E xo.(Yi A c..~ \-3 IY\ EE:N 3L-\~ fq \\ ()_Q I\ !\Ia YY'Ie: OpQ.(t ·uook-,..~-C-io_s_eJ-,.-N-o_t-e._s __ _ \c. (33f>t) A'l \-t-B«~ W\~ 0, voll..{fY'C. 0~ Oo\ ~3 IS critcrc:~,e~ tv o rop&. When S4btn~<2<J r·o water-+he -tenst~t"' o"n t-1-,e. _rotx= Is looo/\1. UJhd1-1s 4e.. s~eci*i<:. ~ \OV1't/ o ~ +he 1 1-e!YI ~Exo.M A Ch \-3 \-+-fe,uo -~~r~ = 0 :r: t.of.i\~1 --( + o 'dV- S .. G.A 9..~ =o ift.O ) H-tl? ./ I1.1.P \J ', . WI~ IOooN+ 994· ~~ 9.~\ ~ (O~! r?)- S.b.(]1'i 1~-~{1/Bi t!Js')(o .. .J:t1;;)~-:~' tv' S .. G. =AI 1'.-...,, (3., ( 3L\ p t ~,; D e-ter-«1 \,n e the n e..t ~ve.,t\c.a \ ~rce o.c;-,n~ on the C..t.Arvd sur\ac€... o.r0 ,·ts \ ,ne o \ act-,'on. ---r\1e ~~te is 7 M w \·Je .. y T XfxatY\ B C~'n 4 S""a0 __) MEEtv 34l..\ Ft.1l \ Qo' \ No. (Yie; ~ --------Open Boo~.., C los~J NoTe.-:::.. L~ (33 p-t-s) G",ve.n ~ s.-rreavY\ ~'u•'lc"tlo•'IS LV\ = (X '-+y ?.)(_ l/.s) and lYz.= ~ (3 fY'/s) c,) W~t-;_s the veloc.•-ty vector? 'a) ::r" s i+e J; /o<v CoYYlpres:s;hle-? c.) Js fhe ~ lcx.u \o-t'"~t-;on_ol? o\) W'ro.t-1s ~e acce\e.ra+,o.-, os;. C{ ~ L..~. ,-J ~ rt"ic....b.~1. ~~-= C 'f.-2 -~r '/7 \)( i/s) \_\)z_:: .2;-( 3 M /'sJ lJ~:: d~y= ay)s 7 d;-1.-\ v= . -~ ~ -·ax/s ) Y.. U)-=:~ :::0 ! (' .~: y 1\ ,. ( r:-\ c r ~)-~ · ··" .:7 ·) \ ' -:-J ' ' .~(3~ pt.s) A Two ~nc~ \ns,c\e J,'at,,e+er f;pe \S ollle3r\Ted ver-t\ca I. A norr\e ,s o:ttoc~ed -t-o the ~~ a\ the ~~pe. 1.<_/h,~h has Clt'l e~fC J. ;qmeter ?~ Oo ~I ;.c.hp .I~ t~e pressvre I f) +he ~ ,r,c__h p 1 pe LS JOO ps ~~ J u.Jha-t-I.S -H,e Sf,<2~ o.f +he wo-re. ex.,T<q +he noz~le a,..,cl \-,0w h~h w, I I 1t shoot-~~ \ ~ = o-ps'f I \ ~~~·('.? tJ \\\ so,-Te.r~. As;su.{Yle ~ Steady Stt:1+e. ~)/,==-~~q '\j/m3 3) NtJ\ee,-r b~/ ~rces l..\) A;tJ le«'ai.I'"S Co~-S;t?:i()+ 011 turn;J. va.Y\e... 5) ~\J~ .sp\ \-T o~ je+ Top! bo;mi'Y\ L<2 Vt-op = VBo~r! b J Un\~o\'f(\ propert,es A+op= AscrttvM eo~T; ft=§)f'd-\1--+ \\;o V.c\A:o ~ -_f VJ 1\)+.fVt-or ~ .. ,vM."' A% cv cs 0 } r Vtvp = "~Ito... . x~m.~ Fs/5£ ~ J{)~~Y~·~J-t!--+)~(v.~)(p\i.dA) ~ C\J ~ ~ = vJ (-.?Va ~ l ~-(-v~ ~L\5") (fl v~ ~) + (-vd C8JL\s~ v/~) = j> v; 1\j ( -1 --k eos 4.s-• - t UoS tlS ·) " '11'11~ (3o,.!s),.'d.c.ro2(r';c,...~ (-l-0.3S"3G-o.3;;-~b) - I I <1. 0 ~a. "'~ M (-1-. 7 0 7) = -30 7 N s~ r ::: -t ( 3 0 7 N) -:: Is 3~ s N .. (Y).. /' ') ~ \ " ' ' ~ Ba.l/ ~--p: D ~I I I I \ I h 1 VI L -1r~d {\--------~-l..-.-...l-._.__,'------'------'--~---~~----Problem 2 T=70 F PI := O·psi ft VI:= 0·-zl := 200·ft zi = 60.96m D := 0.824-in D = 0.021 m Q:= 20·gpm 5 (70-32)·-= 21.1 I I 9 sec erough := 0.0005·ft -4 erough = 1.524 x 10 m z2 := 20·ft p:= 999-~ 3 m Q V2:=--n 2 -·D 4 T = 21 C V2 = I2.033·_!!_ sec 2 v:= 9·10-7-~ sec z2 = 6.096m m ~:= 9.8I·-2 sec V2 = 3.668 m s 2 -6 ft v=9.688x 10 ·-sec V2·D ReD:=--v 4 ReD= 8.529 x IO Turbulent erough -3 --= 7.282 X 10 D [ 1] 6 3 erou h 10 f '~ 0.0055 · I + ( 20000·----t-+ ReD) f = 0.035 Rearranging the pipe flow headloss equation to solve for P2 and determining the head losses for the straight pipe, the fully open globe valve, the four elbows, and the pipe inlet: LeD_Globe_ Valve:= 340 LeD Elbow := 30 K Inlet:= 0.78 Lpipe := 80·ft VI2 V22 ( Lpipe ) V22 P2 :=PI+ p· -----+ g·(zl-z2)-f. --+LeD Globe Valve+ 4·LeD Elbow ·--... 2 2 D --- 2 V22 +(-l)K Inlet·-- 2 P2 = 20.517-psi 5 P2 = 1.415 x IO Pa VI2 V22 m2 ---= -6.726-2 2 2 s 2 m g·(zl-z2) = 538.216-2 s V22 m2 K Inlet·-= 5.246-- 2 2 s VI2 V22 ft2 ---= -72.394·-2 2 2 sec 3 ft2 g·(zl - z2) = 5.793 x 10 ·-2 sec V22 ft2 K Inlet·-= 56.467·--2 2 sec (. )V22 2 Lp1pe m f. --+LeD Globe Valve+ 4·LeD Elbow ·--= 384.641-D - - - 2 2 s (Lpipe ) V22 3 ft2 f. --+LeD Globe Valve+ 4·LeD Elbow ·--= 4.14 x IO ·--D - - - 2 2 sec ~~ 3 --+LeD Globe Valve+ 4·LeD Elbow= 1.625 x 10 D - - -0.(3L\ p-t-:;) /~.~c,~-· '',}. li·l\ f-2-F' 1" COY"''Sih~c..t-ed ·--:-If(> t·u I' c ':·-:· 'I 1..-:r r ~,s'~s.. as s~?'J.Jr. ~~e 1i ··lcr : c, .--. D ..;..-o ~',..-r t' \ ~·-, ..;... I ,...., ,-·· p "''V1 I~"' n , __, l ., I C \ .. ~] (. r r~~, r ~ , ·-\0\:)0 .',Je:;..se \ Cof\t"CIIt'l~V:;I ~r~.ne s; 0~1-t-._ ('rl ( S 6 = !. I ) V t)<9:.ff 1 c c.+-me d. r a a o (' ,! • .,., e r oci s n , · 4 ~.Jv ;'d i ·, · ~ +--, ~ 1·, 1 ~ ~e ~ \ u ;J, be t-err-<1 \A e. the f"E'th,~.~),·rcA t-o ~\\Ve ~e.. rr\;xer, ~ • · .::-:1 11 -~ et:f . -ro,0[..fe. ~~\c\ fowe-r l.lProblem 3 Radius := 0.6·m D:= 100-mm MN w := 60-rpm Cd := 1.17 From Table 9.3 if Re > 1000 U := W· Radius m u = 3.77-s Use kinematic viscosity of water at 21 C 2 -7 m v:= 9·10 ·-IW\ sec kg ,..R,_:= 1.1·999·-3 m U.D ~:=-v 3 kg p = 1.099 X 10 -3 m ReD = 4.189 x I o5 Larger than 1000 so Cd OK A:= 71-D2 A=7.854x 10-3m2 lWV 4 Drag on one disk is then given by: Drag:= Cd·.!..p.if·A 2 Drag= 71.757N Drag= 16.132lbf There are two disks so multiply Drag by 2. Each has a lever arm of 0.6 m = Radius so Torque is then equal to: L= 2·(Radius·Drag) r = 86.109N·m r = 63.511 ft·Ibf Power:= r-w Power= 541.037 W Power=