midtermsolw08

midtermsolw08 - w vskywtWzidvkxztt pe pw w p v e z y z s uw...

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Unformatted text preview: w vskywtWzidvkxztt pe pw w p v e z y z s uw WuqtDxsvyDd6tqqq ld u ys s y l e s zsq dvvuvsqWbtvqrndruttbqvq$ttG yuWdfto|khtrp ss u oe w o sq us y l p x nd$td Vmax s zw y xtqxsyu D|dWQto|ko z ps oe w s se y ue s pwes q s j z p s se se y s sq j uwq y p zzw yd u w y tvquqdbqDdzu}tvq6uqxWdt}tvqvdq|tvdtvqWtfsqtdvwxsxDsW$vtvq~Wvsl Tv = AR = TM = M gR yuW|dtbqvq5vdhtthqdtrp q s j z p s se se y sq yuhtvdGqDdzubtq~vd}dv|tvyWhqr{wfqDdyuvuvsyxtvqbtrp se y ue s e dz sq p v u z u u yws u sq = V R = h h x v wrqut6WssvsurIwqeondmkihvsfWtGIWruIbtvqIvuvsyxtvqbtrp p y l jdg sed s w s u u yws u sq hCg BF a e8 a` X V T R P C HFE B @ 9 i$DV6fUdc bYWB UDFSQI6GDCA68 7 ! 4 ! % ) ' % # ! 653 (210(&$" Vmax v qw l Vmax = 0.38 kg/ms b = 0.1 m R = 0.025 m h = 0.001 m [Vmax ] = Vmax Vmax = R = 2 = R3 b = M gR h M LT -2L = LT -1 M L-1 T -1 L2 R3 b R 2RbR = 2 h h M gh 2R2 b M gh 2Rb Vmax = 0.6 9.81 0.001 2 3.14 0.38 0.025 0.1 1 m/s M = 0.6 kg v z u u z s s uw z s wq uw yw s w o s uwus w o s w dvDxvsudDy$itehtvqxvsvsWyqxWsd}qGxs6dt~bqvqulrqWitIbtvqIkqq$d d u y z j jdg s w s s jdg s j s s s o l sd o y eg y wsq s qivxsvyDd{ppkq6qvqIq5dtvetvqkq6duppsWytqqiqve tqQvdny}k~WsUyu&ytqxsttql vswAkqhtqrtqqtd y jdg s u s p1 - p 2 Q = V2 U Q 2 D2 = 4 4 1 D2 us y s o l p u y s z u u w u wes u p s w jd xfuihtvqvdnyrtvexsbtvq5tvDwvyfqtve}qqdvqx$Uwbqvq5t|ttbkU p3 = p4 + SG(z4 - z3 ) p3 = p1 + g(z1 - z3 ) p4 = p2 + g(z2 - z4 ) x v iut6Wsvssur~uivdyDdrqdkbtq}xWsWddkywWsUyzvwfd||bqvquIdvkxztt s d p z ue yw s s js p y u yq s ld w p h$VDFfadc 6DFb}~mDBDRI6}{r I6QDEhu6{~ Cg B e8 V Bg ` H R H F V V ` C Bg`gC F 9 o u u s ld w s w ye xvsf|f6tqzkWotqz ~vstut Vmax h = z4 - z3 1 2 gap h viscosity span b 1 1 p1 + V12 + z1 = p2 + V22 + z2 2 2 z1 - z 2 V1 jdg s o pd yd uw o ld w u z o l w kq~tervu}dvWyvsqDd1vdnyqq u s ld w ps d tqiqd }dkq~oWdiv skwy v d p dz d w s o u s w ps sq s vtxuddvyWqdkb~w6tvqyudvxsxhtrp v d ss s ped ys u qw uiIWxGjWipttWtf ld ue sw o swq s j ysq bvsqh|qhhvsxtj 2 2 V 1 D1 = V 2 D2 V2 = p1 - p2 = gh(SG - 1) 1- 2(p1 - p2 ) 2gh(SG - 1) R D2 D1 4 - 4 M 1 D1 4 w p tvq5oi g vsv~xGxspx5vx|qfevsqvqhtfipquuv y j wz s j y yws s ys p u y s ue pw t dh dt 2 s y uws o p u u s y l s p u w s z y s y z u s z ps s j x~Wostfex~sWwzvqihtqrndvdqDwtbtvqIoWvsqDdxvs6tqDxsxthG{l A dh dt 2 u p s o pdp z w y u z uw o p qxs5qedvyDdyutvq5ddvkvxfsqDdu~ttt vs o pd p z s s u ys z s ld w w ld q s j s z ps wz s 5qedvyWd6tvqhtvqxtwDd6tqIqy{rxGbtqrxsxtIWbj Wszqfust~ofus|woGuUDszydtqzuqqruq{iuktvqyuGxDsswflqe dvyG~teqdvyGuDsyztqsqvvuiUt p p v v t jd u u z y p d s o pd p d ld d z p ud s hCg B F a e8c BC R ` V R F @ R Fg V F 9 i$DV6fDC~D6}2DH66{$6 s y s o w us ld s ye dtverxvsW5WdxstIqxdqu}qzD |bvstut O 3 SG h 4 z D1 V1 p1 d dt d (Ah(t)) + (Vjet )Ajet = 0 dt CV d + Ajet dh = -Vjet dt A u w sxvz&vqihtqvstve~WWsqt6tvqWy|ddkqxqveW~~o qvqttAkth pw u u s y uws o q s j yww s s s wes o s od s pw jd s qWshsbG}qU|qvd|Ivqx|btrp j l p yw s j w ed u y us sq us o zs q x~Ddxdryutrp z d dt CV wd + Rz = gAh - 2gAjet h 1 - d dt CS w(V .n)dA = - dh Ah + (-Vjet ) (Vjet ) Ajet = (-g) Ah + Rz dt Rz = gAh - (2gh) Ajet + +h Vjet = d2 h 2 - Vjet Ajet = -gAh + Rz dt2 CS Ajet A 2gh (p - pa )nz dA + CS (V .n)dA = 0 gAh 1 - CS D2 V2 p2 Ajet A A z dA + < gAh CV W|dxWstvqdvsq|qrvsxtj z ps s ld ue sw o swq s j ysq gz d + Rz Rz Rz us y y s w xQoWvsrfuihtvq5t|qq| us o zs q x~Ddxdryutrp u d d qwthstq v vqudvkxztt j w p vxxGrWys~rxstve5hsxvzfqdhtriv ~ob5qedvyW6tvqhtvq}ytqhqvqd q s j q p w u y uws o pw u u sq p s w s o pd p dz s s u eg s l q j s w u p p u u s y uws o q s j yww s w u w q xsGtvqqvqruxsyubsWwz&fqi6tvq}xstve5xGWsqqtqkqqrxskxz|iqyztj u z y up z w s o pdp zld d z p ud ye xWsswvltvevdyDdqb5qedvyWduWsztqbsqvvu{thvstut = 103 kg/m3 A = 1 m2 Rz = 103 10 - 2 103 10 10-2 1 - 10-2 3 n3 h t 1 n1 Vjet 2 n2 t Ajet = 0.01 m2 H = 1 m g = 10 m/s2 pa area A Ajet Rz pa g 9, 800 N < 10, 000 N 3 n3 W (t) = gAh(t) ...
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