii l\.

d. Wrh u(u:lnuknons pr.\ethar

MATDIP3OI

Third Semester B.E. Degree Examination,Dec.20l4lJan.2015Advanced Mathematics - |

2a

2a

=:".,,:

a!

a

\met Ahstzr tht FIYEfi qEsbns.

- Li - illl-llrL\pre$

-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.PD\eturtos0r +isin€r)(cos 0r - i sin e, = cos(e, - il, + i sin{or + €r.

l)y,,:0.

b Pro\c 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!11and\e,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.

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,'

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Third SemcsterB.E.D.grecE{amirltion, Dcc.2014/Jrn.20r5lllanufacturing 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-1B.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 invol\ed in rhell mouldingb \!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.ASkethandc\tla IlC qeldirsproccsand nsapplMtonErplah \ilh a next \keich, d,e subDrereed A! w.ldnr! lSAw)proce$\\r,rh a neal skelch. erph $cO\y a.erylene e6 $eldins proces.

E\flain rhe consrtuction md\! ingprinc,pleoI CUPOLA tirmncc. wirh .car skerch.

Skctch hJ explain rheThemir \y.lding poccss xid rnenrion dre adlseges. dnadwragesanti 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 rYeldingb. Elec1tud. usi'rg iD tretding.

a. Dilltrcnriare Soldcnngand BDzingb whar are rhe dlftlLenr \od De$rudive Te$lig NDT) nrelhods and erpianr

skcthcs ollvrrgneric Panicle Inspedion md RadioEapni. InspetioD nenlod.

sslcsrerB'E Dcgtec E{!

i i:l 1o\!r/nurr.-r4i tfrt.lilf/"ttf,. oc' :o r'r' t'r'rut <

uaierlals

r rr--I lli Lll-L i

,,...

I]SN il-lr

* ", :;:::: ;i L"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"'""'"":;""'

t-l6n 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

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Third Semester B.E. Degrce Exalnination, Dec.201,l/Jan.2015Basic Thermodynamics

=

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Noiet t. A s*et ah|' Ft rE fuq questit ts, relectineai.ast TwO qrcstious froh each part,

2. Use ofthemodtaamic .lata hatubook is p.nfline.l.

PAR'I'Ai. 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 nomalhunran bodr renfcratuc (17'C) sere 0'N and 12.N. rcspccrively Obtxin drc rclarionbeNccn dENe*1on scaleand rhecelsius scale. (06 tu'rt,

a Sho* that heai and worh are padr turctioD andnorpropdlr.s olihestsren. (06yarrnb Specilythe nro$iridelyLsed sgn convention lor workard hear ireracrion. (0r\lrk.)c list thediaicrcnceber$eenrorkandhear. {0r \1rr!,d The pistonofan oilenglne, ofarca() 0ot5m: nolesdorn\eards 75mm. dmuing .)(]l](]28nl

olliesh a[ non the atmosphdre The pEsur€ in tie cylinder n unifomdtrdns rhe procesrat 80kl%. while lhe ahrosplreric prcsntre is l0l.l75 kPa. rhe ditle.eo.e berg dud to theIov rcsistan.e m the inducnon pipe and tne inlet lalle. E$imxre rhe disnla.cnrcri workdonc byrhe air. (06 Nr,rkt

r. Describc the clasic paddle \he.l eapcriment pedbrmed by Joule. whar conclLsio. $asd[wD based on the experimenral observationsl ooNhrrn

b A turbo .omFresor derivers r l3 mrt at 0.276 MPa, 43oC $hich is heared ar ris presueto,1l0'C and linally expanded in a rutunre which dclilns i860kw Dunng lhe expansion,tlrere is r heat mnsfer of0.09 \'lj,s ro ire suroDndi..s. Calcula.e ihe turbirc exhNsttenp..at(c il changcs ln kincric and potenrial eneryy arc nceligible A$une a.r atr

a wlat is rhennalcncrsy rcserloirl trplain source ard sink. (0lMlrktb 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 inconrmuDi.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 Bii) The efficic.cy .feach e.Ene..iii) Thchcar djecred ro the cold sink.

!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. (08ltarkgA gas ol nas 1.5k9 undergoes a quasisratic expansnrn which follo$s I rchrionshipP: a + bv, whcrc a and b are comtants The innial and iinal presuEs are l000kPa a.d200kPa Espectilely ard thc coftsponding v.lumes € O.2rnr a.d 1.2tri. The srecln.irrr "z c'crs' o-r\eBas'. -'.e1b, r\ereldr... 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{oraddli\c\ohrnrsr iii) L^!(06Mrrk,(Gnr!rk,

Nin lydrogen gas at a pBsuE of lgas 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{anrvolume. Takec,lorlynDseDas 10400j/kg K. (r0ttr!rt,

;x*'.);.,

VE'/, nr, a rrn,o,,i2 A/\,r r l2/rr.:12

Third Semester B.E.Material

Degree Examinatiotr, Dec.20r4lJan.201sScience and Metallurgy

1?

5:'+4

i)

..1

FlYEfi qu.st tns, s.l.dnu!qucstions ton eo.h pan.

PART-Aa. 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[.iehiior\hip ofcDgnredi.S stmin rDd ruc srrai.. (06 rrirk,

c Consider a rensle sperLoEn of 5nnn dranrerer ard 2smm eluec lcngdr Ilrts dianrern nreduced to ,1m1 tltrough fla{ic defoflnarion what s ir\ lengrh rr rlns stasel, Also tlndengrleen.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!lPafind ori\.6-",6..,,." x.d 6.", " (n6Nt!rk,

Expla,n thc nrechanhm olsoliditimrnr.wh.r ita solidsolurlonl Vcnrionr]t trpes.rsdlidn ution AhocDunuatcrles 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 remFralureli) Thesoliditicari..tenrpentuErii) llcsupohcativ) 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.

I O\{E32A/AI J:I2A/MT32/TI,]2

+iqtaA) _Fig e.,1(c)

PART BDra* the Iron-Carbon eqnilibrium diaemm and label ft Sho* the ,nurianr poinrs on ir.$iire the reactions occuring ar lhese polnts irdrcar g rlre temperaturc rnd composiriotr oledch phase. (r0NrrrktIwo metak A and B havc then mching poinh al900'C and 800"C rcspectivcly Thc alloypan fortos an eutectic at 600"C of conposnion 60% B. They have u.linlired hquidsolubilities The solid solubility ofA in B is l0% x.d ihar olB i11 A is 59; ar eured.re$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. E\plaiD wirh a

a. E\plainthe $rucrue. .omposnion a.d propenies dfstuv cast nonb. Bricfly crplair rh. elecr olalloy,ng elesehrs onpDpenies ol$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! windingsker.h. o0Nrirktskerch tne pnltruionprcces and mentlon its applicarions. (,0]\turk,

I u12

1 0\l F"/A I t32 BU5\

Mechanical Measurements and Metrology

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\or..1. Anlwd dt)'FIvEIttt q atiots, ple.tit,galeast TwO qucstions Irom each pan.

PART ADell.e merruloey Sra.e and explain the objectiv.s ofnrcrology. (06rlrrknSketchand explairr: l) lnternationalprotoqDe rnerei ri) lmpe.ial staDdard yard. (l0NrlrrtWine the slip gruge c.mb ation to build the follo{lne diftnsians using M 87 sliF Saugeser: i)49 3825nn: ii)S7lllsm @rrrrrkt

tr) rr, = 25i

vi) Ftrndancntal dcliarion = 0.b. wnha.ealsketch, explanrthe differentqles of fits\yirhexrmplcs.

x. List lhe.haracterNtns olcompamtorb. 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- l6Dillii) 30nh falls in the diamcrcr stcps oflS-lonnn.

x. wllh a nert sketch, cxpLanrrbcNo nEb. wite sho( Doles on rhe folloxine:'i)

courlei iY ) S ondnrr natcria ls

rirl0HrJ rnd sle(h rhe tir gi\en

$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 rlEadus g taper parallels a.d 6lle6 ('0nhrk,

b. Dcrile aD exprcssion aorbe$ size wne, (06 rkdOc whal areranous t}!es oferoN on scre$ theads and explaiD the reasons lbr the same?

(01}I!rb

PARI'Ba. with a neat block diaeram, cxplai. rhc rhre srages ofg..edlized ntasurment system.

withanexanple 0o\rsrk,b Explah wiih neal skethcapacitive tansducers ofchanging aier and cnaneine dklancc

(10\r$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 sketchb. wllha nelr sketch, explain i\'lo Leod -sauge

principlcolopti.alttro.rtcr. (,0Nllrks)Cauge racror; n) BondinE nethodsi iii) Themo

(r0M,rr,

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Third Sem€ster B.E. Degree Ex,t mination! De..2 014/Jan.2015

Fluid Mechanics

'!!

!:

i.

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aZ

\ore. r,Ahs et FIVE ful .t uesnons, selectihAat 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 rclutreiii) vlscosir] r) Specificeravity (06t!hrktDeltue 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$. (06 vsrktb. An inleircdU tube man merer is connecied ro tm Lonzo$alpipes A and B rhroueh vhi.h

rater isflowing Thelerricaldisranccbetq€entheaxesoldresepipesisl0cm.whenaDoilolspecific gra\ ny 0 3 r used rs a satrge nuid. Tlr refiical hcight olwarer colums in ihctM hrbs of the invertcd Unube na.onrter aE lbund ro be srrne Md eduat i. i5 .rrDcrrmine rhc diileren!e orpN\ur ben\een

'he pipe\

c A rectangular surrace is 2nr vide and 3m dccp n Iies in vcdicd phne i. *arer Dste.nNtu totalpresse ard posnion oaccnreFre$u.e oo the pl.ne surfaue whcn ns uppei edge ishorlzonra!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.luariontion 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 bet\rcen dro n t parallel plates is nlEd wirh oil !ach sideThe lirknesofrhc oil liln is 12.5 mm. Thcupperrlare wlrich moveslbrce 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 3nc. Defin. n1e folbwnrg rEnN:

i) M.ra centre and tudra cenric heilhrn) 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,oer\eh "i. ne:L.l'r .(. Dc,-',1. .e o..o.i.d.odd1- i, L not

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 (t0rrrrlnc. Srare Bnckinghamt r tneorem (0r i\rirk,

Derive an expresion aordncharge $roughv-notch (06rrarknA l0 cn x 15 cm lenturimclff n provrded in a vetic,l pipe line cari.g orl.tspccincgrlvity 0.9. Ile now belng uCrdrds The differcn.o ir1 eleyation ofrlF th.oat sedioi andentBnce sectlon ol.he rentuitoeter n 30 cm. the ltiffercnrial U tube oercuv rnaooDretershorsa 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 \1rosedmsityis950k-s/in'and*hosekincmaricvhcosnvx2lslokesThecenrcolarepipelioeat rhe upper end is 40 m. aborerhan rhar rhe lo*er end Tbedis.hdrge I the upper end harnDsphcric. Find lheFrcssurc ar rhe lo\er end and dm$ rhc hldrauicgFdtent lirc and rtotal 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 hreii) Totalencrsyli.e

Prort that the maiimum lelocity in a cEularpipealerage vclo.iry oithe ilo\r.An oil orspccific srayitr,0.? is nowing rlyoughflo! 500ln^. FiDd the folloni.g:i) Head lo$ dueto liictionii) Powerrequned to nmi.tain the low.

i) PEsu€ drag and tictiondraeii) 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.