Fluid Mechanics for International Engineers HW #2: Area Vectors, Pressure and Pressure Force, RTT, and C-Mass
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1 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Prle Sic lui [ e l Prle 8 8] riine nk hn cnin er n ercur Wh i he gge reure in he ir re in he le cher? Wh reure ul he ir n he le nee e ue in rer ring he er n ercur ree urce he e level? Sluin uin Sic lui lui ech h cnn eciic ei = 98 = 95 ic Equin z z z c z c c z z z c c z z c z 98 z z z z 95 c c z z 48 The gge reure in he ir re in he le cher i 48 kp S I he ree urce re he e level e hve z zc Since he vlue er i cnerve e ill hve z z = Equin cn e evlue give z z z z c z 98 z z 95 c z 5 In rer ring he er n ercur ree urce he e level he ir n he le nee e ue kp gge S P P
2 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle resurce ecr nen nir Preure rce n The e Preure rce Due nir Preure In rer cilie he ecriin n he quniicin urce rce rce h i iriue ver urce re e inven he cnce reurce vecr cnvenin e cnier he re vecr hving he irecin ur nrl he urce he e uner cnierin ie ining r he e he urruning urruning e e urruning In he lling rle e cnier e he urce i ujece n eernl unir reure n e n evlue he ne rce ue hi unir reure he urruning ver he urce he e r ech he lling e n he crrening le urce n e cnier he ri ie he urce e eg e n in he ne eernl rce n he e r hu he le ie i he urruning The urruning eer unir reure n he urce he e in he ne re vecr ech urce re he equl? I h? in he ne rce ue unir reure he urruning n ech e The le hve ih in he z irecin h z l Surce i le here e line in rer cre i ize Sluin z ere e hll inegre r The ierenil ilceen vecr i given i j Thu he ierenil re vecr i given k k i j i j The ne re vecr i hen given
3 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice i j i j Since h urce hve he e en in h hve he e ne re vecr n i i equl i j h i l j 4 S [h cnen in in he negive irecin] lgericll r h urce i cn e een h he ne re vecr een n he iin he en in nl Since h urce hve he e enin he hve equl ne re vecr Geericll recll h The l re vecr i he u i cnen i j Ech cnen i he ne rjecin he urce lng he crrening i he igure el illure h urce hve equl rjecin re n S i i j i j j Eecivel nl hi rin cnriue Thee r cncel ince heir cnen re equl in gniue u ie in irecin e nier n re eleen he e The ininieil reure rce n hi re eleen i given The ne reure rce ver he urce re i hen given Since i unir ver he urce e hve Since h urce hve equl ne re vecr h i l j e in h he hve equl ne reure rce ue unir h i l j S
4 4-65 lui echnic r Inerninl Engineer 4 W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice e Due he ve reul n he ne re vecr n he ne reure rce ue unir reure e in h r ele - ll he le el hich hve he e en in hve equl ne re vecr n equl ne reure rce ue unir h i l j
5 4-65 lui echnic r Inerninl Engineer 5 W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle resurce ecr nen nir Preure rce n The e Preure rce Due nir Preure -ieninl curve le i ujece unir reure l n i le urce n nher unir reure n i ri urce hn el The le h he ih in he z irecin r l h l r z l l l l 4 Deerine he vecr erein in he given rein crine r he ne reure rce ue h reure n he le Sluin ing he reul r l rle i ih unir reure e in r hi lj hi l j j hi l j r l l S
![4-65 lui echnic r Inerninl Engineer 6 W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle 4 euln Preure rce n urve Surce [e r e l Prle 75 87] i e cnruce cr he Wh iver uing he cr-ecin hn](/docs-images/87/95881228/images/6-0.jpg "ue he ih = 5 r er hei = 5 clcule he reuln rce vecr ue lui reure he er- inerce rke re line e ere he reuln rce in quein i reerre he hicl rce h cull c n h urce n h urce nl Sluin = 5 i j = 4 = 9 i j i he")
6 4-65 lui echnic r Inerninl Engineer 6 W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle 4 euln Preure rce n urve Surce [e r e l Prle 75 87] i e cnruce cr he Wh iver uing he cr-ecin hn ue he ih = 5 r er hei = 5 clcule he reuln rce vecr ue lui reure he er- inerce rke re line e ere he reuln rce in quein i reerre he hicl rce h cull c n h urce n h urce nl Sluin = 5 i j = 4 = 9 i j i he iin vecr h in he ininieil rce n he ininieil re eleen h X Xi Yj X Xi Yj i he iin vecr h in lng he line cin he reuln rce 5 5 uin Sic lui nn eciic ei = 98 heric reure = 5 kp
7 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 7 euln rce ecr Inegre r j i j i k j i le] l vericl r - cnen [n cnriuin he ln ln ln g g g g h g h g g g g h g h g j i cnen cnen urce l he r nriuin urce curve he r nriuin ence he reuln rce vecr i given
8 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 8 j g i g j g i g g j i ln ln hich i evlue e k kp g k kp g ln ln Thu he reuln rce vecr i given j i 85 4 S
9 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 9 ine cin euln en u he rigin ln ln ln ln ln 4 g g g g g g g g g h g g g g g h g h g k j i j i hich i evlue e 6 4 The line cin i hen given
10 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice X X Y X X Y Y X k Y X X X 59 S
11 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 45- lui echnic r erce Engineering W # nvecin lu TT n - Sur Terinlg h ier r e l urren Terinlg eril lue incien eril vlue incien cnrl vlue S S i r TT e l le Se nrl he e r eril vlue h innneul cincie ih he cnrl vlue inere he cnrl vlue h innneul cincie ih he e r eril vlue inere S S S Tie re chnge n rer he e S Tie re chnge n rer in he cnrl vlue e cnvecin elu ne re ul hru he cnrl urce S nvecin elu re ul hru n en re r ele he cnvecin lu kineic energ [EnergTie] hru cr ecinl re =
12 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle 5 nvecin lu Thru Surce r e increile ull-evele linr l in circulr ie he velci rile n il lcin i ieric n rli n i given u r r here u r i he il velci riu r i he iu velci hich ccur he cener he ie r i he ril crine n i he riu he ie 5 in he lgeric erein r he cnvecin lu kineic energ [EnergTie] hru cr ecin he ie r lui ih eni [in ] 5 I hi lu equl he kineic energ lu he crrening unir l ih he e l re? I n h i he nuericl vlue he ri he kineic energ lu he ie l h he unir l? e e hll ler ee in hi cure hi ri i reerre he kineic energ ceicien in he nli r echnicl energ l in iing e 5 I he lui i er h i he vlue lre Q er h ul reul in he kineic energ lu hru cr ecin ie 4 W he er icl nen li? ue h he verge l velci Q here i he cr ecinl re he ie i 5 n h he l ill rein linr ê ê r u r r ê lui eni nir l ih he e l re Sluin ê r ê ê r r 5 nvecin lu kineic energ The cnvecin lu n eenive rer ih inenive rer i given Thu r he cnvecin lu kineic energ e hve
13 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice elci iel r e r e n ininieil re eleen n he cr ecinl urce = e r r Since he urce i inr n he lcl relive velci lui r he urce i given Per energ kineic ie Dienin r r r rr r r r r e rr rr r e e e ] ][ [ ] ][ [ ] [ ] [ 8 4 ] [ ] [ 4 Thu he cnvecin lu kineic energ hru cr ecin i given 8 S Since he lre n he verge velci Q in hi ie l re he kineic energ lu in hi ie l cn e eree in er he lre n he verge velci 8 S 5 rin he kineic energ lu in ie l h he unir l ih he e lre r he lre in hi ie l he unir l ih he e lre ill hve he unir velci = Thi unir l h he kineic energ lu hich i n equl h he ie l in unir l ih he e lre kineic energ lu ie l kineic energ lu Th i he kineic energ lu in ie l i ice h unir l ih he e lre S
14 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 4 5 The kineic energ lu in ie l = Q P Q P 4 W Q 6 6 S kg 5 Thi i he ie l in ie ieer ~ c ih he verge velci 5
15 4-65 lui echnic r Inerninl Engineer 5 W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle 6 enl Trnr There TT [e r unn e l Prle 5 8 n W#] nzzle i che vericl ie n eil ichrge er in he here ue h ll rerie in hi l iel re e nier he eril vlue r he cnrl h innneul cincie ih he vlue in he nzzle Deerine he lling 6 Tie re chnge n rer in he cnrl vlue S 6 Tie re chnge n rer inenive rer he cincien e Where rrie reer he inle n he ei ih he ucri n reecivel S 6 Tie re chnge he cincien e PS P 64 Tie re chnge he liner -enu he cincien e PS P 65 Tie re chnge he liner -enu he cincien e S 66 Tie re chnge he kineic energ he cincien e 67 I he kineic energ he cincien e increing r ecreing i l hru he I hi cnien ih ur hicl inuiin l hru nzzle n h?
16 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Sluin c i in j 6 j nrl vlue eril lue The cnrl vlue i inr n nn-ering I inclue nl he er vlue in he nzzle We cnier eril vlue h innneul cincie ih he cnrl vlue uin ll rerie re e The rer i unir ech cr ecin The velci i il n unir ech cr ecin 4 Increile l 5 Wer eni = kg ic Equin TT - S S lculin r Q = r Q = kg Q D D Q Q kg D D Q Q kg Q kg
17 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 7 6 ne Ter Tie re chnge n rer in he cnrl vlue [ i inr n nn - ering] [ n re e ] Since n re e n he i inr n nn-ering he l un in he e n chnge ih ie Thu S S 6 Tie re chnge n rer inenive rer he cincien e Where rrie reer he inle n he ei ih he ucri n reecivel e nvecin Elu Ter S S [ i unir ver ech cr ecin] Since he l i increile i e n unir n he velci i il n unir ver ech cr ecin e l hve Q Q Q Q Thu e l hve Q Q S TT Wih he ve he TT give S Q Q The - l give n Q Q Q Thu S Q ii S S 6 Tie re chnge he cincien e ccring he hicl l cnervin e hve S
18 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice 8 PS P 64 Tie re chnge he liner -enu he cincien e Wih Eq e hve P c c S kg c 866 The liner -enu he cincien eril vlue incree i l hru he nzzle 65 Tie re chnge he liner -enu he cincien e P P S Wih Eq e hve P in S kg in 5 The liner -enu he cincien eril vlue e n chnge i l hru he nzzle 66 Tie re chnge he kineic energ he cincien e Wih Eq e hve KE kg 5 75 kw S S 67 The kineic energ he cincien eril vlue incree i l hru he nzzle Thi i cnien ih ur hicl inuiin h l hru nzzle ccelere hence reuling in incree in velci n kineic energ S
19 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle 7 nervin [unn e l Prle n W #] 9 ir nr cniin ener he crer re I leve he nk hru -in-ieer ie ih eni 5 lug n unir ee 7 7 Deerine he re lug hich he ir in he nk i increing r ecreing 7 Deerine he verge ie re chnge ir eni ihin he nk Sluin nrl lue nrl vlue i inr n nn-ering I inclue vlue ir in he nk ell he rin in he inle n ei ie u he in here e hve eg eni velci uin nir eni ver ech cr ecin Dieren cr ecin hve ieren eni elci i il n unir ech cr ecin nir eni in ic Equin - S 7 Deerine he re lug hich he ir in he nk i increing r ecreing e nvecin lu Ter S S Wih unir eni n velci ver ech cr ecin e l hve Q Q S Q - The - hen give Q
20 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice S lug Q 8 8 lug lug lug Thu 8 94 lug 456 lug eglec n cnriuin he r he h i n in he nk = Tnk + Pie e in h he ir in he nk incree he re 456 lug S 7 Deerine he verge ie re chnge ir eni ihin he nk ne Ter [ hu n e i unir in ] gin neglec n cnriuin he r he h i n in he nk = Tnk + Pie e hve he ie re chnge ir eni in he nk 456 lug S 456 lug 4 lug 8
21 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice Prle 8 nervin n enl Trnr There TT [e r unn e l 998 Prle n i Ter] recngulr el ih cr ecin i une hriznll grvi i in he z irecin ir ener he el ih unir ee u leve nn-unirl In c here i regin erin r revere l hn in he igure ue h he l ir in he el i e 8 in he inle ee 8 in he ie re chnge he -liner enu he eril vlue r cnrl h PS P innneul cincie ih he vlue ir in he el [in ] Tke ir eni e kg Sluin = i he ih he chnnel = i he n ih he = 5 5 nrl lue The cnrl vlue i inr n nn-ering I inclue ir in he el nl eril lue We cnier he eril vlue h innneul cincie ih he cnrl vlue uin Increile l i e n unir elci iel i e nir velci ecin ic Equin TT - S S 8 in he inle ee
22 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice - S ne Ter [ i inr n nn-ering i e] e nvecin Elu Ter S j j S ] [increile l ] re unir n [ elci - - hen give S 8 in he ie re chnge he -liner enu he eril vlue r cnrl h innneul cincie ih he vlue ir in he el [in P P S ] TT S S P P ne Ter P P [ i inr n nn-ering velci n eni iel re e] e nvecin Elu Ter S
23 4-65 lui echnic r Inerninl Engineer W # re ecr Preure n Preure rce TT n - Due ri Se he ISE ice kg j j S TT The TT hen give P S he inle he ir re e n hve he enu ever i l hru he el i gin ne negive enu Thu he ie re chnge he enu r he cincien i negive
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