solu0002

solu0002 - ( 5 C 33"3%)7 5 5 9 5 5 9 5 (...

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Unformatted text preview: ( 5 C 33"3%)7 5 5 9 5 5 9 5 ( 3tq5" ( C s r I s tuW Y p ` b si Y "3R d "V b DQ e )I Dc v c d %a's b D%"V c I b 3%IS)I cDc"b t%I c s b )3RDV V h r r I S H eb i RV s RH R V iH R h Q i H c b iH i R R H d i R S RV s H r R s R H s R H R p H v s R r I RV i HV S V H V R P V i v S R H c tr 3D%as%Rq3ut"VAI Y %s b 3iq%)ut"Vg1D)"as c I3R d ID3R"VD3's b V b%c I b 3"QHI e )I e R1y E "! ( 5 C 5 ( C 33"3%)7 5 5 9 5 5 9 5 ( 3tq5" ( C H R h h s r H I R p h P R f S I e d cb ` Y Y %aiut%R c qi3gU)H DaX W V R T %USDP)G RQ I H F F C - Solution EDB@A7 C! 3583"321)'$ 9 7 6 5 4 ( 0 ( & $ %#"!" h 2 2 x(t) DS DS s Sewer Sewer 1 E "! Surge Surge y y F DM DM 1 1 5 ( C V vQ I w xc I b "T Y W 5 5 3%01) '&%$# "! 2 " # $(! V i v R w xc I b tDV b v "b V c I c s b 3"trqR 3i c i H RV i S v s s R tr 3% d uQ V R R s I I c s b V b v c I V d "VqR R RQ s R H h S Y "P b s)I Db c RH v R R S vQ Q H R V R c Db T Y p be "V cDb "I%I)"V c I "qR3T s I h I pH v c I b V b V c )H e RT R V DHI e V " S b s X s V v I P i QQ s i R H i R V i i V H RQQ S s v S R H i R Q R s R V s VH i Y " S X tDDi b Pq)t%DV DV c "A3""3i q)'s%%D3uS%D'R"Q b 3h "b v"Q e d R R h s QQ i v R R p v I I R H R R h s V R P S R S R H R P S i Q i RH d tD"3"V iqDV Hs e V c H e VI ed 3's b s b DH%3%H %v c p b Pqt"DQ%'s b s d 3usqpqDV 3X Q c ii 3 b )tHusqV c tr c I b Va "V cD"e DQ b It R R h R H v s R R I S V s R H H i R p v R R s R v R r v b b d cb Q S i R V Y 33)H"as c rI d d RDQ b q%DV %Das c I d r"Q e D)i P Q r RH R S i RHV r I R V H H I H R r R R "VA3q3sqDV e t"V b hai DV I i R R eb DV D% R s b "Q b Wq" c 333DQ3Dtq2 H Q r RQ I i S V i Q R R H RV i r R ID's b V I V b V bDb us b %"I "D3i "b p b Wq" c U)H e 3I V b sqtr rH R V QQ c H I RQ I i S S I s R S R S v s i R e R F F C - Solution EDB@A7 C! 3583"321)'$ 9 7 6 5 4 ( 0 ( & complicated. R"Hh c i d H V i p i h I R S R pH v us d Q R H b c i c 3t%tDQ"3i3)'s Db )H d I R P i R I"3i X c S H e s3I sQ RQ I i S I R S s R S 3I i H i R R cDb )t33qDV c Rgf $ %#"!" 0= d L A1 dx - A2V2 + A1V1 0 dt x dx dx = A2 - A1 - A2V2 + A1V1 dt dt = A2 (c - V2 ) - A1 (c - V1 ) d dV + (V n ) dA dt CV CS = d dt Fx = fo x A2,V2,P2 A2 dx + d Vd V + V (V n ) dA dt CV CS 6 6 P2 - P1 - S 2 - S1 + G = 2 x d dt x S2 A2Vdx + 7 0 x d dt x L A1Vdx - A2V22 + A1V12 2 7 4 S1 L-x C.V. 1 A1,V1,P1 s "x&n$@s62p6um&Ht"u&"vv6u&2nk ki kxl vuv ktur q { j l l s ~~w { {r vl l m po l kx s ~ | { zi mp o m l m po l kxw v u nti s olnri m l m po l k m $&o@"o&kA"uq&n$I}"o@Al6nlol6yqn&$A@"lAIFAlq&n4&lkji 8 dV = A2 x 2 + ( A2 - A1 )c 2 - A2V22 + A1V12 dt h AF""d"@4 g fe $$v6&6A"&t&vt w u x S2 = i8$2w8FA@("t x u u t w x w t &A&t&x"62ut62yv&u4s P2 - S 2 = A2 &&#$B&%rE6%@' B #' R 9 # ## # # "@&%"E4%q$E66"@&%# 5 S1 . &!A&$B 3 06&%&(" D "#$!% 5 C&$B&%E64$"# 5 $! 5&5 $BE6 ' # #' B9 !'% 3 3 I 5 C 5 %"#6!U!36$$$U 5 R"8A@'&F"i&# ""' 0 % '% % B 0%! 3 # ! p p Since t flow negle V1 P2 - S 2 = d dt 0 x a 5 ! ' &% # ! 5 ' ' &5 D # 3 E 5 #' ' hA%' &6"% #i5% "@A%!%@"$"%#' "!&&# &! "&# # $ D HAH' &! A #6@F#09 "&"$E' !6%&40 A @%"0&&# # &CC E6 &$B ! 6F 6 # ' % 3 3 R 9 ! 5 R % 5 ' "%"# P62#6A@@6"1%&@9&#! ' Q 0 ' 0% 0 # 0 R ! g @' TB % f # 5 $ $&2!&&# 5 6%69 D @"%H"'9A! Ade ' "F$ 5 &@A!&3bc% 5 $! 6X # # E %! 0 # 3 # @ A! 0 B Y " &$ 6 #B &# &aA" 4 6&%9 E6 "%' RU &5 #42R$E5 $F&IF"' @#" 2!H$#3 I0&6` FA@9 $X5 8 6U% 5 "EHW"6"64# $8" A# ! # "E E ' "% % 5 8 &@% 9 ! # 3 0%!R # ' 3# ' 0%! ' 9 ! 3 ' ! % V@A36% 5 "@A' &!&&"E8"'F@RU5 !%@AC&6F&#&A'&T% 5 5 ' A@'F& 36% 5 S@A3E "' 694%6' #@"0("@2!6$$!6&% "%&# #"C &$B8 E A!@A # ' # % 3B ' E # ' ' I0&# D ' HE62'& 5 ' D @"%2# P062#6AI@06"# D & 5 I"08 5&5 B"# H'"% 5"5 %&2H&'G 0 #! E R ' Q ' 0% 33 E 3 #E ' ' 0 4D&5 # ! B 3 5 ' % % 5 5 3 # # 0% @A% ! !6% ' # &# C EF& $C&&A6 $6% @ A@9' 3 8% 5 !76"#46&% "5 3421)%(!% &%"$"! F F C - Solution EDB@A7 C! dV d d (V2 x) - A1 (V1 x) + A1 L 1 - A2V22 + A1V12 dt dt dt dV dV dV = A2 x 2 + A2V2 c - A1 x 1 - A1V1c + A1 L 1 - A2V22 + A1V12 dt dt dt 3583"321)'$ 9 7 6 5 4 ( 0 ( & $ %#"!" P2 - S 2 = A2 x P2 - A2 (c - V2 ) = A1 (c - V1 ) choose fV22 fV22 P1 , P2 8 Dx = A2 x Dx . uniform. A2Vdx + dV2 + A2V2 c - A1V1 c - A2V22 + A1V12 dt V1 dV2 + A2V2 c - A1V1c - A2V22 + A1V12 dt d dt forces S1 , S 2 G x L ( A2 - A1 )c = A2V2 - A1V1 A1Vdx - A2V22 + A1V12 We . al ational 3 1 al V2 pressure ). P1 es # tl n m j t { zt r v { { l n ! t {o AF&o{@"6u&@2u{&k"6u"i{&2k6t"} "u{"&kuy uj@t "u"{H"tt$6q&nF&o{48x 2u&{Ai61umj u&uHAH$l""y{2t{@t"@u m kipl q { ml u l k w zti t k pl s m j l v o tir l x v r my { l2nkl62t{Is "l@"uk"l8y@&sF&o&k{&o$"n"u"{&kA6A&i2{k&t&F@ m klz v {oou { { l { ml k ux t { z tur v { { oi t ut l (1) (2) 2u{&A6n"@u"t""l2p&k"{k8o t kipl lui l k k { k fV22 8 46z8l&k(o"{ l$$@po8Al i o t l l s oi &n"kq 8i6A@Ar$qo&nki&lkT&uvjij6kA1su"jpU&nkTk r@@u&uk { l t nr ti l mp l m ji u miy m {t l un ut l n p s lA6AzAn@A$Iwe2t{6"n&kF"o@2nk6Azi&lA6"n&"vIsm6$6Au&v&("ok$Alm"8"n@Al6"$@l"ml qtinr v mi tirx s { { yl m ki l k vi utx zlzu j { l ko l k t n vl s k r "t@I@"uk$q6A@A$r "&vA6"p$r 6"u&{AIsut&{Tlj "nk"1l"u6"n$&u@&uk l {o nrp s u l ti nrk u t ti vi k t ki m j { s v my l k l v o un k &"vlm$uF&o{ ut tuz vi l x mlkut Ai AAu6Uqpn"H62t{Ht"$nAF&o{ j zt kiqiy my l m o l k q mpz q {qti r time. W F F C - Solution EDB@A7 C! 3583"321)'$ 9 7 6 5 4 ( 0 ( & $ %#"!" sub P2 = P2 - gh1 A2 = ( A2 - A1 )c12 - A2V22 + A1V12 x gh1 A2 + P2 fV22 x=L 8 ,P2 fV22 dx , dt m j ot kipl { mluq l k u uF"u&{Aq62t6t"n@o V1 , A1 should system. fV 2 fV22 dx D s x + ( A2 - A1 )( ) 2 = gh1 A2 + 2 Ds L + ( A2V22 - A1V12 ) 8 8 dt 2 2 2 ( A2V2 - A1V1 ) - ( A2 - A1 )c1 + gh1 A2 = 0 c= Also, DL - gh1 A2 = A2 L DL + gh1 A2 8 D( L - x) = ( A2 - A1 )c 2 - A2V22 + A1V12 2 don' V2 so S2 x V2 dV2 . dt So, ion (2) t = 0 x = 0. x are, 4 "ti { q l r&t{ t Aln dV2 dt L-x P2 C.V. 1 A1,V1,P1 ,h1=20m ' ! 0 3 # 0 & $112#) ('& % # $ !" F F C - Solution EDB@A7 C! 3583"321)'$ 9 7 6 5 4 ( 0 ( & $ %#"!" s Forc V2 + h1 + z1 = 0 + hC + z C 2g 1 h1 V 2 / 2 g |1 a T 4C TC7 272`Y245X284 (2V$US2HRAI2HREC98AIEG8FE)@A94 W P I 7 H R4 6 T 7 7 5 B 7R I 7B H 6 @ Q 4 P 7 H 7B @ 8 7B D 7 CB 8 8 hC = h1 + ( z1 - z C ) = 20 - 5 = 15m 2 FC = ghC DM / 4 = 1000 9.8 15 3.142 1.0 2 / 4 = 115kN 5 7254 6 ...
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This note was uploaded on 03/19/2012 for the course CIVL 000 taught by Professor Kk during the Spring '10 term at HKUST.

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