Unformatted text preview: jRja aIRRjCq} R)q~8aSQ} hU8ijR'8jR~a|eCRpqvaij}R } | } } } } | } } } } } } | } } | } } 3gq}BS~a| q4a Iqg8aaGq8a tjS RRxS p qR } h qx pS! aha|Rt3qaa )S jptq}RR4~ gRpja)aa )S }} ! | } | } } f4}RR}8aRq}a4xIqSaaxBja8~|Bax4}pa } } } q} R)UYSa4}"gBSxRGRjRUR8a4qsI8q"8sq}gRb%tfRSR8xRgRpsa } } } | } a4q}Ba4}"4}Rf84h8Rf8qQ~Cq} ))Qt88aqq}Iv8qQ } | } } } } } " 8GaB4~aRSgqIBaq ))q~4} } | } } } | | }} 4}8xq4 q}8RaRSpSqqIx4)4RR8 } } } } } 44jRtSq8a4j3aRRj8a)~aarqRrR } } } } q8aaRSR | } | | } } j}a4aBg4a}8Stq} ))q~88Bq}a gRb%~qqB q8R"}a}a xa4}I)ea4)I4h}x)Iq}|a8Rjj8q}q} } | } | } }} } } } } }} | } } | } } | j4I)}qRIq~8R8Y)hYBSv8I} hYaS%q} ))q~{ s zt gvWByxutr w v ut s Dw V A o k kd eih f ed (7 X&c Dp 'CW3$"Gqnmbl R'ejWjsgRU"A3Wf`R33()& iy)3RvRP Dx9 &1P 1 3 D( qR3cF7e)f` '3c%)33 33))R3( RIW7e34u3W7 R) D0 3S42tWi3SW7 qR)i&Ri23( iS7)R8g V 5 2& X T c& D w& `& D ( 10&P & DP X c ( 2 ` ( DP2 5 $ $ T 7 & V 5 2P20 X& y V D y 0& WQRW343( DY` )[email protected])& 3gW7WsqR0 Rrq2W$YRP BS7Pa)&R&)I D( T 7 X& V ( 2 c D P0&g ` & 1P ( 7 E 7 7 gP &P H( 2 P2 1P ` y 5 X $ 5 2 DP0 X ` D T ` X P 342HP& DR't3R%( )0 DXGf` Dr)&I3fbR2 3)0 RP R3$` 3siR3)%RP xR42)3Q7)%RFW'wI( &Rvf3RP c ( X2 w & 1P D 1 7` P0 g ` X 5 D X2 D 1 y& 1P 1 D 95 & c P c&E 7 D X2 P2 1 `)& 3$ )3( D4$s3RuhQH RP R3i3qt3W7 RfR D0 3342s0 )aP` D)Rrq2F3)i( 4RP X)RpWi(W7 ff`)ffW'$bRP QhQH RP R3$ 5 D0 X & 1P Hg 5 X2 $ c ( 2 ` ( DP2 5 $ $ D X&P0 X2 10 D 2 &0 T 7 D` &`` 7 ` D Hg 5 X2 c& D`` 5 c (2 c& ( d& A ` X&P V X&& D V ( T 7 D $ 7P H(2 & 5 A 7 5& ( 2 0 & $ )8d [email protected] )034eR38)3c` DbRaP)&R)I( DY3( DR)3( W3)&USG0 3SRQI4GF DE [email protected] )33(431)()'%# !" q g f } qa}GhRfC5 8a Q edc bYW VT a`XU R } SSaq~ 4Qqa}4U4}RRipaRSIIax4qqa} jqRapSRgaia4q8q } }} P } } } | } | | } } a)qR ai4RR}fISj8aRSIax4qqa} 8p8aRWIqgIR R aq} )H } } } | } } (GFugECAtr (9e0 6 x v D 6z B @ s w 86)g4e5zW31)tr 7 s vz t 0 4 2 0 ( w ' Sa4}RRq~8aB4Rj}SB8qjg aaRfpq}x8 } | } } | % % Rfj4IqRYq~Y j} }R4q~8 jps&"j pjs& $ }} } } }} | } } " # S ! S jut "S }aS sq} R)q~8a4qgRSR| ! ! } | } } 4}8eu8e8"4q}Sqa}apqa} |g8qQaq} R4qRh Q8~R8aR4Rh } } } } } } }} } }} | } } | } } } } 4 %8q q4}~Sq8S44}a8RR jqRu8p8gR8)IRj qRR 4~8Rqa}aag4Rh q8g4qIq|b8aaRfSBSuqRR } } | | } }} } } }} } } } | | | } } } } 4"8a%4a}ajRpupRS~auI8gi}bG}aq}%qRi8qq} fpqRSa hx } | } | q~RS8aqqII8Rja j 8a } invert invert invert } } } } 8 ) 4YaaqIYajRQR8aq4Y84RR3P fa4ja48RSq8} } } } SjRS84Iax4q4a}x8R hRpjaBj4}q~4apaj} fSjRS 4x4aq} } } | } |} P } } } } } } | | } 4gIR)j4a}qg}j4qRSaIqgagR Rg4a}q~8aaRSjpg f4RR} } } | qRa pR~8aS4}R 8a } x1 x }} } } hR ~a 4P )paj4}aR3aq~xSIR P )BR Sg4p P } }Ra h8pqfB}sRuag8aIRGa ~8aRjaaasq8GU4~q} R)B | | } } } } } } RQ)Sp8qa 8} 4q}fq~a}8R} ha q} xb a RS)q88a } }~ Rj 8aRSqa}4qqRe)paq8gR 88qBa) q}g I)a~8ax4RR} } } } } | } 4a}GgH}aS5 a } RSSaq~ 84}Sq}a4tq )R } } } P } } } } | } | } } } j8aRSxq4qa}QjqRapS|RaBa4}q84aaR4)aq~tq} R) } } | } } | } } f Sp8aRWIYaBqq4a}GGj8aRSqIRgaR ~RI 8~ap} fP 4~U4RR} y1 y R GG qaRSjGtq} )q~|tYS34}hR ~a }4P Sa4~Bq8 } { } } } } hB4}S R g # P Sa 4a}RG3a D B R S4}g8qq~fjap8q}q}pS~S RB ~SaBqa} } } } } } RSpgIa)pSq8q}SG } } BY R qB)f )S4qBatqRR } } } } axR8G R "a qIPS jRx8a8jq4}8 qBa)xR P } }} } } |} } X 6Y R j}Re8a8j4q}}i4|}} RaB #X P }q} x R D b B BDfd R b B d pGqq} RSjqqa}% 8a } } } } p8}%4}a)SI8h jpBa}Iq|B)gag IG } } } R "a qIP qRq4}%}BaBRY4q}ga4~4q} Bag}q} x }} } } } } | } } } } } } }} j4Rh qq}q8SqRS8qja P1 - Z1 - Ff x W W sin C.V. dp dx G g 51 3xSaa8BReaBapjaaRjaR4}R IqY)p}}%Rj451 4h8a4a} } } g } 8a } Z2
- P2
- } } }} YSa4~4q}Ba 8 tRfj4q~("Ba & ' %q}B8aRpq}8q4} 8 8 & $ } } } 3aBR 8a)jq8q} q}8 h8U)fpq4}"#"} 8a4h4 aa jiaB } } } } } } } 8aqa88} g}Ba R 8q4aqapg } } } } !X 3qq8YIq|Y}s8Y ) 8h4qRfj4~Y8"YGa } } } } } } } | } } X p4}q}URfjq8~}RajS888} iaiFX 8aRpq} } | } } } 84qx}ga qg)Rp}"8ga8a8x js S j sp)S8~gaeaqg4jqua } } | } } } C C C )C b e)C b hR 84Ba8 qRRqSa3b4RR4~a8aRj4}4qtRjaRRqg} } } | }} P } } | } } } s vz t 0 x WY) 1 u s @ G() R P X YS b4}RR4~ )p ) 8 8aRj4} j4}g8g)a x } | } ( } b B G EY b B X b B C c` X aqa}p8aRpq} } } pq a 8aqa Rj8aq}ujq8Iq g88aI4h jq h4} } } } | } | } } ca b ` aIuD` b 3p aIxRBRjbaRIBa~8atq ))B)gag IG } } | } } a8j4}5 8a } y-h h Z y !&
} hS 8 a G8hR f5 ~4RRYRpqQaeg aYRS88q} q} } | } } } } } 8~aI} 3ai) pfajS88} hj 3}4R aq~ia4qRaBBR } | } } }} } } } } } } } RS}CRpqxa8aqa8aRa|Ia 84}qU8)S S 8av8jjq q}G gH! } } j8qq} bb { & g X b Re S g X ! R )C P R )C P hqp } 8aBaS} hf C X C b } | fq} R)4"8a 8aRj48q}4i}C88 Rfpqq~(" i}%q4j q4 %4j8 $ RagaaGapR } } }} } | } } } p4q jg [email protected]@ R } }} X X @ 47 @ 9 $ $ $ C X F ) X X X $ X $ X F C X $ RRj}}ea R 3q8a8 } $ 'p88g 8aRSeRRj} }aB qBS % }} X $ X X$ C X 3q8a8p 8aRS } Ra8G }a }RSE 8q} u ! 8a & } 2 Z2 S0 aapa) 8aRj4}8qq} haRf|a ) } } h1 1 Z1 x dh/dx=-Sf h2 hL1-2 EGL Datum !g 8 b4}RR} g8aRRjq abax } } 3axR b)C fajRp}jq} a)~Bag X q a)q } } } P } | } | } RQR g 8q}q}eRa|IaSe}jqIQa %fajS8s88Y} s8GRq )C b & g X R )C P & !g } } } 4xpRBq8{ g atq} )R}g aR q4q~taax } } } )C } SaB) 3j4g } } } | } qapq8aRa|IaxaaRSg S pqIxC fajRp8xhRq } | } b & g X } } qBpjqRSIax8 Raja |gaR & g X ap} fP qqRfR8Rqq88aqaRfapS} 4v 8ar8BaS} hf } } } } B8 8aG8q% aqq~3 88aRfRG 8 8a } } | g } x & g X & !g R )C P ! R )C P } } qRRg aRejRS 4G )C b y+v2/2g y0 x S0=Sf fap)jg axSaa8 8 g aB r x8 8aG8q}%aq4~|S 8aRfRG 8 }8a } g g aB r x!&8 ~G&& S & % C g S % }RjB } } } RBIq}aB RBq8RfBaaRBa & 1.5 1 5m y0 B B
h 1 m b h
1 B h m B B D h h b Rectangle Section A Wetted Perimeter P Hydraulic Radius Rh Width B Hydraulic Depth Dh
* Trapezoid (b + mh ) h Triangle Circle 1 ( - sin )D 2 8 1 D 2 1 sin 1- D 4 (sin / 2) D Parabola 2 Bh 3 B+ 3 h2 8 B
* bh mh 2 b + 2h b + 2h 1 + m 2 2h 1 + m 2 bh b + 2h
b b + 2h 1 + m
b + 2mh 2 2 1+ m 2 2mh 1 h 2 or 2 h (D - h ) - sin D sin / 2 8 h a}R G 8a } 3 G %1 2 ' )0 (& 0 < 1 = 4h / B >1 P = ( B / 2) 1 + 2 + 1 / ln( + 1 + 2 ) (b + mh )h b + 2mh ( b + mh )h mh 2B 2 h 3B 2 + 8h 2 * 3A 2 h
2 h 3 $ %"#! !&
} hv8vQ~RIQ}tR pP RCR qp88'aj} fP S aIqtR aP R Q qp8'j} fP } | } } } } }IpR88%RfqR}xR aP R 4j88Uaj} fP ~8aIxR Iqaq}q} Rj}aR } } } | } P } 88QRRiq}RRa8a4}R 88QR " &#Sg!! Wb } & ! j8~Rp YapRBa RaBxR qpfRSq48f } |} } } } & }8aq ) S Yap)qa}Rjq} ))})QRj}a4aQa~R|S8 8 } %$q}aRS 8a 8)BR q}4gRfgt)j4Ba|4 } } } } qRe}q}B ap} fP 8aa8qS Qq8q} & |a4 e"RS8ef R 8G } } } | } } } } } 3 8 4RSP 8aqqI8qRfqa48qaIaq4)SRR SBS ~a I } P } R 8 S 84RS8aqqIB8qBRfqa4GY8BqaIaq}qRSRRS 8a } G G 8 B 9 jQq~ReqP a4RRaQIq} eaI~4eagqq} s8QjQ8qg j } | | }} } } | } } } } } }} | } | } } } } Rq}jSpq4vBj4aRfpj}axq}qRS8xq8RaRSq84R%qRR aRxga4~R3%aBsq8a368~x}8 4aaxRi4axgRaxgasaRRj } } } C } } } } C RSqia 88~}i iRf8}RgaaRY}}q} xGq}g 8RW8~Rf pa4ai4}agRtu } } | R G 8a qP Iq}88pqq~(" 8qqgq~e4q"Rpq}q~("R R a4 } }} }} } }} } | }} } | } } ! ))RSRgaYaaRf4q~4}3Rjx} 4sf & " j !b 4#u% #g } | P } } | } } } } } 4}x4)}qaBfBaaBI8x}8Ba8aq4xRf )S4q}j3aB) t } } } R) }8}YaqqIRf8RSq4Iq~} h4}bb C d 8aR}4aS } } d S4a8 & @h4S } } d C d d d R jRS P X T R X P 3axR ~q4 gxa qaq}I ) QBqq~|Iq } } } } } } }} aBS~R}hRfpqq~(" j qaRS8ga 4q}~4}aB d 88aRj aaag } | d R p)SI8 P R X dP
& d AjRS R R X YP d }} j4qGb R X YP d R Pd 3p b C aR 4 fqRRiRf8RSqq}8 X d } } } } q} R) iq} aqq} 8)Q R aaaq4a gaa4aj} P qq}aq~4h4U4qa ga ag } } | }} } RR hRpj44qa aagaj} P jR} 4}qa aag)h8aa4qI4~} } } } } } } } d d d AjRS8 & jRSI8 Q } } } qpq}pR Q R q } jRS aaag jIRj8a)f4aBx4qg~Rj8aqq} 8R ) S ~a aa ) 8aRjpq} } } } } }} } } } hGqa ga ag%%q8aq4} 8u 8bi} 8Sq4}a8q8a4}vGUfq ))ib8aIqa } } } } } } } Q Q Q 8 Q !!# & "! } } RBqg I)8 R 0 YhR48qBIR8BaI)} 8qaRS8BaBIq88a P } } } } 8~g8q88G%jq qG 8feq8aQ8Iq8 i)jR 8)aRSu( | } } } } } } } } } } | P qRY8S 8 8G iS4Rh f SIq}88eR aI8~g8qj4}aRapq} Q }q} x } } } Sq8 3bRS8g RpqiaUq}RR R)pBBS}8 I}aI)Upa}gRb4B8 j44RSaIq } } | } } } } RS8i}Y"Rj4}%a~q}RR )Rja%4qRSaIqb8Ii%88C S"RS8iY"Rpq} } } } } } s4RR )Rp} aBSv I}UC aqpaq8ua)S43u)jqs4RR } } } } } } } } } } } RRjaaqpaq8}RgIR aq} ))a8~|g84 aaRS88j 8g8 0 0 Q & Q 6 Q 6 d 6 d R 6 WRR d 4qga4~4qG }} } | } } } } } } } R jRR)RaBb)Rp}%a4RR ja~qRRGYaaparI84R } } | ReIq}88aI~4ga aRW 8Bj q}g} R Q VS S Q ap} fSq4RSaIqBj4h4~(" S P } } }} } } Rq}gR R ~ RpR' Q% aq4a8uaa )S jGi8xR8F q} }} G&& 4}RaI8~|g85 G 8a } } n3 C C C n5 n4 n2 n1 ! g 8 3phpC 4qRfR } } } } } 8R4}q88aqaRfajS8YS a 8i8iRq4 aR|q~iIeB } } } } | fq} ))})4RSaaxa)RSB4}a) S4xa)qq~Iq} 4he}a )IRjQRja}S 8ar8hRpq} aRhs88a4j4Y} } } } } } Q Q g S { g S R a bRf4"aP 8aRpq}g aR } | Q g Q { g R h P 8aRpq}g aR g # ! { g # ' ! } 8aRpqq4} g # b { g # b 8aRpq}R)a4} pqRQ( 3xSaBR ~8aCq}RRG} tQqRfaGg }aaQRS8g8q} qG} tQ~8aQeaaIIaaRSpq} } | } | } } } | } } BS 8ar8a8aRpqaR }R 8aRpq4q s88a)paa|R} } } } | $ " 8 & " "! d Q 6 Q d 8f Y8B aq}IauB48a 0 R) tqRRg aaj~S } } } d Q dQ dQ !!# { R } } } 3aa)B}~8eaaRSq}4BRQh48agRQaRRjSa4}RRgaux3a eSsqR SaaRuR } } } |} } } 4}h4}qia4a}8}RB4a}aRapRja8aIia qiq}R}q} xRp} b ! %b $& ! S4g8qq~q4~q8 } } }} |} } R !# ap} fh84a}vv}R4Rfap)pa8aIae44Rv"aRv8G P } } |} } } } b $& b $& } }} |} } ! 3q}g8q4~4q~48pR # ap} fP 84a}}RQ4a}aRapRja aIaqqRuf SqRq4R } |} } } } |}} } } } | } 4}h4}qa 8q}gg} h Rq8RfapRja8aIa q} 4)g} hqBgRjg} }} } b 84)S } aa|gGtaRS5 8a } } } % % % % R R 7 "C 7 P R 7 "X 7 P RSpaj} fSjq8RSaa8~q~pj6RS}q} x P } } | ! )S b ! 3aqRBqR} h8R !" qa} } } }8 ) qxqRgqR|g8qbaRIxa aa)jaj} fP qRIa } |} } } } } | } } } aagR~aRIb8q' aR~R8|p4q~Is tHqp8tqRsqRuq}%4aI8 | | }} | } |} } } } } & ) $& & 6 '( $W 6 $
6 1(0 1 W0 u v 1&uQ( tz 6 (z t u y A 3 @vsu 7 yz W630 8 } } } & } } } & pxp8aq}8}Bqq qa8 ! j8q}4}Bqq qB)taRGtSaB) S & S & g & g
g g } j8q}q} |88 g b B g R | 88 b B R aR} gaq } 4}iqRUap} fP }a|gR8UR @ RUR aRaq hI8qiqRUj} fP } g } } } } 84q}Q8CR g 4} R )Qeh4 4G} e8a'ap} fQ} aagR8~Rf } | P | } aa R aR} QaqI8qv}Q8aSap} fP 8q}qv8pRfaa q} " !" | } } SaaRGjI8xp8aqR qa8a4 } } } } } } } } | } } } } } 84}qq} vapq}Q8RaaRfq4~q}vjRS8~|gavava j8aqQ8QQq4~aR Yqj ReStj8q} q}v8vaRY4hR|uaRS4484q } } } } }} } } } } } }} 8Y}g8YRa|Ia RpiRGaaRGqI8q4 8G4qa84}8 G j8q}q} } j4Qq4Qjq4) R 8Qqq8e8)fQ4Rp"C a|a|IR 8aR~ajQ8 eaR4a}8| } } } } } } 4}g8q4~Raaqg8g}~IaRRq}g aRa|I aj8q48aqghR| } } } } } } } } aRjqpqB )Rp}"RSR} h)agaaq}8 G aRRf4q} # % % } }} } pfaqpaq8 } | } | C 888 88 RGDR R 7 % X 7 P aap} fP aIaa8"4~|jp a}q} x % } } | 8 b B R ! P a C S & b B ! Sg" q}aq8R aagR ! } } | 8g8eaxqRf4jIRR Rfpq8~| Raq} aj8 Ibaj} fP 4quRW8 } } } } } } 3q84q}R } |} } } } } } } } } 3aa)8xaga}q4}fq~q8RbS8~)if8qaQg aBq8xRRpSq8 |aI )8~hR R )pqp aq8 qRSq}48 aj~|pf Sa)QIaR }R } } } } } } R 48)jRj} ax qRf4jIR8Caj} P 48sgRI ph8I ) p~jfSa) } } } } } } | } hu8IaRRjRIqQ4a)p} hx4)qjIR8R R~Sx3Ra j~pf } } } f } } } }| G & G SaBR faRIa jaaRIBaB4qj|g RaxBq8Sq )SIaq } } } } } } } }} | 4}h88a~Rj44)p}Ie} " }QBQaxaq~RSxS} a}q} x } | } R C P R CF P bajhp8 R 8 9 P 8qRS } ha|gG8R a } } } } } !& } } |} } } fa4ja48 aIR ) RB 4GeR88xpa 3Q} 3 fa4ja48Qa8RRR q}iRQ8Qa4" SQ fqRR } } | } } } } } } hBpqaRSiq8qI8)Bq4~4haBfaqpaq8Rj}g4ia j aIRa } } } } |} } } } } } R8G aaRSpjapSgg88I8Uj8~) q4} 4Ya aagR | } } } } } | }8Rfa hSSaq~8g4 faqpaq8a8RRxs4RR)f )S4qbSIqa}8a R } } }} P } } } } } | | } } | } } qajfRSj8qa 8Gax4)~R88qRI SaaRIi} aagR8Rfxq} a8 } Sq8 } } } } }} } | } qR Sa)R8qBaaB4jx8 } hpj8qq p"pfSaaR8gaR}R R 48)jRj} ax qRf4jIR8Caj} P 48sgRI ph8I ) p~jfSa) } } } } } } | } hu8IaRRjRIqQ4a)p} hx4)qjIR8R R~Sx3Ra j~pf } } } f } } } }| } } } } | } } 3aa)i}b8aaRSq}48i)q8aRaRRj8Sa4}RRa%xS pa8apq4jq%G &%6 &H$76 6 & ( ) (( W 6 $& $ $ "6 7& V1 C y1 y2 V2 6 "! a8tq} ))B)8)S4q } b 0 } q R aRI%qg84q~i}aa)8%R"ap} fh )xq8"%R% uRi8G } } | } P } } } } } } } } j8~8aIx4aqa 4qR}je4}q8S8a R ~Sa~ j}H8} aagRRfuqq~ISj8q}q} |} } } } P } | } }} | } } )CF b C b Sa q4~G aBgapSgx48q RBqq~Iq}ax}8~} 84q~} }} | }} } | }} | b e C C } C 3q8a8Q e 8gapa8S R )X P C C } R Ce P R X P R F P R )e P R X P b pqg8g " axSaa8}Ba4a}j8aRj4} hpqgjaB4hIqaq}If } } } }} C e P R C P tfapaj8 R S48aajhp8qp8aaR f' e } C R C B SR}8G R X P B R X P b B } axBaBq~| j4}g8g R X P b B Y b B X ! b B S48aaBxa x4~Bqq8Iq}q}BRf8RSqq}Batq ))4aS } } | } } } | } } } } | ~8aIbaRIxtq}RRG R |gaaRSpjGe8 & c` b } } | } jq q}Ga)apBagaaRSpj 88qa}e}Q)aaRf4q~44 ae~Rp|g GRq8Gpa4%equR q44 } |} } } } } } } } }} } P } | } } } RxIqa}3'ap} f~aIba)iYRxbRWp8qa 8v8xabq} R)ajj8gq !& 4}RRbRSp4a x8 & D` b } } 4}bRSp4a 8Bab4RRap8aaR f G } } } } } } } | } j8~ax|)48~}aq~B48 aagRa)pj8q}q} b C ) Ce b RB b C 4q~Q88~a4"B48 aagR }} | } } } } } } | aRIS8aa Rf Sapaq}IvR8~v} h"8p8hga4xaa|)aR3j8q}q} | } } } } } )CF b 0 b } p} R & aj} PSqRbagpagapSg8~GY4aI8 } } } b b S b } jj4q}R R } R 52 q} xRf8RSqqBatq} R)} hajp}8G 5 8aq4SS84R5 8a } } } }} } } 4P qRIeqRB8ax} b # b SBSaa8B)eBa8S 8ag I)4)SaaRu}s4x)Q~R8RSq} q8p'qRRqq~Is8s | } }} } | } } }} | } } ! ~# RYagagap)Spx4a}aRj}qaRS88BR}RSBa) } } } } } |} } 4aaRSjpBa RthR 8 8 } ) S }B8jRR8aqqI8qa 4}q} x } } } A T G S Rjaa 1 } } } } jRY4~Yp}8 BqaaRj aI)qS R33aq~8qIP RjIx3 )RjI8"Bq8SSa4R } } }} } } | } } } } h a 4}sR fa4ja48Y8e}RGqa}aRIGfa4ja4SY} h ap} fP q } } } j} a RjIxS} h 8S } } } 8j8qeQa}aI8~|gaQ~~aaBa''" R8av)p)S8~|gaq8Q)qv8aRjaa ga } } }} | } R3Sq~Y 4P Rj |U4SG Rj SY4Ra 4R faqpaq8 } } }} } } } } } } }8g} Rq8Rfafaqpaq8S}Caj} fP q} xCp}agRb4 q} x } } | } } }IRj}ap4}" 3} jq4~(" aaRjaIRSa 4xIRj8 }} }} } } } 8ajq~ S}x)h xaxajjaaRjjpCf Rv4a}aRx8 )vq8Rfj faqpaq8 } } } } | } } } 3}Rpq}eq} hq}~)p Svq}RR 4~a8ge8faqpaq8jaRj} } q~ej} 1 } } j8qq} 4q~4Is} hU)Ga}RpBh4RSta )gaqpaq8j88a q}gautR b 8hRg8q}s} }} |} } } } B 4}"ep}8 b 1 3{ b } 3afajIW8hQfqaaRW} b B 1 } } SaB4q8 B 4apgGf4a } } } } } 8hRS 3q4q} i8 aRS8aRfq}p qRSq q} gag8apq~ S} } } 4~YpBa8pq} # } B SRaB8a)p8aqapaj} fS)pSH } } R P } b B 3a)a x8}aRjIfapSE } F B 3a)a x8a}RjI}R qq8qRfq8ajap} fSq4h8t)h4f } }} P } } R Sb4RRq~8aB4q8aR} } } } | } 62 ( s 0 &1)se)B D s G( 3 s 6 Wz 1( A zg( ) 2 04vI( !& Rj}B8 8qRS } aagGtaRS5 }8a } } } | Rj}B8 8qRS } aagGtaRS5 }8a } } } | V V C C V<C V>C 8 b CT } } } | 3a4qa4q~} 6 vz t w v )sWWzsgD 230 yWz 4uu D )t wY0 tz ( B s A 6x A zWsz 7 ( u )Q x D 1 u s @ Q(9 yBQ( z y 35 } R 8a &RSvE p8j~ 8 4RSSqa4SB8aRBxS R } P } } } } } } } | } } } 3aq~B B fRjaaq4~")paaq~I 88aaIRSB%q~a4q} eaaaRSuq~ gjG}8 } pqq}%RagRf88aaRSiq~aqIqaaaRS aqRfq } } } } }} q~ejxa8pq} # } Sq}haaRSaU8v4~jffQR4v)4Rhvq4qxxSC4 } } | } }} } } } } } } ))q~|8avjRS8~|gaQRq}~epQ}8 Rq~epva8pq} # RvqRQ } } } S Sa )paaqq~| S 1 } Sa )paaq~3 1 8 b } 4 @ @54aS } & @ b X @ b X @ @ SaBR "4q gBaIq}gaRpq}R Qx4q~4}aB aRfj4h4~(" } } } | }} p4}ag4q}}"Rj 88aRjpa} pa}aI8~B8Ba 8}RSxS )a x Saq~ } | } } } }} } } } } | } 84}qBRjaa4aqR} aq8q )p}84 8q4a4q~I 8 } | } 8q}%aq4~S 8 8a E } } } 8Y} hG48a 8YaRq}pg } eSaq~ 8h4}qYqq~I} G49qYa8aCf } } | } |} } 4} q} & & & & & b CT } } } } 3q8a88aRpqgf8S~Rgaa |8 } } )S8aRpq}fa jap4gaIG y E=y+Q2/2gA2 )eRqa8G } Ac;yc Emin E=y )a}a x 8 5b 3xSaa8BR4aa|a~Rjaa 8q } } } } } } } } Rjaa4Q'aBvava14}x jRhxv)8)S4qvaCq} R)tavRQ8G j8)S8~Rf)R8~xjqB8gBBS } } Rjaa4 8ajBQ8RjaRe}se}8QaQa YDRSSGjRSI8q qq8ega } } |}} } } } )3}R R 8h4}qa ||I8RjYpR YagYaRa8q4}aq4~| } } } } } } } q} p8q}qi aqq~|Iip8~i~uIe X g q qq~"(i} )%q8Rf%aig q} x } }} } } } } } R%q~eqg4h%Ie883aRS4Y pga8qSiG )R"aaB R%q8Rf } } } } } g R RaBqRIae4a}aRIeR a}RSI~aaB SRjhh48a } } } } j}aR eaagaR a 8q4}aq4~})Rja8qGRjaaq4aS } } | } } } | } 38aa8qt)paaqxR 8SG RjbaaBb4}RRGRaxxR~8ax jaaRpaR 9 Q Q Q pq4G } } }q} x 8aRj4B " aR q}aRS8}"Rj } 3xSaBR 4}RR8~aIbRjaa4} hpj8q}q} } } | } 8q4}BaB8aa8qtRjaa4xR S8fa4ja4}} } } } b aBaIqRY84a8I~Rj hx } } } } } 4}hRf4jIR SejR} Sja8~aRiRjhh4aSg q} 8q4} Ya ag | } } } hiR DqaS Sq~ejY}8 } hGa aRq4"I8ia b # }q} x 1 } } 1 }} | } } 1 hBj4}aRaj4Ba)a x } R Sq8a8ta)Ba8qa}|g j}q a8aIqq} ) |gp} xReq}I8a)pg a f } } } | } } } | } } } } } |} } } } 84q}Gaq4~xfjq4jaRR4~iRSi88aIq4x8|gpx%qq~" i 8q} q} aqq~Ifp q4 jaRR4~a S } 8GR q Rj| g8IP j4q~" } } | } } |} | } }
"#(& & (6 ) & ) $
( ' 6 !$ && % #$ 2 " 3) 8 } } } } RSx3x)pRj~q} ))aR8aR Q R 8q}a )~4hGgR3i} %i)a S & R 8 S P } qpSR atqRR } } } | } } Rf8RSqqaaBa q~RSxS g} abja} |gRb48 Q R 8q~q} 8 } | ) R RIB8aa 4tRjaa4} c)SBSq8a8Qe ! } } C b C } } 3atqRRxRf8RS4qG a8q4 aqq~Ij3p } } } | } b b b b } } } q84 a hx b b b & 5 }} } } q4~|Spj8q}q} b b R P & S4qpBa 4g8qBa8Rj} 8aa84bRjaa4xR } | } } ha8Qa8a)jq}ae}qa3aBGa G4~eRRa eQaRax }q} x } | } } b } } } } 8aIq |jqax3aaBqq q})a x 8 | } hR gp} 8S~R 4q}sRfpq8~g}R 8g}q4Cap} fP ha4q}e e $ 8q} q} } } | } Rfj4~|agIRjq ag}|a3g}q44hbj8q}q} q4q}a } } } } } } } } |g jY}G) 4} SYq}fRjaq~GjYs RjI SYq I | } | } } | } } S4IRj} 8qq8S } } } qIvaRR)4a}qaG8RRQG4q8Se| q}Iva4qQa4q~Q | } | } } } } } } } } | } } } 8QhR|"pq4GGR & $ j} fP 4~qRRe} haeI)pqa4IQagp % ! } } } } } | } } } 4 4qqa}84}i~ R8 p8a)SIBa" 88aIaq ajpRjB BaBa } } } 8884u8Iq8%a8aIq4%|ji} C88qa}i} } } } |} X $ X XeR X P
X F e C C C & e C C 3qq j|8q} q}aq4}~88aa4gaIG } | } } C b C e C b |g G G h } z1 y E1 E0
z z0
z E G GG S & R )b P & R " S 8 S |} } 3a qt)paaq " !" |gp}BReqI8a)px4q}a8q} 8j}8G @ } } E R E i}Rq8S ji}%q8S4"RjaaqiRph4"q} R)a%I4)ai~ } | } |} } } } $ IGR |g jG8Gp8aq} eaageQaGR R~& S & Q apR 8& G& & 8 } & }~8aI%8g)fj}aB qRRsRf8RSqqaeag8a SsR 8 % % | } } } } } } } } }} } } } } 4)Rj~RSIRj4G aaRpq8qReqI)p}qah8a)4}aqpj8q}q} jx} a Rj |}R q8aq~YaYqRRYq}a|gaRaxgp | } } } } } | } 8 RjI| S} Rq}Saq4q~ j } 3"R S Ra q~|R } } } | } } } | | } } Rja}aI8~Y8ee8aa8q q8a8YR S )pg4U X $ QI } } GGeq8{ Sa 8a | } } R } } }} } } } 3Sa4~h 4P RjaaqB|j8S~R Sj3a R R X @ $ P 4} R)I8848aGajYaG)hY}8G I } | } bb 8h4}qa4}ajaq q}G 88Q $'8q} q} } } Rfj4~|aYIRjq aY}GGaSYG4q} qY j8qq 4}Rj}q aGa } } } | } } } } }} |g jG}%R q}S i} q} 8fRjaaq4~|a|gpGb8RphISGq} I | } } } | } y E1 E0 z yc ! E G~ S & )G S & X R S X C X & C C C & b C CY C C b C } } j8 4 a |gjgR8q} q}} h R ajg}8q~84q} u~j8q}q} } } | } } } } } RG S & G S & S Satq} R)BRf8RSqqQY84q9eaagP Rjaaq} } } } R S b R S C G S C R G S C P 8 S | } | } } 3aj} h8 RphIB)8q} q}aq4~| S4Rj4q}gp}xR q} xqRGtfRjaaq~IBaS4aS } } | | } } } S & G S 8S S b b 1 Sa RjI|B)Bq~Y j8x4Rhf fRjaaq~IBa } } } } } } 3Y} GG S & G S 3}qaIjaRpa} G S Sq8a8G4 )xRfaIG Q Q C && R 8GG& S & P 8 S | } | | 3aj} h8 RphIB)q} 8a} GGeq8{ Sa 8a | } } y depth E1 z E0 E G
GGeq8{ Sa & 8a | } } E0 E1 E } } } | j8q4aq4~ } haI)pqaR aYa4RaBfapSx8}a}Rjq apq4GR & $ } } } } } } ap} fP q~4}RR} aBR4 RjBSP 8 q} Iea 8aIq q "W& S% } |} | } |} GGeq8{ Sa 8a | } } G~ S & $ X 1.12/2g 1.28m Vc2/2g=2.392/2g Yc=0.589 y E0
0.458 z
jump! 4j aq4a}8q}G } } } } } Sq8a8BqI8aRjaq4a}4 } } } } } } Rq8a88aqRSj84vq}RRi8q4}"" I8aRj4}8q4ja| |G } a4RWp8Q f Sa 8 8a 0 A0 A1 C b e C G C b C 8aqRSp4}8aRjpa}8 Rj xSRRj| 8~ } } } } } } | } } q84a}v4)} h88RR}8v4)|ga}8x q~q} h axbq} R)G8RR8Rj Re Sb8aIaq4}i} aB Si}i4qYaRq8axQ8"q} ))xa%q}|i8a } } } } Sq8S4QR8aqRSp4aB"aj} f5q ))Q8 axaq q}u8 8Qq} h8Ra } } P } } 8aRRfq4Rf8aa ) f fq} )RY}s8axY} Yq4GiI8qGaY44 } } } } } ! { } } } Ig} jaI8qg~g8)YI8qR8ae aq " j $ & "7 & " 6 "& (" & & " &
% ) & !$ && % } }} } } } S4Rj4q8aIq|4xR 4 S x}g4}3R YRjaaq4~|uag8aIq4}x~8RjI Sxg4 I |} 1P } } | } } | } } 3qRp}qa8aIq|4xR } } } } |} } 4Sq}pR YP Rjaaq~ Ba8aI4h q}} 8 Rj Sq} I 1 } | } | } y E0 E1 1 E
#$ 2 "!" S & 1E` G S C | } p}agRtqB8apq}| } ha4}aRS8Gq}B4qjb8vqa}apRjQ}8h4RShp8qQt RjQ % % } }} } } | 8aqRSj84} 8 )pB R } | aq4q~j4~)Y q}xRxjaB q}SRxa8aqRSj8qfg j }} | } } } | } | } hRqI8aRj}q4a}8q}8BpG [email protected] E )43Ia aa8qqR } } } } | aaB)a x8aqqIqqRSj84i}C8axeap)i%a%) 8aq4...
View
Full Document
- Spring '10
- KK
-
Click to edit the document details