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- 1. I I!J I .. l Vox J':3 ~ .:::. (_&t.4-1) ( 'lt·:n) 9 .<61 - ~9 .9tr-~ Un~t:- a IT"i'l. ft- (~~{ dvJ
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- 3. C ~ 1'o~t{o~ c~ndu.nt . To obta.Yn ~ VQlw.. {of' Constant C. a..pplcft'18 ~ t:?allJ)d ~ ·Cbnd~ fl6i) in ~ ubve e~~~~~oo u :::o I cy :::::- R &r I)_ 0 !::. __L .g_ +c. ~~ drx. ~ R'l.. --~ I dp . R'l. --- ~~ ~ ~ u_ ~ ~~ . ~~ . 1('Y~-R~) U. ~ _I d-p (C'V'~ ()'>.) 4-l-l d-~ • _,, LL ~ . -_1 ctf ( R'L-r-c'l.) 4-U. d-<'),_ From ~ veloti~ cH&~'il bu.f~ dJC.~CA~ TI.9 ve!ac.~~ -::_!___ . it_ .R'L ---?@ 4-P- ~)l
- 4. TIs. d~sc~OI'>? ~ cu:.nos~ ~ r4S.e~h0 cn fs: obb=t~oe-~ bd LOOA~dQJ~()d ~ .._Jlow Rn~"'Oh th.9. c_j~uJOv'l ~C'Id ele«nent bF ')'o..d?u.s '¥ o.C)d lt~cKne!..S dry. ~ -fl~d ere.t'f_Q()~o1 suno- d ~ ~ =-L . d-p . R'>:~x !Lrroo .dry lt~ d-~ ..1C)+ecra.hoD)cr Oi) ~0 th s~de.s ....... - ~ d-p Jcll 2 -<¥"- )ih- .!LIT 4t-t- ~ ...... -I ct-P . 'Lfr J(r.l.rr -"''l.) d'Y- Ltt-l· ~ ' ~lR{)) " -I d-P . &n [~:"(~ -- 4-~ d-~ lt- 0 ....... -I d-P ·2..n r~~ -:~J- - . 4-~ d-~ . d-p . rr~~ -
- 5. u ~ - l d--p RQ_ ---7- {1) &~ drx. Ca._h~oo betw~ ffio,_')L~ mLUY) a.nd · ftV~ClO JQloc_~hJ: uffiO.")l -I cl-P 'Q'L .::: lt~ ct"'L '.U -I ,df ·~'l.. - ___, 8;~ d")t u 1J: fu pcroble_fY) llrl~ IO..m~no.J ..f'lt~w~~h~v~ ----- ·-- x, ([) ~~® )(2.. ~m e~u.oJfoi) @ v !::::. -I - . c}p . Rr:t.. ~~ d-~ -dP ~ Ll ."f?-}-l J~ R2.
- 6. I I II II I I I 1 I P,-p2. 2 - ,.._ slJ • {S'~ d~ RQ.. I r"rom ~ d~~0..{'{) I Fj -P'L PJ-P~ ~ u. &1-t. [L] (Df,_)'l. r, -p')_ ~ PI-P2.. g~ Ll· p.. [L] Los<; (J-M-S~ tV.Q ~o__d D'L =------- P1-P2... 3~U · rt .L '::::.. ttl5 IJ't .P.s h~ ...... ~ ll · f-l· L c)l · F3 ,....,._..,........-.-~......~.~.. ....,...,.,,..,..,..,........____ Drro..eJ we?s.bo..eh 9--u..a..~co() ~ Con~id€..b 0 ;shat~n"~ 0 -r~·r·a. P1re o..s. (C) - _ ____.
- 7. P, Let P1 o..o d p.,_ P-'2 ~J. uro. ~oleosH'j oJ sec.lf1)-{1 (]) c.od@ v, ct()d v2 velou hj Q.t ~edf~ CD o.od ~ Let]l-b L . ~)n0tt? oF tNt prpe betw~ ~ed)&tJ Cb CI.J)d ® 0r1d d be ~ -foro Uo~t- tvett-ed OJ.Q_c._ rQ.f) .Yn?t velac..H~. li~ be. ~ l~~s 1 of ~Ckd ~ ~ ..fdt.htY> . A ppl(fo 0 11eJ no lAIIis e~ tLO..~on p, -+"''l+'L,.::::. ~ +V~'1 t2.'L +hr fj ~~ fj 2-j r 719._ ~7pe • ,o, rl be:. u.- I> · dr ""-.) '- fTIYY1'La() teLl ~1~ l2::.'L OJ) "- p2.. + hi= f:J hF- ~ r,-P"L ~m fg Hf - h.stctd losl'. dLL!l to f.rJt.hooo o.C)d ThQ.t fol-e.nsh~ ...
- 8. ·~ )W '1 '!=' l :::: cf. '><. ITI'Jl " J 'l. We.. kf'low tho..t P~rn.oJeJ (P) ::: tr~ I ~ ~ J ':f:PL X ,}'2. &~c.rrot' (§;) ::. ~x..f1 t<_e ~ c/v~n9 +r-- f P~u I h.9. o..Jt.es -r't"{ ' Q._~u..fIIi b.rUu.ro I P, A -P_l A -.f1 Pl.V'l.. ...:. 0 ·. P, -P2.. rro~ ~LLn.hC)~ CD I , ~ f PLV~ P,-P'l_ ~ f. 3. hF ---=>® ~ h~ I !::;_ ~PLV~ A h,: !:: J== PL V'L f>.5 .A ...... f: X IIX.D XLXJ'l..- '·~ .4-~ LVI}_ ' P3 ~
- 9. i ;1'. • I jl ~i[J I II il We (now 'tho..t- Prrobern: D}.l38 . Given: 1=-' - f- - -p ~ h1= ~ 4-JLv'l.. -'l. &oxto m .&:JD 8 ~0.1!> f-L ~ ~. ~~ Nf>/m '1- u_ rv ~1 •3% mjr. , 1. Qe_(f'olds ()umbtl - P,-p.,_ ~ B~p.. LL . L D')_
- 10. 1. Re(fnold~ nuMb~ I .2. Pe ::.. fVd. ~ ~ !:::. ~/ o.ICfx.tb~ !::;_ n (s~xti5'>}-v '+- Re 3.P~s.s UM d~o-.d~6..nt P, -P2 !:::: 3~ X() .DD~X C .oq k, X. SD-o ( So X ( t)~)'1-
- 11. I . PN2..Ss UJ.St Loss hJ: ~ P, -P'l.. Pj hF ~ 3~ p.- u L P. .J .D'l. hj: ~ 3~ '< D. Oo& X' D.t>9'~ X Sctl &c'D x<J.~ x(sox1 ;1 )')__ T~ -(~)Rd-~ -2.
- 12. I .)-I'tO ·l en:ven : ~ S::: o.l L :::. )ooc NJ o.&9 x ,a-'1 ~ --l--- '{) .1.X..' Qoo l-t ~ D .o~S 3 NS/('Y)'L 2. ~ ~Av .-~ ~ lL cd)'L vSt~o X to Lt- ,__ JL c3DXl 01..)11.. v - 4- j ~ 1.tl '1 f'() r5;.
- 13. Re ~ 13131·4- '7 ~ooo s'o ihst. 4'lcw ~s ~buo.C')t J?lo--w. hf- ~ 4-FLV')_ I g)3IJ F ~ D. Oi9 (f?e JD.~~ { F "' 4-· &X I 03. J hF ~ 4-r-:-Lv~ 2. X..j ~D - 4-X: 4-· 9 X1D':) X Qoo X 1· oirt- 2-X 9. %I X 3'0 X I o'l [~h-,r-- - - ] - r- ~ lb.3.~ fY) .3. pcweb I .&3'l ·IG,~lll?f : I l11 ~Is pol~e I r- .hr= !:':: SOI:)O(Y) L ~ act){'()
- 14. r ..' f ' l . hF .__ 3~f-1...G:.L ~ 3 .b'l. 3oco ..... 5<XXD·I~ X LlX.&oo B 4-%·'3. X'l.% X Q3obX t:) 1) 'L ..-! gooou ..... XQ-i%·3. x,.g, :>< - ~~X 0 .s- ~~oo ,_ ~~4-o . '3t rnj3u ~ 2. Reonods oMh:t<t I '2e ~ fVd p- t1 ·IS' Re ~ 391o9 a9 .&~ Re =- 3.~ X lob = =- o.oicr ( Re)a.~c- 0-019 cs.~x:to6)0 .~~ I -~ r ~ t.11 'X.IO c -~)2.1Dc X.o
- 15. : i _2._ D ~ l&X.tD m fi :: t S'c htrut lfYlfn -~ r::::.. I~e X lo ~t. ~'.1 3./:::: &.s-><:lo m ~ R ~ fvd. c -l () ~ AV ... .~'! '2 . ~-~Xo -:::..!L(l~xro'l.J v I 4- V ::::. D. &~I m/s. l--. e <:now it:'a.t O.DI'l. .... , a ......_/_
- 16. We <new tho.'c- -(~) I lO u l X .(S .~91.) X l..p( o. o'l. u ~ o .ci4-~ rnjs.Lttn) lt· l-4ea.d Lo~'l.. h~ ~ 3~ l-t U L [OJ D'l- ~ f 1-P2. P9 ...... 58-8 3. - r?bc X'.~ l h~ ~ "'t.l) x.lc'SM
- 17. 5- <'She.o.n ~t-"fes~ T :; - c)-p . ..£_ dx ~ ::- "?,.sen X.. L -'2.)(lo ~ [ Lo - D.16 N/m~ Legses io pipe : , hF ~ 4-flv~ ~jD r: ::::- lb Re CH e.~cr J='c"frnu.l~: v ~c J- rnx~ t C;k L J 4 velo~~hJ q ._fbw c -> c..~e~cr to~tiE»"t rn - ~(j~a.t ic rYLQ.o.n ctstp1t
- 18. 0f'f o.~ we~bClCh ~u..o..f~ r~ ...):)eel {ory ~l,.~-V TIrttHAt pipe . Ir .--- Lt~S~ ot Qf)~(Y1 dlll. h~ ~ ud~ C.orJ!"fo.ti~ he .~ (V1-V2. ') rt. 2_~ 'l. kV2. &j. I k ~ c~c -1) C .. c -.- ··~ Cc~c..l~t c{ c...c()t'los..Hoo nc::J crove_C l.os.s he ~ - () .s}2.. ~J 4 e_neJcr oJ el')ha..~c.e. at haI ~ 'C).!)v''L 2.3 V- VeJocJ ~ o..l:- ho :: V'L 2_3 fnel J-7 rdo~lf:j o.t oLLie:. Los~ ~ eneJ'Icr dWLto (pa.d.uol 0 P'Pe.
- 19. : I, ~ I ' Co~cie..nt w~d.. ckpe_ods 0() ~ a.r Of- ('O(We.J)o CQ Ci'ld dfve.n~ Ce . loss ~· en~~ dl.LQ 1n knd e o. pipe:f() h~ :::: .J(v~ - ~3 k- Ce.~c~e..ot depends . ao (ocv) 'Da..d~us 4 C.-t.l)') vo..+uno._ 4 benc . lo~~ ~ eoeJ)QJ d WL i-t> p~pe. -fi'tt~o(J : hv !::: kv'l.. ~:1 fotol ()fi~ ~ be1~ K- to~c.~eot c1 p~pe f'fillod w~ W~th depends. ~t') I ~re. ~f: F~~~· lc&s crt-(?_{)~ d:u.o.: ~ 0 b-~~J"fC'.letfl'H'I t0 ~ Q~ ()._ p,pe hob,·=~ ( A -')'1~J (C (A-a_) cc .::: Ac_ A-o.. A.c.- AflQo.. ct ·1e()c. Lont<Y Qch 0 00 a.. - OJl..O.n. at c.bht'Y och()&o A - A~o. c{ "p1pe. ~.
- 20. -F Q_o()fnv.~~ €_~Ao.H~ I ~ ~ At v, D .6) ~ IT ( 2> ·S'o X I o'3)'L ---vt 4- Vr;_ ~ 0 .~4- M/.c ~..1.1'C'n o..bove e.'tu..~tt&-o ci<i-~oS1to.~~ &.?Ab +-~1= [ he ~ o.I19M I L !:::-I oco ('()
- 21. ~ ~ Av o .o& ~ l!:._ "t ( IoX lo'l)~V '+ ( V "' &.s'+ "'Is ] f2crol ds n u.m bQ;) I Re ~ fVD f-t-
- 22. sif)ce Cl.t Du..h:cm~()d -luld ~ lh9. p~S!:.lAJJt lb ~c. p, ·Q. 'l_ + ~.c;i;- .c t- ~S4 --{) ~ 9':l.eX1.%I ~X 9.g.1 92.-b X )'. S>l &x.~.~l f2.i;;b ''d.(' t'lt..s. r; P1 - 9~~ X tt>b N/ro~ Pow~ <Sf pump fp ~ f~ ~ h~ pp ~ ~'::. 13~.t1X I'D pow~~ I'C)chiy I i)~ O.b "- ~.t~ ~~veo: f ~ <i_oo kj/n·? y :::: b.~xt;lf rr?/<;. r -5D ::::.. bX..ID f'( PumP mota"( 3 138.11 X.lo p mc.l--o rv ::._ I~R .11 X (b~ 0.~ " ~ 3 b · ~8 X I 0'1 W '' '
- 23. (f ~ ..t:__ f ~ ~ l? ~r r--- b-~ X IeLf X ~a c p- ..... c.SS & N&/~'L P~s.s W.n kuto..d Qt tb /2!)then at t4 +ei.~k ~ot ~ f3 h ~.111 CA~Vt(): :::. 9oox.~.%1 X3 ~ ~b-4-~ 'XID'l "-'/miL I ~ ':::= 6Px nx o4 :::::. ~ ~o.&s m'?./c;;ec d1 ~ D·&.m c·.2._ -;:: 0 . 4-tv) f!l.~ x 1-l XL ~ b .4--~ X 0' X ( b X Ic)'3 P, e: L~ () X I).'3 N/fY) 1)_ .) ~ i l I
- 24. A1 ~ a. a3.1tt-M<l.. AJOC (JF th9 sec.h()oo @) fh ~ IT (d~j'l.. '+ .=. IT (D.lt)'L 4- 'l. ::::: O.l~.bM Velot~~ a..t sech0 o{) CD o()cl @ H-e.o..d los~ Dun. 'hJ eoICVLffYLQ__rt 1 he :: C_v,-v'L.j'l. !L3 'l. == (1.96-l.q~) ~ X'l.~ he ~ 1·9-I&M looo X.9 .g-1 • !'. ..... C>. " 0 , • LJ- ""')..- , I I P1.. .... I 3 I" 911 X lb 1 N/m'L
- 25. ~.(,1. ~~ven! veo c~ t j d, ~().brf -l ~ I Soo M I hF "::. 4o :::: f-1<c ={I - :: d~Qme_ ~ o.tm f-- "iso--1 ltfl/l 2-5d 4- X (L 04 X l S'O o xv'L 2X~·~t X c.h I V "'- I- 4- ro /s l bjt c__h WI~ ~ ~A1 ll_ :: '14- Cd,) X 1. 't r::- ry4- (o .b)'l. X I. 4-
- 26. I !' I !t J I ~~~I +f}J'l. ~I :::.. ~'l. ~ ~ ~ hF ~ Lt-~ Lv'l I -i:J[) h~ 1 ::: 4- X t) • 04- X1 !rO X V 1. ~X Cf •£l. X t'l • b hr, ~1~.193. v'L We know tho..t ~ ~ AV v ~ r:t!/A hF1 .:::. (b./93, x!i___ f1'L ,.... lD.I9~ x. ~?-- [ %-(d)~ J2_ ~ I o.19 ~ cv"_ [ £)4_ (o .b)'L]~ hFI .::: I&1.b1 ~'1.. ·~~ hr2. ~ 4FLJ '1. 2~D q> ~ fi'J v ~· ~~~ fwopire So.f'r9. d; e~.rmte "f Sc I./
- 27. ~ 4 X a . o4-- )(. '1 S'"o '!.-. ~ ')__ 2.. ~X~ .Sl X C. bX l o/q X 0 . b'1- ><'l.) hF .lf-o ~ I~1· 4-b ~')__ t 3 I ·e-" ~ [ 9J "' o.s m'l.jw. ~ ·lb1· ~iveo: I ~ p -::=_ tto kw ~ tlo X Lb W P, ·~ SDab X I o3 N/m'l.. P!Q.&S lAI.S) drrop ~ IDOD X lb~ N/"l'0'L ~ c o.oob~. ~UJSL ~ o..} iolet. f PS Sooo X tD'?. lDDD X ?-8-1 ~SD~.b@.M 'l. lo9s· ~ ~a.d .DLU. +u ~~ ~op
- 28. hF .::: I'D •~~M J-osg, ~ ~a..d D.t end or ~ pfpe ' . I hFe - h, -hF ~ 4c1.14- f'() ft.~ p~~ dl>or ove.Jl ~ len(Jth ~¥-~ .p~re cJve.() . Nu e')tt~.f-a.-{on. rrr , ().0~1<;; MYse.L] We 1<now tho.( 0. 0~~ ~ lL d'l ')(~ 4- J "' o.o>s)d" '<f~
- 29. !) C) • ~~·c.renc:~ o~ powE:h f"fa..nmiMon X)Oo I 5c9.b2 -oL9 ! I I ~ o.% I I I d -'2. '!!::" l~XIo M G) d:2. ~to lX 1o'l.M II!) t¥ -:::: looXIo'1 rr?•j$et P, ·.':::: &.So X.lo~ NjrY'l.. P2 ~ ns xu? .":/('()~
- 30. I .I We kno I..J Th o.t "- 'l. I ~ S-b~<)_ i~:X.C '2.1~ ~Sc xo ;-o - t + -. bCC X9· R'l ~X'l.i lt)CO '><--<1.~ Jl '}(~ .~ -I +hf hF ~ ~1.1ll ~l:,.t>9 +t I hj: " ~.0('t) ) tl ~ h.o.o.d fM5. 0 · pM:.~tfv~ ~ {tow t~ ~~o ce IS. (ij Q.()d @ . Se ~ ().1,Q_ u.pw~ck. d 1 :::: bco K l o~~ -~ d'l- ~ goD X Ia- ~ P. ~· ~ .1$~9 ')(ID'-'" N/M')_ l) ~ tl)o Xtn?. lY?, / ~e
- 31. We <.now We !<now Tta..t r;; ~ A2. v2. bf:lo'XIo~::: ..D_ (2eoXID3.)'l. it- . I v2 ~ S.4& mJ~ he ':: kv,__'l. ~.5 r'L ..... 0. &s- X 8.Lt~- 2..X9. 2-j h(J .!::;._ 0 .Cf ,, ('( We. Kno "V n;~l:- v'l. ! I ~I
- 32. 'l ! f I I I. 1. ~ it~~l1i .~, I' 1~ P.n.>lJ'tIJJ.S2. ~Jtl.. IS. D.S k ~ {1°neel 14e'1t~ fhg. p.nabl€'M i~ 1-o be SC~v~ ~n~ b'j rnaN.QO~ e9,u.~hbcl'l rvuttod. till p~. ~ :::: '199.! kg ff't•? 1-t ~ 1.13<6 'X', D:l ~3 c;; rM '}... ~ 1.~~ x1o~ x~ .~, .L ~3oM D ~ 4XIb(}_ ('()
- 33. i III .. ! j I II I I I II. ~.~~I !! I I I I 2. '"' l;- X C. 0 IS' X. 3 C:l X b.~ b .2...X 9.<iS I X 4X I1;)-'l. Dj2 .11 ::::: ' PI -f_ 99'l.l x~.~~ p!:: fJ~ hF !:: 99 9. I X ~ .g-1 . X 9 ~ Io3 X 12.·I 1 p ..... 1 .~6 X Ib~ W r; ~ o. n~ 1=2- ';:' ~. I~ F3 ~ o.t) ~ h~ +h.e +h. t t '-'e
- 34. I i I f (i (ru)'l V1 ~ ..!!._ ( c.lb) 1 /2 Lt Lt VI ~ ~.'S6 "'l.. I h~ ~ ")_ ().!; / 2-«J 'l. ~ b.S' v, 2X~.~ M ~o Dcy Io~.s. dLUL fc et' Mr- rY..Sl"- he .... (_v,-v'l_ j'L ~j '2... ~ ( V, - o .~9V1 J ~X.C}.<61
- 35. I i Hea.d Lt)s~ at- e.~t hb ~ ~ - ~ lo~s o.tMa.JO!'f Ft-11 hF, ,... ...... - ...... I 0 JaS!. o..l:-MO..JCC'( Qc. hF':l. == '"' v3'l. ~j (o.bC1V1 )'2.. ~X 'l·<}l 2.. O.D~4--V 1 m LrfLV~ 2.j D lt X 0 .t>l. X ~ o x v,~ ..2. X9-~I x. o .1 ~ 0 -~ v, (") 4fLv1.. .2j D Ltxo.ons x~s-xV2-'l.. 2!X9.&1 X o.lb 'L hF3 ~ 4F3 l3 V3 2j D ~ 4-Xo~~ X IS X. (o.b9V1)'L &.x, .~1 x t~.l'l.. hF~ . - o. &4-2v1'l. ro
- 36. I 0 Cct~e (I) [ VI '=' !3.S11Ylfs ~ ~ A1 V1 b,J ~ l!_ ( o.t)'L. X~ ·~ I 4 ~ ~A,v, ~o x,c3 ~ n xo .l2- x v , 1;- H - 1.&18 v,~
- 37. D1 ~ttco Xtbg M 1)2. ~ ~SbX lc~M b3 0:- ~()0~ LbS (;) h._ ~ (). b':L.l s ~C.bt9 J__1 ~~Oo(V) L~ ~B. Oo<'v:l Los~ I We know TJ.,~t A 1v, ~fh. v'l- c.I~Sb v1 ... D.c~t, v.,_ V2.. ~ t. stlbv, rofs. A, v, r:: A'313 'l.. 'D • 12~~v I ~ fT c30t) " l D?>) v':?, 4- VI ~ 0 .Sb'lS V3 rnjs. v3 ::: l .1'1 v, rnJs.
- 38. INqjo'Y L.,s, o.t ftl?. hr: ~ 4fLv,2. r l" J+~cd los~ !2...-j D h~1 ~ 4Xo.o2..4-X-&coxv1'.. ~ ~ cr .'&.x ftoo X. o~ hi;_!::! 4fL v?.,_ 2..3D 'l.. ::.. 4X.b.t~~l X.'~oo X (j.'SbbVt) hf:3 ~ lt-f L/3'L 2j j) 2X,.g. .X 3~~XIn~ ~ 4-X D .bl9 x~sc x Cr .11v, ')'l. .2 X'}.& x Soo ><I o-'l hJ:3 " I o .11V12.. fi ~ ht=I -t-hF-~ +hF 3 I& ~ ~. 4Lf-'bv?- +b .1.~ V12- tID .11 V','l 12.. ~ 19.g~v,~ v ~ ().grnfs. we ~now Tho..t v'l. ~I· ~1)6 X D .~ ::: I. nt.rf'() I~
- 39. V3 ::: 1.rr1 ~ t> .<iS " I. 4-l f() J$. kf e l<nflw Tho.t ~~A-,V, - ~- z o .I rn?./s:e.c.. d .-~ 1 ~goc >( lo M <::12.. ~ &6oxtoV) d ~~ 3 ~ ltDc~ I b rv> I We Know .thcxt ~~A, v1 ffi'l.v2. t A?.v~ ..!!:_ (3oDXo)'L VI .4- VJ ..._ - -.-+-I ... h_ Q_ ~- 0D1~ F3 ~c. Do) <t.
- 40. I I I I At v1 ~A~V3. o.o1o6~vJ " l!_ (Lttlf:l'X.Ic?.)'LV~ 1t v1 " o.I2-S6 /3. D .01bb~ v, ~ 1.11/'q, «)/~ V3 ~ a.s; 6 V 1 mf.s. ~ 4-.5Lv,~ .2..5 D' !:: 4 '<D. boir X 4ro V,f)_ '· I <.:L'<9< lSi )( 2.o o X Io- 1 I h~, :::_ ~. d.i V1'Lrn i ""~o"f Loss cJ:- · Gt l I 1.. f)_ ~~X D.Ool~ X&~~}( c~.'d_s)Jl 2 X Cf • 8-t X t!tOo X b~ hF3 ·~ 4JLv~'l.. ~:t D-2 It_ .... 4- )<. D ·Drtt2 X 3 IS X [ o. t; 1.:. V1) .2-x r.~, x 4ob ~tv~ /.
- 41. 2.~~.<J.t !:::.. D . 0 ~s; VI"l. l""l he. ::: kV'l..'l. 2j ~ o.!; c~. d!" v, )')_ 2.X. ~. %1 I he 2- 0./2<}o V1 'l. M 2j ~ ( ~.~~v,- o.sbv1)"L 2.:) ~ ~-~-b v, J'L 2X9 -~I e ca.se c_t) ' i I
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- 79. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 27 UNIT - II - FLOW THROUGH CIRCULAR CONDUCTS PART - A 2.1) How are fluid flows classified? [AU, May / June - 2012] 2.2) Distinguish between Laminar and Turbulent flow. [AU, Nov / Dec - 2006] 2.3) Write down Hagen Poiseuille’s equation for viscous flow through a pipe. 2.4) Write down Hagen Poiseuille’s equation for laminar flow. [AU, April / May - 2005, Nov / Dec - 2012] 2.5) Write the Hagen – Poiseuille’s Equation and enumerate its importance. [AU, April / May - 2011] 2.6) State Hagen – Poiseuille’s formula for flow through circular tubes. [AU, May / June - 2012] 2.7) Write down the Darcy - Weisbach’s equation for friction loss through a pipe [AU, Nov / Dec - 2009, April / May - 2011] 2.8) What is the relationship between Darcy Friction factor, Fanning Friction Factor and Friction coefficient? [AU, May / June - 2012] 2.9) Mention the types of minor losses. [AU, April / May - 2010] 2.10) List the minor losses in flow through pipe. [AU, April / May - 2005, May / June - 2007] 2.11) What are minor losses? Under what circumstances will they be negligible? [AU, May / June - 2012] 2.12) Distinguish between the major loss and minor losses with reference to flow through pipes. [AU, May / June - 2009] 2.13) List the causes of minor energy losses in flow through pipes. [AU, Nov / Dec - 2009] 2.14) What are the losses experienced by a fluid when it is passing through a pipe? 2.15) What is a minor loss in pipe flows? Under what conditions does a minor loss become a major loss? 2.16) What do you understand by minor energy losses in pipes? [AU, Nov / Dec - 2008] 2.17) List out the various minor losses in a pipeline
- 80. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 28 2.18) What are ‘major’ and ‘minor losses’ of flow through pipes? [AU, May / June 2007, Nov / Dec - 2007, 2012, April / May - 2010] 2.19) List the minor and major losses during the flow of liquid through a pipe. [AU, April / May - 2008] 2.20) Enlist the various minor losses involved in a pipe flow system. [AU, Nov / Dec - 2008] 2.21) Write the expression for calculating the loss due to sudden expansion of the pipe. [AU, April / May - 2015] 2.22) What factors account in energy loss in laminar flow. [AU, May / June - 2012] 2.23) Differentiate between pipes in series and pipes in parallel. [AU, Nov / Dec - 2006] 2.24) What is Darcy's equation? Identify various terms in the equation. [AU, April / May - 2011] 2.25) What is the relation between Dracy friction factor, Fanning friction factor and friction coefficient? [AU, Nov / Dec - 2010] 2.26) When is the pipe termed to be hydraulically rough? [AU, Nov / Dec - 2009] 2.27) What is the physical significance of Reynold's number? [AU, May / June, Nov / Dec - 2007] 2.28) Define Reynolds Number. [AU, Nov / Dec - 2012] 2.29) Write the Navier's Stoke equations for unsteady 3 - dimensional, viscous, incompressible and irrotational flow. [AU, April / May - 2008] 2.30) Define Moody’s diagram 2.31) What are the uses of Moody’s diagram? [AU, Nov / Dec - 2008, 2012] 2.32) Mention the use of Moody diagram. [AU, April / May - 2015] 2.33) State the importance of Moody's chart. [AU, Nov / Dec - 2014] 2.34) Write down the formulae for loss of head due to (i) sudden enlargement in pipe diameter (ii) sudden contraction in pipe diameter and (iii) Pipe fittings. 2.35) Define (i) relative roughness and (ii) absolute roughness of a pipe inner surface. 2.36) How does surface roughness affect the pressure drop in a pipe if the flow is turbulent? [AU, Nov / Dec - 2013]
- 81. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 29 2.37) A piping system involves two pipes of different diameters (but of identical length, material, and roughness) connected in parallel. How would you compare the flow rates and pressure drops in these two pipes? [AU, Nov / Dec - 2013] 2.38) What do you mean by flow through parallel pipes? [AU, May / June - 2013] 2.39) What is equivalent pipe? 2.40) What is the use of Dupuit’s equations? 2.41) What is the condition for maximum power transmission through a pipe line? 2.42) Give the expression for power transmission through pipes? [AU, Nov / Dec - 2008] 2.43) Write down the formula for friction factor of pipe having viscous flow. 2.44) Define boundary layer and boundary layer thickness. [AU, Nov / Dec – 2007, 2012] 2.45) Define boundary layer thickness. [AU, May / June - 2006, Nov / Dec - 2009] 2.46) What is boundary layer? Give its sketch of a boundary layer region over a flat plate. [AU, April / May - 2003] 2.47) What is boundary layer? Why is it significant? [AU, Nov / Dec - 2009] 2.48) Define boundary layer and give its significance. [AU, April / May - 2010] 2.49) What is boundary layer and write its types of thickness? [AU, Nov / Dec – 2005, 2006] 2.50) What do you understand by the term boundary layer? [AU, Nov / Dec - 2008] 2.51) Define the following (i) laminar boundary layer (ii) turbulent boundary layer (iii) laminar sub layer. 2.52) What is a laminar sub layer? [AU, Nov / Dec - 2010] 2.53) Define momentum thickness and energy thickness. [AU, May / June – 2007, 2012] 2.54) Define the term boundary layer. [AU, May / June - 2009] 2.55) Define the terms boundary layer, boundary thickness. [AU, Nov / Dec - 2008] 2.56) What is boundary layer separation? [AU, Nov / Dec - 2012] 2.57) Give the classification of boundary layer flow based on the Reynolds number. [AU, April / May - 2015] 2.58) Define the following: (i) Displacement thickness (ii) Momentum thickness
- 82. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 30 (iii)Energy thickness. 2.59) What do you mean by displacement thickness and momentum thickness? [AU, Nov / Dec - 2008] 2.60) What do you understand by hydraulic diameter? [AU, Nov / Dec - 2011] 2.61) What is hydraulic gradient line? [AU, May / June - 2009] 2.62) Define hydraulic gradient line and energy gradient line. 2.63) Brief on HGL. [AU, April / May - 2011] 2.64) Differentiate between Hydraulic gradient line and total energy line. [AU, Nov / Dec - 2003, April / May - 2005, 2010, May / June–2007, 2009] 2.65) What is T.E.L? [AU, Nov / Dec - 2009] 2.66) Distinguish between hydraulic and energy gradients. [AU, Nov / Dec - 2011] 2.67) Differentiate hydraulic gradient line and energy gradient line. [AU, May / June - 2014] 2.68) Differentiate between hydraulic grade line and energy grade line. [AU, Nov / Dec - 2014] 2.69) What are stream lines, streak lines and path lines in fluid flow? [AU, Nov / Dec –2006, 2009] 2.70) What do you mean by Prandtl’s mixing length? 2.71) Draw the typical boundary layer profile over a flat plate. 2.72) Define flow net. [AU, Nov / Dec - 2008] 2.73) What is flow net and state its use? [AU, April / May - 2011] 2.74) Define lift. [AU, Nov / Dec - 2005] 2.75) Define the terms: drag and lift. [AU, Nov / Dec – 2007, May / June - 2009] 2.76) Define drag and lift co-efficient. 2.77) Give the expression for Drag coefficient and Lift coefficient. [AU, April / May - 2011] 2.78) What is meant by laminar flow instability? [AU, Nov / Dec - 2014] 2.79) Considering laminar flow through a circular pipe, draw the shear stress and velocity distribution across the pipe section. [AU, Nov / Dec - 2010] 2.80) Considering laminar flow through a circular pipe, obtain an expression for the velocity distribution. [AU, Nov / Dec - 2012]
- 83. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 31 2.81) A circular and a square pipe are of equal sectional area. For the same flow rate, determine which section will lead to a higher value of Reynolds number. [AU, Nov / Dec - 2011] 2.82) A 20cm diameter pipe 30km long transport oil from a tanker to the shore at 0.01m3 /s. Find the Reynolds number to classify the flow. Take the viscosity μ = 0.1 Nm/s2 and density ρ = 900 kg/m3 for oil. [AU, April / May - 2003] 2.83) Find the loss of head when a pipe of diameter 200 mm is suddenly enlarged to a diameter 0f 400 mm. Rate of flow of water through the pipe is 250 litres/s. [AU, April / May - 2010] PART - B 2.84) What are the various types of fluid flows? Discuss [AU, Nov / Dec - 2010] 2.85) Define minor losses. How they are different from major losses? [AU, May / June - 2009] 2.86) Discuss on various minor losses in pipe flow. [AU, Nov / Dec - 2013] 2.87) Discuss on minor losses in pipe flow. [AU, Nov / Dec - 2014] 2.88) Which has a greater minor loss co-efficient during pipe flow: gradual expansion or gradual contraction? Why? [AU, April / May - 2008] 2.89) Derive Chezy’s formula for loss of head due to friction in pipes. [AU, Nov / Dec - 2012] 2.90) What is the hydraulic gradient line? How does it differ from the total energy line? Under what conditions do both lines coincide with the free surface of a liquid? [AU, April / May - 2008] 2.91) Write notes on the following: Concept of boundary layer. Hydraulic gradient Moody diagram. 2.92) Briefly explain Moody’s diagram regarding pipe friction [AU, May / June - 2014] 2.93) Describe the Moody's chart. [AU, Nov / Dec - 2014] 2.94) For a flow of viscous fluid flowing through a circular pipe under laminar flow conditions, show that the velocity distribution is a parabola. And also show that the average velocity is half of the maximum velocity. [AU, May / June - 2013]
- 84. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 32 2.95) For flow of viscous fluids through an annulus derive the following expressions: Discharge through the annulus. Shear stress distribution. [AU, May / June – 2007, 2012] 2.96) For a laminar flow through a pipe line, show that the average velocity is half of the maximum velocity. 2.97) Prove that the Hagen-Poiseuille’s equation for the pressure difference between two sections 1 and 2 in a pipe is given by with usual notations. 2.98) Derive Hagen – Poiseuille’s equation and state its assumptions made. [AU, Nov / Dec - 2005] 2.99) Derive Hagen – Poiseuille’s equation [AU, Nov / Dec - 2008] 2.100) Obtain the expression for Hagen – Poiseuille’s flow. Deduce the condition of maximum velocity. [AU, Nov / Dec - 2007] 2.101) Give a proof a Hagen – Poiseuille’s equation for a fully – developed laminar flow in a pipe and hence show that Darcy friction coefficient is equal to 16/Re, where Re is Reynold’s number. [AU, May / June - 2012] 2.102) Derive an expression for head loss through pipes due to friction. [AU, April / May - 2010] 2.103) Explain Reynold’s experiment to demonstrate the difference between laminar flow and turbulent flow through a pipe line. 2.104) Derive Darcy - Weisbach formula for calculating loss of head due to friction in a pipe. [AU, Nov / Dec - 2011] 2.105) Derive Darcy - Weisbach formula for head loss due to friction in flow through pipes. [AU, Nov / Dec - 2005] 2.106) Obtain expression for Darcy – Weisbach friction factor f for flow in pipe. [AU, May / June - 2012] 2.107) Explain the losses of energy in flow through pipes. [AU, Nov / Dec - 2009] 2.108) Derive an expression for Darcy – Weisbach formula to determine the head loss due to friction. Give an expression for relation between friction factor ‘f’ and Reynolds’s number ‘Re’ for laminar and turbulent flow. [AU, April / May - 2003] 2.109) Prove that the head lost due to friction is equal to one third of the total head at inlet for maximum power transmission through pipes. [AU, Nov / Dec - 2008]
- 85. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 33 2.110) Show that for laminar flow, the frictional loss of head is given by hf= 8 fLQ2 /gπ2 D5 [AU, Nov / Dec - 2009] 2.111) Derive Euler’s equation of motion for flow along a stream line. What are the assumptions involved. [AU, Nov / Dec - 2009] 2.112) A uniform circular tube of bore radius R1 has a fixed co axial cylindrical solid core of radius R2. An incompressible viscous fluid flows through the annular passage under a pressure gradient (-∂p/∂x). Determine the radius at which shear stress in the stream is zero, given that the flow is laminar and under steady state condition. [AU, May / June - 2009] 2.113) If the diameter of the pipe is doubled, what effect does this have on the flow rate for a given head loss for laminar flow and turbulent flow. [AU, April / May - 2011] 2.114) Derive an expression for the variation of jet radius r with distance y downwards for a jet directed downwards. The initial radius is R and the head of fluid is H. [AU, Nov / Dec - 2011] 2.115) Distinguish between pipes connected in series and parallel. [AU, Nov / Dec - 2005] 2.116) Discuss on hydraulic and energy gradient. [AU, Nov / Dec - 2014] 2.117) Determine the equivalent pipe corresponding to 3 pipes in series with lengths and diameters l1, l2, l3, d1, d2, d3 respectively. [AU, Nov / Dec - 2009] 2.118) For sudden expansion in a pipe flow, work out the optimum ratio between the diameter of before expansion and the diameter of the pipe after expansion so that the pressure rise is maximum. [AU, May / June - 2012] 2.119) Obtain the condition for maximum power transmission through a pipe line. 2.120) Explain stream lines, path lines and flow net. [AU, Nov / Dec - 2012] 2.121) What are the uses and limitations of flow net? [AU, May / June - 2009] 2.122) Briefly explain about boundary layer separation. [AU, Nov / Dec - 2008] 2.123) Explain on boundary layer separation and its control. 2.124) Considering a flow over a flat plate, explain briefly the development of hydrodynamic boundary layer. [AU, Nov / Dec - 2010] 2.125) Discuss in detail about boundary layer thickness and separation of boundary layer. [AU, April / May - 2011]
- 86. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 34 2.126) What is boundary layer and write its types of thickness? [AU, April / May - 2003] 2.127) Explain in detail Drag and lift coefficients Boundary layer thickness Boundary layer separation Navier’s – strokes equation. [AU, May / June - 2012] 2.128) In a water reservoir flow is through a circular hole of diameter D at the side wall at a vertical distance H from the free surface. The flow rate through an actual hole with a sharp-edged entrance (kL = 0.5) will be considerably less than the flow rate calculated assuming frictionless flow. Obtain a relation for the equivalent diameter of the sharp-edged hole for use in frictionless flow relations. [AU, Nov / Dec - 2011] 2.129) Define : Boundary layer thickness(δ); Displacement thickness(δ* ); Momentum thickness(θ) and energy thickness(δ** ). [AU, April / May - 2010] 2.130) Briefly explain the following terms Displacement thickness Momentum thickness Energy thickness [AU, May / June - 2014] 2.131) Find the displacement thickness momentum thickness and energy thickness for the velocity distribution in the boundary layer given by (u/v) = (y/δ), where ‘u’is the velocity at a distance ‘y’ from the plate and u=U at y=δ, where δ = boundary layer thickness. Also calculate (δ* /θ). [AU, Nov / Dec - 2007, April / May - 2010] 2.132) Explain the concept of boundary layer in pipes for both laminar and turbulent flows with neat sketches. [AU, Nov / Dec - 2013] 2.133) What is hydraulic gradient line? How does it differ from the total energy line? Under what conditions do both lines coincide with surface of the liquid? [AU, April / May - 2008] 2.134) Derive an expression for the velocity distribution for viscous flow through a circular pipe. [AU, May / June - 2007]
- 87. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 35 2.135) Write a brief note on velocity potential function and stream function. [AU, May / June - 2009] 2.136) Derive an expression for the velocity distribution for viscous flow through a circular pipe. Also sketch the distribution of velocity cross a section of the pipe. [AU, Nov / Dec - 2011] PROBLEMS 2.137) A 20 cm diameter pipe 30 km long transports oil from a tanker to the shore at 0.01m3 /s. Find the Reynold’s number to classify the flow. Take viscosity and density for oil. 2.138) A pipe line 20cm in diameter, 70m long, conveys oil of specific gravity 0.95 and viscosity 0.23 N.s/m2 . If the velocity of oil is 1.38m/s, find the difference in pressure between the two ends of the pipe. [AU, May / June - 2012] 2.139) Oil of absolute viscosity 1.5 poise and density 848.3kg/m3 flows through a 300mm pipe. If the head loss in 3000 m, the length of pipe is 200m, assuming laminar flow, find (i) the average velocity, (ii) Reynolds’s number and (iii) Friction factor. [AU, May / June - 2012] 2.140) An oil of specific gravity 0.7 is flowing through the pipe diameter 30cm at the rate of 500litres/sec. Find the head lost due to friction and power required to maintain the flow for a length of 1000m. Take γ = 0.29 stokes. [AU, Nov / Dec – 2008, May / June - 2009] 2.141) A pipe line 10km, long delivers a power of 50kW at its outlet ends. The pressure at inlet is 5000kN/m2 and pressure drop per km of pipeline is 50kN/m2 . Find the size of the pipe and efficiency of transmission. Take 4f = 0.02. [AU, Nov / Dec - 2005] 2.142) A lubricating oil flows in a 10 cm diameter pipe at 1 m/s. Determine whether the flow is laminar or turbulent. 2.143) An oil of specific gravity 0.80 and kinematic viscosity 15 x 106 m2 /s flows in a smooth pipe of 12 cm diameter at a rate of 150 lit/min. Determine whether the flow is laminar or turbulent. Also, calculate the velocity at the centre line and the velocity
- 88. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 36 at a radius of 4 cm. What is head loss for a length of 10 m? What will be the entry length? Also determine the wall shear. [AU, Nov / Dec - 2014] 2.144) For the lubricating oil 2 μ = 0.1Ns /m and ρ = 930 kg/m3 . Calculate also transition and turbulent velocities. [AU, April / May - 2011] 2.145) Oil of ,mass density 800kg/m3 and dynamic viscosity 0.02 poise flows through 50mm diameter pipe of length 500m at the rate of 0.19 liters/ sec. Determine Reynolds number of flow Center line of velocity Pressure gradient Loss of pressure in 500m length Wall shear stress Power required to maintain the flow. [AU, May / June - 2012] 2.146) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the center line) is measured to be 6m/s. Determine the velocity at the center of the pipe. [AU, April / May - 2008] 2.147) A pipe 85m long conveys a discharge of 25litres per second. If the loss of head is 10.5m. Find the diameter of the pipe take friction factor as 0.0075. [AU, Nov / Dec - 2009] 2.148) A smooth pipe carries 0.30m3 /s of water discharge with a head loss of 3m per 100m length of pipe. If the water temperature is 20°C, determine diameter of the pipe. [AU, May / June - 2012] 2.149) Water is flowing through a pipe of 250 mm diameter and 60 m long at a rate of 0.3 m3 /sec. Find the head loss due to friction. Assume kinematic viscosity of water 0.012 stokes. 2.150) Consider turbulent flow (f = 0.184 Re-0.2 ) of a fluid through a square channel with smooth surfaces. Now the mean velocity of the fluid is doubled. Determine the change in the head loss of the fluid. Assume the flow regime remains unchanged. What will be the head loss for fully turbulent flow in a rough pipe? [AU, Nov / Dec - 2013] 2.151) A pipe of 12cm diameter is carrying an oil (μ = 2.2 Pa.s and ρ = 1250 kg/m3 ) with a velocity of 4.5 m/s. Determine the shear stress at the wall surface of the pipe,
- 89. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 37 head loss if the length of the pipe is 25 m and the power lost. [AU, Nov / Dec - 2011] 2.152) Find the head loss due to friction in a pipe of diameter 30cm and length 50cm, through which water is flowing at a velocity of 3m/s using Darcy’s formula. [AU, Nov / Dec - 2008] 2.153) For a turbulent flow in a pipe of diameter 300 mm, find the discharge when the center-line velocity is 2.0 m/s and the velocity at a point 100 mm from the center as measured by pitot-tube is 1.6 m/s. [AU, April / May - 2010] 2.154) A laminar flow is taking place in a pipe of diameter 20cm. The maximum velocity is 1.5m/s. Find the mean velocity and radius at which this occurs. Also calculate the velocity at 4cm from the wall pipe. [AU, May / June - 2009] 2.155) Water is flowing through a rough pipe of diameter 60 cm at the rate of 600litres/second. The wall roughness is 3 mm. Find the power loss for 1 km length of pipe. 2.156) Water flows in a 150 mm diameter pipe and at a sudden enlargement, the loss of head is found to be one-half of the velocity head in 150 mm diameter pipe. Determine the diameter of the enlarged portion. 2.157) A 150mm diameter pipe reduces in diameter abruptly to 100mm diameter. If the pipe carries water at 30 liters per second, calculate the pressure loss across the contraction. The coefficient of contraction as 0.6. [AU, Nov / Dec - 2012] 2.158) A pipe line carrying oil of specific gravity 0.85, changes in diameter from 350mm at position 1 to 550mm diameter to a position 2, which is at 6m at a higher level. If the pressure at position 1 and 2 are taken as 20N/cm2 and 15N/cm2 respectively and discharge through the pipe is 0.2m3 /s. Determine the loss of head. [AU, May / June - 2007] 2.159) A pipe line carrying oil of specific gravity 0.87, changes in diameter from 200mm at position A to 500mm diameter to a position B, which is at 4m at a higher level. If the pressure at position A and B are taken as 9.81N/cm2 and 5.886N/cm2 respectively and discharge through the pipe is 200 litres/s. Determine the loss of head and direction of flow. [AU, Nov / Dec - 2008] 2.160) A 30cm diameter pipe of length 30cm is connected in series to a 20 cm diameter pipe of length 20cm to convey discharge. Determine the equivalent length of pipe
- 90. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 38 diameter 25cm, assuming that the friction factor remains the same and the minor losses are negligible. [AU, April / May - 2003] 2.161) A pipe of 0.6m diameter is 1.5 km long. In order of augment the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. Neglecting minor losses. Find the increase in discharge, if friction factor f= 0.04. The head at inlet is 40m. [AU, Nov / Dec – 2004, 2005, 2012] 2.162) A pipe of 10 cm in diameter and 1000 m long is used to pump oil of viscosity 8.5 poise and specific gravity 0.92 at the rate of1200 lit./min. The first 30 m of the pipe is laid along the ground sloping upwards at 10° to the horizontal and remaining pipe is laid on the ground sloping upwards 15° to the horizontal. State whether the flow is laminar or turbulent? Determine the pressure required to be developed by the pump and the power required for the driving motor if the pump efficiency is 60%. Assume suitable data for friction factor, if required. [AU, Nov / Dec - 2010] 2.163) Oil with a density of 900 kg/m3 and kinematic viscosity of 6.2 × 10-4 m2 /s is being discharged by a 6 mm diameter, 40 m long horizontal pipe from a storage tank open to the atmosphere. The height of the liquid level above the center of the pipe is 3 m. Neglecting the minor losses, determine the flow rate of oil through the pipe. [AU, Nov / Dec - 2011] 2.164) Oil at 27°C (ρ = 900 kg/m3 and µ = 40 centi poise) is flowing steadily in a 1.25cm diameter 40m long During the flow, the pressure at the pipe inlet and exit is measured to be 8.25 bar and 0.95 bar, respectively. Determine the flow rate of oil through the pipe assuming the pipe is [AU, Nov / Dec - 2014] Horizontal, Inclined 20º upward, and Inclined 20º downward. 2.165) The velocity of water in a pipe 200mm diameter is 5m/s. The length of the pipe is 500m. Find the loss of head due to friction, if f = 0.008. [AU, Nov / Dec - 2005] 2.166) A 200mm diameter (f = 0.032) 175m long discharges a 65mm diameter water jet into the atmosphere at a point which is 75m below the water surface at intake. The entrance to the pipe is reentrant with ke = 0.92 and the nozzle loss coefficient is 0.06. Find the flow rate and the pressure head at the base of the nozzle. [AU, April / May - 2011]
- 91. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 39 2.167) A pipe line 2000m long is used for power transmission 110kW is to be transmitted through a pipe in which water is having a pressure of 5000kN/m2 at inlet is flowing. If the pressure drop over a length of a pipe is 1000kN/m2 and coefficient of friction is 0.0065, find the diameter of the pipe and efficiency of transmission. [AU, May / June - 2012] 2.168) A horizontal pipe of 400 mm diameter is suddenly contracted to a diameter of 200 mm. The pressure intensities in the large and small pipe are given as 15 N/cm2 and 10 N/cm2 respectively. Find the loss of head due to contraction, if Cc = 0.62, determine also the rate of flow of water. 2.169) A horizontal pipe line 40 m long is connected to a water tank at one end and discharges freely into the atmosphere at the other end. For the first 25 m of its length from the tank, the pipe is 150 mm diameter and its diameter is suddenly enlarged to 300 mm. The height of water level in the tank is 8 m above the centre of the pipe. Considering all losses of head which occur, determine the rate of flow. Take f = 0.01 for both sections of the pipe. [AU, May / June - 2013] 2.170) A 15cm diameter vertical pipe is connected to 10cm diameter vertical pipe with a reducing socket. The pipe carries a flow of 100 l/s. At a point 1 in 15cm pipe gauge pressure is 250kPa. At point 2 in the 10cm pipe located 1m below point 1 the gauge pressure is 175kPa. Find weather the flow is upwards /downwards Head loss between the two points [AU, Nov / Dec - 2008] 2.171) The rate of flow of water through a horizontal pipe is 0.25 m3 /sec. The diameter of the pipe, which is 20 cm, is suddenly enlarged to 40 cm. The pressure intensity in the smaller pipe is 11.7 N/cm2 . Determine the loss of head due to sudden enlargement and pressure intensity in the larger pipe, power loss due to enlargement. [AU, May / June - 2009] 2.172) In a city water supply systems, water is flowing through a pipe line 30cm in diameter. The pipe diameter is suddenly reduced to 20cm. estimate the discharge through the pipe if the difference across the sudden contraction is 5kPa. [AU, April / May - 2015] 2.173) A 45° reducing bend is connected to a pipe line. The inlet and outlet diameters of the bend being 600mm and 300mm respectively. Find the force exerted by water
- 92. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 40 on the bend, if the intensity of pressure at inlet to bend is 8.829N/cm2 and the rate of flow of water is 600 liters/s. [AU, Nov / Dec - 2007] 2.174) Horizontal pipe carrying water is gradually tapering. At one section the diameter is 150mm and the flow velocity is 1.5m/s. If the drop pressure is 1.104bar is reduced section, determine the diameter of that section. If the drop is 5kN/m2 , what will be the diameter – Neglect the losses? [AU, Nov / Dec - 2009] 2.175) The rate of flow of water through a horizontal pipe is 0.3m3 /sec. The diameter of the pipe, which is 25cm, is suddenly enlarged to 50 cm. The pressure intensity in the smaller pipe is 14N/cm2 . Determine the loss of head due to sudden enlargement, pressure intensity in the larger pipe power lost due to enlargement. [AU, Nov / Dec - 2003] 2.176) Water at 15°C ( ρ =999.1 kg/m3 andμ = 1.138 x 10-3 kg/m. s) is flowing steadily in a30-m-long and 4 cm diameter horizontal pipe made of stainless steel at a rate of 8 L/s. Determine (i) the pressure drop, (ii) the head loss, and (iii) the pumping power requirement to overcome this pressure drop. Assume friction factor for the pipe as 0.015. [AU, April / May - 2008] 2.177) The discharge of water through a horizontal pipe is 0.25m3/s. The diameter of above pipe which is 200mm suddenly enlarges to 400mm at a point. If the pressure of water in the smaller diameter of pipe is 120kN/m2 , determine loss of head due to sudden enlargement; pressure of water in the larger pipe and the power lost due to sudden enlargement. [AU, May / June - 2009] 2.178) A pipe of varying sections has a sectional area of 3000, 6000 and 1250 mm2 at point A, B and C situated 16 m, 10 m and 2 m above the datum. If the beginning of the pipe is connected to a tank which is filled with water to a height of 26 m above the datum, find the discharge, velocity and pressure head at A, B and C. Neglect all losses. Take atmospheric pressure as 10 m of water. 2.179) An existing 300mm diameter pipeline of 3200m length connects two reservoirs having 13m difference in their water levels. Calculate the discharge Q1. If a parallel pipe 300mm in diameter is attached to the last 1600m length of the above existing pipe line, find the new discharge Q2. What is the change in discharge? Express it as a % of Q1. Assume friction factor f = 0.14 in Darcy – Weisbach formula. [AU, May / June - 2009]
- 93. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 41 2.180) Two reservoirs with a difference in water surface elevation of 15 m are connected by a pipe line ABCD that consists of three pipes AB, BC and CD joined in series. Pipe AB is 10 cm in diameter, 20 m long and has f = 0.02. Pipe BC is of 16 cm diameter, 25 m long and has f = 0.018. Pipe CD is of 12 cm diameter, 15 m long and has f = 0.02. The junctions with the reservoirs and between the pipes are abrupt. (a) Calculate the discharge (b) What difference in reservoir elevation is necessary to have a discharge of 20 litres/sec? Include all minor losses. 2.181) Two tanks of fluid ( ρ = 998 kg/m3 and µ = 0.001 kg/ms.) at 20°C are connected by a capillary tube 4 mm in diameter and 3.5 m long. The surface of tank 1 is 30 cm higher than the surface of tank 2. Estimate the flow rate in m3 /h. Is the flow laminar? For what tube diameter will Reynolds number be 500? [AU, Nov / Dec - 2013] 2.182) Three pipes of 400mm, 350mm and 300mm diameter connected in series between two reservoirs. With difference in level of 12m. Friction factor is 0.024, 0.021 and 0.019 respectively. The lengths are 200m, 300m and 250m. Determine flow rate neglecting the minor losses. [AU, Nov / Dec - 2009] 2.183) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths450 m, 255 m and 315 m respectively are connected in series. The difference in water surface levels in two tanks is 18 m. Determine the rate of flow of water if coefficients of friction are 0.0075, 0.0078and 0.0072 respectively considering: the minor losses and by neglecting minor losses. [AU, Nov / Dec - 2011] 2.184) Three pipes of diameters 300 mm, 200 mm and 400 mm and lengths 300 m, 170 m and 210 m respectively are connected in series. The difference in water surface levels in two tanks is 12 m. Determine the rate of flow of water if coefficients of friction are 0.005, 0.0052 and 0.0048 respectively considering: the minor losses and by neglecting minor losses [AU, May / June– 2012] 2.185) Three pipes connected in series to make a compound pipe. The diameters and lengths of pipes are respectively, 0.4m, 0.2m, 0.3m and 400m, 200m, 300m. The ends of the compound pipe are connected to 2 reservoirs whose difference in water levels is 16m. The friction factor for all the pipes is same and equal to 0.02. The coefficient of contraction is 0.6. Find the discharge through the compound pipe if,
- 94. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 42 minor losses are negligible. Also find the discharge if minor losses are included. [AU, Nov / Dec - 2010] 2.186) A compound piping system consists of 1800 m of 0.5 m, 1200 m of 0.4 m and 600 m of 0.3 m new cast-iron pipes connected in series. Convert the system to (i) an equivalent length of0.4 m diameter pipe and (ii) an equivalent size of pipe of 3600 m length. [AU, April / May - 2003] 2.187) A 100m long pipe line of 300mm in diameter contains two 90º elbows and two gate valves (wide open). Calculate the equivalent pipe length and total loss of head when the flow rate is 0.5m3 /s, f = 0.005, and the pipe has a sharp entry and exit. [AU, April / May - 2015] 2.188) A pipe line of 600 mm diameter is 1.5 km long. To increase the discharge, another line of the same diameter is introduced parallel to the first in the second half of the length. If f = 0.01 and head at inlet is 30 m, calculate the increase in discharge. 2.189) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another line of same diameter is introduced in parallel to the first in second half of the length. Neglecting the minor losses, find the increase in discharge if 4f = 0.04. The head at inlet is 30cm. [AU, April / May - 2011] 2.190) A pipe line of 0.6m diameter is 1.5Km long. To increase the discharge, another line of same diameter is introduced in parallel to the first in second half of the length. Neglecting the minor losses, find the increase in discharge if Darcy’s friction factor 0.04. The head at inlet is 300mm. [AU, April / May - 2015] 2.191) Two pipes of 15cm and 30cm diameters are laid in parallel to pass a total discharge of 100 litres per second. Each pipe is 250m long. Determine discharge through each pipe. Now these pipes are connected in series to connect two tanks 500m apart, to carry same total discharge. Determine water level difference between the tanks. Neglect the minor losses in both cases, f=0.02 fn both pipes. [AU, May / June - 2007] 2.192) Two pipes of diameter 40 cm and 20 cm are each 300 m long. When the pipes are connected in series and discharge through the pipe line is0.10 m3 /sec, find the loss of head incurred. What would be the loss of head in the system to pass the same total discharge when the pipes are connected in parallel? Take f = 0.0075 for each pipe. [AU, May / June – 2007, 2012, Nov / Dec - 2010]
- 95. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 43 2.193) A main pipe divides into two parallel pipes, which again forms one pipe. The length and diameter for the first parallel pipe are 2000m and 1m respectively, while the length and diameter of second parallel pipe are 200m and 0.8m respectively. Find the rate of flow in each parallel pipe, if total flow in the main is 3m3 /s. The coefficient of friction for each parallel pipe is same and equal to 0.005. [AU, May / June - 2007] 2.194) The main pipe is divided into two parallel pipes which again forms one pipe, the first parallel pipe has length of 1000 m and diameter of 0.8 m. The second parallel pipe has length of 1000 m and diameter of 0.6 m. The coefficient friction for each parallel pipe is 0.005. If the total rate of flow in the main pipe is 2 m3 /sec, find the rate of flow in each parallel pipe. [AU, May / June - 2014] 2.195) For a town water supply, a main pipe line of diameter 0.4 m is required. As pipes more than 0.35m diameter are not readily available, two parallel pipes of same diameter are used for water supply. If the total discharge in the parallel pipes is same as in the single main pipe, find the diameter of parallel pipe. Assume co-efficient of discharge to be the same for all the pipes. [AU, April / May - 2010] 2.196) Two pipes of identical length and material are connected in parallel. The diameter of pipe A is twice the diameter of pipe B. Assuming the friction factor to be the same in both cases and disregarding minor losses, determine the ratio of the flow rates in the two pipes. [AU, April / May - 2008] 2.197) A pipe line 30cm in diameter and 3.2m long is used to pump up 50Kg per second of oil whose density is 950 Kg/m3 and whose kinematic viscosity is 2.1 strokes, the center of the pipe line at the upper end is 40m above than the lower end. The discharge at the upper end is atmospheric. Find the pressure at the lower end and draw the hydraulic gradient and total energy line. [AU, April / May - 2011] 2.198) Two water reservoirs A and B are connected to each other through a 50 m long, 2.5 cm diameter cast iron pipe with a sharp-edged entrance. The pipe also involves a swing check valve and a fully open gate valve. The water level in both reservoirs is the same, but reservoir A is pressurized by compressed air while reservoir B is open to the atmosphere. If the initial flow rate through the pipe is 1.5 l/s, determine the absolute air pressure on top of reservoir A. Take the water temperature to be 25°C. [AU, Nov / Dec - 2011]
- 96. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 44 2.199) When water is being pumped is a pumping plant through a 600mm diameter main, the friction head was observed as 27m. In order to reduce the power consumption, it is proposed to lay another main of appropriate diameter along the side of existing one, so that the two pipes will work in parallel for the entire length and reduce the friction head to 9.6m only. Find the diameter of the new main if with the exception of diameter; it is similar to the existing one in all aspects. [AU, Nov / Dec - 2007] 2.200) Kerosene (SG = 0.810) at a temperature of 22ºC flows in a 75-mm diameter smooth brass pipeline at a rate of 0.90 lit/s. Find the friction head loss per meter, For the same head loss, what would be the flow rate if the temperature of the kerosene were raised to 40°C? [AU, Nov / Dec - 2014] 2.201) Determine the Pressure gradient The shear stress at the two horizontal parallel plates and Discharge per meter width for the laminar flow of oil with maximum velocity 2m/s between two horizontal parallel fixed plates which are 10cm apart. Given μ = 2.4525 Ns/m2 [AU, April / May - 2011] 2.202) In fully developed laminar flow in a circular pipe, the velocity at R/2 (midway between the wall surface and the centerline) is measured to be 6 m/s. Determine the velocity at the center of the pipe. [AU, April / May - 2008] 2.203) A smooth two –dimensional flat plate is exposed to a wind velocity of 100 km/h. If laminar boundary layer exists up to a value of Rexequal to 3 x 105 , find the maximum distance up to which laminar boundary layer exists and find its maximum thickness. Assume kinematic viscosity of air as 1.49 x 10-5 m2 /sec. [AU, April / May - 2003] 2.204) Air is flowing over a flat plate with a velocity of 5 m/s. The length of the plate is 2.5 m and width 1 m. The kinematic viscosity of air is given as 0.15 x 10-4 m2 /s. Find the (i) boundary layer thickness at the end of plate (ii) shear stress at 20 cm from the leading edge (iii) shear stress at 175 cm from the leading edge (iv) Drag force on one side of the plate.
- 97. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 45 (v) Take the velocity profile 𝑢 𝑈 = 3 2 ( 𝑦 𝛿 ) − 1 2 ( 𝑦 𝛿 ) 3 over a plate as and the density of air1.24 kg/m3 . 2.205) A plate of 600mm length and 400mm wide is immersed in a fluid of specific gravity 0.9 and kinematic viscosity of = 10-4 m2 /s. The fluid is moving with velocity of 6m/s. Determine Boundary layer thickness Shear stress at the end of the plate Drag force on one side of the plate. [AU, Nov / Dec - 2012] 2.206) Water at 20° C enters a pipe with a uniform velocity (U) of 3m/s. What is the distance at which the transition (x) occurs from a laminar to a turbulent boundary layer? If the thickness of this initial laminar boundary layer is given by 4.91√(vx/U) what is its thickness at the point of transition?(v – kinematic viscosity). [AU, April / May - 2011] 2.207) A flat plate 1.5 m x 1.5 m moves at 50 km/h in stationary air of density 1.15 kg/m3 . If the co-efficient of drag and lift are 0.15 and 0.75 respectively, determine the (i) Lift force (ii) Drag force (iii) The resultant force and (iv) The power required to set the plate in motion. [AU, Nov / Dec - 2007] 2.208) A jet plane which weighs 29430 N and has the wing area of 20m2 flies at the velocity of 250km/hr. When the engine delivers 7357.5kW. 65% of power is used to overcome the drag resistance of the wing. Calculate the coefficient of lift and coefficient of drag for the wing. Take density of air = 1.21 kg/m3 [AU, May / June - 2009] 2.209) For the velocity profile in laminar boundary layer as u/U = 3/2 (y/δ)-1/2(y/δ)3 . Find the thickness of the boundary layer and shear stress, 1.8m from the leading edge of a plate. The plate is 2.5 m long and 1.5 m wide is placed in water, which is moving with a velocity of 15 cm/sec. Find the drag on one side of the plate if the viscosity of water is 0.01 poise. [AU, Nov / Dec - 2003]
- 98. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 46 2.210) Consider flow of oil through a pipe of 0.3m diameter. The velocity distribution is parabolic with maximum velocity of 3 m/s at the pipe centre. Estimate the shear stress at the pipe wall and within the fluid 50mm from the pipe wall. The viscosity of the oil is 1.7Pa.s. [AU, Nov / Dec - 2012] 2.211) The velocity distribution in the boundary layer is given by u/U = y/δ, where u is the velocity at the distance y from the plate u = U at y = δ, δ being boundary layer thickness. Find the displacement thickness, momentum thickness and energy thickness. [AU, April / May - 2010] 2.212) If the velocity distribution in a laminar boundary layer over a flat plate is given by 𝑢/𝑈∞ = sin(𝜋/2 𝑦 /𝛿), calculate the value of 𝛿, 𝛿∗ , 𝜃 and shear stress. [AU, April / May - 2015] 2.213) Water at 20°C flow through a 160mm diameter pipe with roughness of 0.016 mm. If the mean velocity is 6 m/s, what is the nominal thickness of the viscous sub- layer? What will be the viscous sub -layer if the velocity is increased to 7.2 m/s? [AU, Nov / Dec - 2014] 2.214) The flow rate in a 260mm diameter pipe is 220 litres/sec. The flow is turbulent, and the centerline velocity is 4.85m/s. Plot the velocity profile, and determine the head loss per meter of pipe. [AU, April / May - 2011] 2.215) An oil of viscosity 0.9Pa.s and density 900kg/m3 flows through a pipe of 100mm diameter. The rate of pressure drop for every meter length of pipe is 25kPa. Find the oil flow arte, drag force per meter length, pumping power required to maintain the flow over a distance of 1km, velocity and shear stress at 15, from the pipe wall. [AU, Nov / Dec - 2010] 2.216) Consider the flow of a fluid with viscosity m through a circular pipe. The velocity profile in the pipe is given as where is the maximum flow velocity, which occurs at the centerline; r is the radial distance from the centerline; is the flow velocity at any position r; and R is the Reynold's number. Develop a relation for the drag force exerted on the pipe wall by the fluid in the flow direction per unit length of the pipe. [AU, April / May - 2008]
- 99. R.M.K COLLEGE OF ENGG AND TECH / AQ / R2013/ CE6451 / III / MECH / JUNE 2015 – NOV 2015 CE6451 – FLUID MECHANICS AND MACHINERY QUESTION BANK by ASHOK KUMAR.R (AP / Mech) 47 2.217) Velocity components in flow are given by U = 4x, V = -4y. Determine the stream and potential functions. Plot these functions for φ 60, 120, 180, and 240 and Ф 0, 60, 120, 180, +60, +120, +180. Check for continuity. [AU, Nov / Dec - 2009] 2.218) A fluid of specific gravity 0.9 flows along a surface with a velocity profile given by v = 4y - 8y3m/s, where y is in m. What is the velocity gradient at the boundary? If the kinematic viscosity is 0.36S, what is the shear stress at the boundary? [A.U. Nov / Dec - 2008] 2.219) In a two dimensional incompressible flow the fluid velocities are given by u = x – ay and v = - y – 4x. Show that the velocity potential exists and determine its form. Find also the stream function. [AU, May / June - 2009] 2.220) A smooth flat plate with a sharp leading edge is placed along a free stream of water flowing at 3m/s. Calculate the distance from the leading edge and the boundary thickness where the transition from laminar to turbulent- flow may commence. Assume the density of water as 1000 kg/m3 and viscosity as 1centipoise. [AU, April / May - 2011] 2.221) A smooth two dimensional flat plate is exposed to a wind velocity of 100 km/hr. If laminar boundary layer exists up to a value of RN = 3 x105 , find the maximum distance up to which laminar boundary layer persists and find its maximum thickness. Assume kinematic viscosity of air as 1.49x10-5 m2 /s. [AU, Nov / Dec - 2008] 2.222) A power transmission pipe 10 cm diameter and 500 m long is fitted with a nozzle at the exit, the inlet is from a river with water level 60 m above the discharge nozzle. Assume f = 0.02, calculate the maximum power which can be transmitted and the diameter of nozzle required. [AU, Nov / Dec - 2008] umax u(r) = umax(1-r / R )n n R r o