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midterm0

# midterm0 - 'G'VtbYtEURl%uU` x VR U V b X b e W b e V U T e...

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Unformatted text preview: !'%'G'VtbYtEUR%6c'%uU` x VR U V b X b e W b e V U T e ` p b V b T b V b Ye T qEG%d6bEtI`etubeIEG`%6e%U1'u'v b X p T ` b V U P pW U W UVe T U d b U a b Y V U UW TR Y e ` f b Y R d W b XR b V b Ye b d TR d V dV + V (V n )dA dt C .V C .S V b RX T %f!Uya x V final = 2 gH /(1 + fL / D) !EuGq%tV%WqIb i x w v T UR X X b s r b e p X ( & # # # " '\$\$%! 1 equation P1 V P V2 + Z1 + = 2 + Z 2 + 2 + H L1-2 2g 2g P1 = P2 = 0 , Z1 - Z 2 = H , V1 0 , V2 = V final 2 1 IGE86'1) H F D 0 CBA @ 9 7 ) 5 43 2 0 H L12 fL V final = D 2g f be d bW c b T b b a X ` Y X UW V U R Q II%TEI1I1X!TS%P Fx = x w v T URe ` p b pe T b U IGEIIIQ g ( H - fL V final H = (1 + ) D 2g gH - (1 + fL V 2 dV =L ) D 2 dt dV dt = L fL V 2 gH - (1 + ) D 2 d V 2 fL V 2 ) A = ( LAV ) + AV 2 - AV 2 - 2g D 2 g dt 2 H 2 1 fL (1 + ) / 2 D C.V gH gH - V 2 fL (1 + ) / 2 D !tEIII%t%'i1e v u m sjn o r q g p ojn m gl gkkj h g f d . dV = dt L Valve h g V final = 2 gH /(1 + fL / D) = 2 * 9.8 * 30 /(1 + 0.02 * 800 / 0.3) = 3.320m / s t = a = Vinitial IsRsyhvpu xw tab / L = 5.293 b = 1 + 0.02 * 800 / 0.3 = 54.33 t = 5.293 * L / ab = 5.293 * 800 / 3.32 / 54.33 = 24.36 s e d t r qF Q hIbpRWs1TpG g i @ @ V = 0.99 * V final = a e tab / L - 1 e tab / L + 1 0.99 = e tab / L - 1 e tab / L + 1 e tab / L = 1.99 / 0.01 = 199 IcXRXUV1TERII1EBCA e d b a`P Y QW G F Q S QP H H GF D )0 ) ' % 1&(&\$ 1 fL (1 + ) / 2 D 1 1 a +V t = +C ln fL a a -V L (1 + ) D t=0 V =0 C=0 e tab / L - 1 V = a tab / L b = 1 + fL / D e +1 2 EIIIgign g s g m sjn o r q f dx 1 a+x + Const = ln 2 2a a-x a -x 1 a +V t = +C ln a = 2 gH /(1 + fL / D) 2a a -V L 2 34 !" 567 9 ortk j r p l s m @ 9 9 S g hG cf e &Y # 8 Ip1 x v "IE v v 7 5 vR 1v x 8 9vp ) R v ) ) P x 0 v x ) "x v ) ) xX Is2E# v 7 ! 5 "63 " ! ! # @HXFv 2 E62X E2 [email protected] 2 vR w # v G w ) v w v 7 v & & v 7 \$! E 5 E ! 5 \$! C D A @) R &" 2 #v x E& 8 V v v 7 v 2 E1v "x x0 ) 9 1 ! \$4 64 5 3 & % x v hIs%'# E#\$IpXX h ! " X v h u h C1|u' R # Q sx b) - w L + Lhg sin = 0 + 0 ) v A Fx = w = hg sin d dt C .V udV + C .S 1 u (V n ) dA W g efflux 7 1vE2 \$ ) E ! # 7 'v x ! B ( ) 2 C.V. h y 2|v'| x c) u* = w = gh sin = 10 1 0.00001 = 0.01 u* 2 2 u* = Ky e) u max u 1 1 = ln h + C C = max - ln h u* K u* K u max 1 1 u u* y = ln y + - ln h u = u max + ln u* K u* K K h f) e = 1mm 10 -6 70 = 70 = 7 mm u* 0.01 u* (1) E B 2 7 9 @) % 7 0 2 2 % \$ \$ FD'&7C4%'3&A4614&94846&\$&%5\$#4301)&(&'%&# " V < e < 70 u * = ( Ky ) du dy 2 du dy ! Prandtl' A l1 = Ky ' approximation = W = l 2 1 du dy w R 5 5 2 2 w ) !"6 3 72EP XcP v 3 4) IwIw w x w d) Prandtl' (1) 2 du 1 dy = u* K y u 1 = ln y + C u* K (1) I pE7 v V = 5 =5 IE 10 -6 = 5 10 -4 = 0.5mm 0.01 ! 16 = (1 + f * 3000 V 2 ) 1 2 * 9.8 2 (1 + 3000 f )V = 313.6 f = 0.02 V = 2.267m / s 76 @2 8\$5 9 Q = AV = 3.142 * 12 / 4 * 2.295 = 1.8m 3 / s u* = f / 8V = 0.0195 / 8 * 2.295 = 0.113m / s CFeFD I V = 5 * / u* = 5 * 10 -6 / 0.113 = 44 * 10 -6 m = 0.044mm (0.5) RSA 4 86 4 B7 G Q P a ` X W BY!I 0.99 * 10 -3 = 10 -3 f = 0.0195 D 1 f = 0.0195 V = 2.295m / s Re = 2.295 * 10 6 Assume calculate I 4 !UT V I E6 G ED A C A 7 2 8BFB0BB7 = H T 6 4 E c BgB1 7 C h 1 ) ) H L12 . Re = VD = 2.267 * 1 10 -6 = 2.267 * 10 6 (1) (0.5) " 8A [email protected] 4&52\$ % ' 0) A % % A #!5\$ #\$B " ! %A &A6 [email protected] 34!457 4625\$ 7 A2 2AA 0 ) fL V 2 = (1 + ) , D 2g 6&&\$846A 2 %09 862 )A V12 P2 V2 = + Z 2 + 2 + H L1-2 2g 2g P1 = P2 = 0 , Z1 - Z 2 = 18 - 2 = 16m , V1 V2 0 P1 + Z1 + I D ) BQ b 7 2 % 7 6&\$ '9 ' E 7 c 4 f6E 4 Q V E 6 d c 4 e0B7 b 4 2 1 ) 3)0( eBP 4 c G V ) -0.5) EGL (0.5) 18m HGL (0.5) 2m ...
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