PERT (CPM & OCF) CLASS TEST-SOLUTIONS

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1 PERT (CPM & OCF) CLASS TEST-SOLUTIONS. (d) A projet is omposed of jobs, ativities, futios or tasks that are related oe to the other i some maer, ad all of these should be ompleted i order to omplete the projet. Ever projet has oe speifi purpose. It starts at some speifi momet ad it is fiished whe its objetives have bee fulfilled.. (d). (d) Ma outries, rih i material resoures are exeedigl poor i terms of level of produtio or pla ahievemet, while there are other outries whih have ver limited atural resoures but have ahieved higher level of produtivit mail beause of talets, skills, experiee ad kow-how of their people. Shortomigs of bar hart: (i) (ii) (iii) (iv) Lak of degree of details Revieo of projet progress Ativit iter relatio ships Time uertaiities. (a) Loopig : If a ativit were represeted as goig bak i time, a losed loop would our. 5. (b). () 7. (d) Daglig : No ativit should ed without beig joied to the ed evet. If it is ot so, a dumm ativit is itrodued i order to maitai the otiuit of the sstem. Suh ed-evets other tha the ed of the projet as a whole are alled daglig evets. Daglig A D B C Dumm I the above etwork, ativit D leads to daglig. A dumm ativ it is, theref ore itrodued to avoid this daglig. Nodes are umbered to idetif a ativit uiquel. Tail ode (startig poit) should be lower tha the head ode (ed poit) of a ativit. Evet umberig should be arried out o a sequetial basis from left to right. E F A B C The expeted mea time is iteded to be a time estimate havig approximate a 50% hae that the atual duratio will be less ad a 50% hae that the atual duratio will exeed it. A losed loop would produe a edless le i omputer programmes without a built-i routie for detetio or idetifiatio of the le. T his situatio a be av oided b hekig the preedee relatioship of the ativities ad b umberig them i a logial order. Thus, oe propert of a orretl ostruted etwork diagram is that it is oli. 8. (a) 9. ()

2 () CIVIL ENGINEERING PERT (CPM & OCF) CLASS TEST 0. (d),,0 5 do t t p 0 8 0,0. (a) 5 9, 7, 5 7 t e. (d). (b). (b) t t 5,5 t t t 0 m p t p , The earliest expeted time is the time whe a evet a be expeted to our. N M P O The ritial path will be as maximum time is required alog this path. smith t t p (b). (a) 7. () 8. (a) 9. (b) 0. (). (b). () smith > Do () 0,0 () 5 () 8,0 8 (7) 8,8 () Time sale versio () 7, 5 9,9 7 () 9(8) () () 9(8) 5 7() 5() 8(7) Crashig ativit 5 b da, -5 b das & - b da. Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

3 PERT (CPM & OCF) CLASS TEST CIVIL ENGINEERING (). (). (b) 5. (). () 7. (b) 8. (d) () () () 8(8) 5 7() () 8(7) 5 Hee, mi. time required for the ompletio of projet is weeks. SFF i 0.0 i Ist optio: Aual equivalet ost of tuel 0,00, ,0,000 Total ost of tuel Aual ost + operatig ost aual,0, ,000,00,000 IId optio: Aual ost of pipe lie P CRF ,0,700 Operatig ost of pipe lie 9,000 Total ost of tuel auall,0, ,000,95,700 Relative disadvatage of tuel 9. (b) 0. (),00,000,95, Book value from deliig balae method, B C FDB i I this method, there is a large amout of write off ie depreiatio i the earl ear of utilit period is more tha i ompariso to later ears of utilit period. Depreiatio of equipmet from straight lie method. D Ci C s Average aual ost of the equipmet A. (). (d) P Charge o ompa ever ear CRF i i i Sigle pamet ompoud amout fator SPCAF For CRF i i i i Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

4 () CIVIL ENGINEERING PERT (CPM & OCF) CLASS TEST. (). (d) 5. (). () Expeted profit (profit) Probabilit of makig the profit Projet order of preferee Expeted profit III IV I.0.. V II FDB Cs Ci i 5%,, CRF 0.5 x p i SFF SFF CRF i 0.0 x Let us osider a ase i whih the speifi eerg is kept ostat ad the disharge is varied. E s ga or A g (Es ) where E s speifi eerg ad disharge through hael A C/s area of the hael depth of flow A (g) (E s ) ga Es ga For a give speifi eerg, the disharge will be maximum if d 0, d differetig above equatio ields d d da da ges A g A A d d da d A ge s (AT) g (AT) ga 0 or, E s T T 0 T(E s ) A E s But E s or ga g A T ga A T A T This equatio is for the ritial depth. Thus for a give speifi eerg, the disharge i a give hael is a maximum whe the flow is i the ritial state. The depth orrespodig to the maximum disharge is the ritial depth. 7. (d) max Itrodutio of hump will ause a derease or irease i flow depth depedig upo whether the flow is subritial or super ritial. Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

5 PERT (CPM & OCF) CLASS TEST CIVIL ENGINEERING (5) 8. () Depth Where C E E Z Sp. eerg (E) E E Z E E Z q Subritial flow Superritial flow sp. eerg at upstream setio sp. eerg at Hump Setio Height of Hump. Disharge per uit width (q) urve remais uharged beause width is uhaged. Speifi eerg, E ga For simpliit, osider a retagular hael of width b, for whih A b. The E, g expressig E as a futio of the disharge q ad the depth, or g g (E ), expressig q as a futio of E ad. The urve of q as a futio of for a fixed E is plotted. a q b Sub-ritial q max Super-ritial d We otie that q is a double valued futio of ad has a maximum possible value m. For depth smaller the the ritial depth the veloit is greater tha the ritial veloit. Flow i this regio is alled super ritial. The same disharge is possible with give e i either regio. Suppose that there is a lateral ostritio i the hael, reduig its area ad ireasig disharge with per uit width (q). Assume there is o head loss, the speifi eerg does ot hage, so the flows i the ostritio are represeted b poits b ad d. we ote that i subritial flow, the depth of flow dereases while i super ritial flow the depth ireases. We a also plot as a futio of E for a ostat disharge, q. The poit a orrespods to a upper stage or trasquil flow. E b a d E E Let us suppose there is a hump i the bed of the hael that dereases the speifi eerg E to E. The height of the hump will be the derease i the speifi eerg. If the flow is subritial, we see that depth will derease slightl to poit b. If the flow is superritial the depth will, o the other had, irease slightl to poit e. This is exatl the same as the respose to a lateral ostritio. If the hump is high eough, the flow ma beome ritial at it. For a larger hump, the speifi eerg a ot derease further, ad istead the upstream depth must irease to keep the flow ritial over the hump. For this reaso, suh a poit mabe alled a otrol setio, sie it otrols the upstream depth. The vertial taget at ritial depth meas that small hages i E will ause large hages i, so the surfae ma appear disturbed. Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

6 () CIVIL ENGINEERING PERT (CPM & OCF) CLASS TEST 9. () 0. (d) Eerg dissipatio i a hdrauli jump is mail aused b the large sale eddies geerated due to high turbulee & shear atio of the reverse flow roller. Large sale eddies forms or trasport the fluid over a short distae. Depth irease diretl froms superritial to subritial flow without reahig & a hdrauli jump forms i short reah, therefore suh tpe of flow is also kow as rapidl varied flow. A positive surge is oe whih results i a irease i the depth of flow ad a egative surge auses a derease i the depth of flow. Positive surge (Advaig dowward). (b) v V w v V w Negative surge (Retreatig dowstream) V w v v Positive surge (Advaig upstream) V w v I ruig irrigatio aal whe the regulatig gate is partiall losed, suh a movemet gives rise to a positive surge travellig upstream ad a egative surge rises i dowstream. v Due to extreme old whe aal surfae freezes the wetted perimeter will irease. For same disharge, the area of flow has to irease.. () Cross-setioal area d () () Substitutig, h d (). m. () Eerg at a poit : os s se tioal area wetted perimeter. 0.9 m. H Z + + v g...(i) For ustead o-uiform flow, v v (x, t) dv v v dx dt x t Differetiatig (i), w.r.t. x, we get H x s f s 0 + s f s 0 + s f s 0 z v x x x g v v dx v dt x g x dx t dx v v v x g x v t v v x g g t v V SF S0 x g g t Stead uiform Stead No uiform flow Depth of flow irease. Ustead No uiform flow Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

7 PERT (CPM & OCF) CLASS TEST CIVIL ENGINEERING (7). () 5. (b). (b) A R S / / / / B S / BS 5/ h 5/ 5/ 5/ 5/ / 5/. 00 5/ 5.5% 0.5 R R 0. m 0.5 RS (9.80 ) N/m * shear veloit 0.07 m/s O B z For a trapezoidal hael setio to be most eoomial or most effiiet, the hdrauli radius must be equal to half the depth of flow. R... (i) Moreover, for a trapezoidal hael setio to be most eoomial half the top width must be equal to oe of the slopig sides of the hael. B z z...(ii) The above oditios are based o the assumptio that side slope z is o stat. As suh these oditios will ot provide a most eoomial or most effiiet trapezoidal hael setio if either the bottom width or the depth of flow has to be limited due to phsial osideratios. However, it is possible to derive the oditios whih should be satisfied for a trapezoidal hael setio to be most eoomial or most effiiet whe either the bottom width or the depth of flow has to be kept ostat. The followig two oditios a be obtaied whih ma be used for the desig of a most eoomial or most effiiet trapezoidal hael setio. (i)for the bottom width to be ostat, B z A...(iii) z z (ii)for the depth of flow to be kept ostat, z From equatio (iv), (iii) ad (ii) B 0º...(iv) It ma, therefore, be stated that the most eoomial or most effiiet trapezoidal hael setio, whih would satisf all the above three oditious, ma be obtaied b adoptig side slope z i the desig of the hael setio. If a semi-irle is draw with 0 as etre ad radius equal to the depth of flow, the three sides of a most eoomial or most effiiet trapezoidal hael setio viz. the bottom ad the two sloppig sides will be tagetial to the semi-irle. Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

8 (8) CIVIL ENGINEERING PERT (CPM & OCF) CLASS TEST 7. (a) 8. (d) 9. (a) a For E Fr T ga T ga E E E V g V g g A d T a A So E E 0 0 a x d a d a a g 7 / / a 7 a 9 E. Note : It s idepedet of a. v R / S / fr 50. (a) / S gd here f h L S hf gd gr f / / L R R H r f f 8g / R V. g 9.8. iitial flow is subritial g / R < (v) g 0.95 m E C.8 m E E Flow is hoked 5. (b) / (.)..9 m g z E E E z Flow u/s will irease Flow u/s will irease Tpe. Smooth emet. Good orete. Firm gravel /. Caals ad rivers i good oditio d where, d i meter..5 0 / h f / fl v flr S gd gd Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

9 PERT (CPM & OCF) CLASS TEST CIVIL ENGINEERING (9) 5. () 5. (a) M Depth (d) M profile CDL 5. (a) 0.7m 5º.m Speifi eerg(e) At miimum sp. eerg, the flow is ritial E ad Y 0.7 q g q g q.99 m /s 55. (b) S S profile C profile A A profile Retagular Chael Elevatio z CDL CDL NDL CDL, NDL I a hdrauli jump speifi fore for pre ad post pump depths remai ostat but there is loss of speifi eerg B B Pla Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

10 (0) CIVIL ENGINEERING PERT (CPM & OCF) CLASS TEST.5 m Zoe + z B m ; B. m Now, E E + z C M Zoe Zoe 5. (a) 57. () 58. () v g v g v g v v v z g from otiuit equatio, A v A v A A B B.5. z.5 z.5. C z 0.5 m H Zoe Zoe Superritial flow o horizotal bed 59. (a) 0. (d) Superritial flow o a mild slope C C Zoe Zoe Superritial flow o a ritial slope C SZ Zoe Zoe Zoe Superritial flow o a steep slope The surfae profile of water surfae i a ope hael is give b for. (a) d dx S 0 d dx > 0; (i) > ad > ad (ii) < ad < Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

11 PERT (CPM & OCF) CLASS TEST CIVIL ENGINEERING (). (b) CDL NDL S Gate Pool So, HJ will our 8Fr.0 m Water surfae profile S E 0. m. (d). () 5. (d). (a) At all, A, B ad C poits, water surfae profile is risig i dowstream. However, at A ad C, depth of flow risig is more tha ritial depth ad at B, depth of flow is less tha both ritial depth ad ormal depth. Hdrauli jump ireases the weight o apro ad hee dereases the uplift pressure. Speifi fore will alwas be ostat for horizotal ad fritioless haels of a shape. Stregth of jump depeds ol o iitial Froude s umber be greater tha. Relative eerg loss durig the slopig floor dereases with irease i the slope. So oe of the optios are orret. Area 0. m m /se V 5 m/ se A F r. 0.5 V 5 g > 7. () 8. (b) d (d /) E H kw 8.57 kw 8.57 HP q / gd. HP (.0/) 80.0 /.0 / m E (d d ) /d d (.55.0) /[() (.0) (.55)] 0.00 m of water The Froude umber before the hdrauli jump is Fr V 7 m/s.50 g 9.8m/s 0.80m Whih is greater tha. Therefore, the flow is ideed superritial before the jump. The flow depth, veloit, ad Froude umber after the jump are 0.5 8Fr 0.5 (0.8 m). m m.8 m/s.m V V 7 m/s Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

12 () CIVIL ENGINEERING PERT (CPM & OCF) CLASS TEST 9. () 70. (b) 7. () Fr V g 0..8m / s (9.8m / s )(.m) The head loss is determied from the eerg equatio to be h L + V V g (0.8m) (.m) m (7) (.8) (9.8) The speifi eerg of water before the jump ad the dissipatio ratio is E s + v Dissipatio ratio Tpe of jump g (0.8 m) + (7) (9.8) s.0 m h L 0.57m 0.7 E.0 m Froude Number F Relative of iomig Eerg loss flow Udular Jump.0<f <.7 0 Weak Jump.7 F.5 5 8% Osillatig Jump.5 F.5 8 5% Stead Jump.5 F % F > % The disharge of uiform flow i a hael ma be expressed b usig hez s formula as AV CA RS K S Where K CA R The term K is kow as oveae of the hael setio whih is a measure of the arrig apait of the hael setio, sie it is diretl proportioal to the disharge. The depth of f low is kow as ormal depth whih is represeted b. For a other values of the speifi eerg exept at the ritial depth, there are two possible depths, oe greater tha the ritial depth ad the other smaller tha the ritial depth, at whih is a give disharge a our with same speifi eerg. These two depths for give speifi eerg are alled the alterate depths. I a hael, for a speifi fore, there are two possible depths ad. These two depths ad ostitute the iitial ad sequet depths of a hdrauli jump. Whe the depth of flow of water over a ertai reah of a give hael is equal to the ritial depth the flow is desribed as ritial flow or i ritial state. The ritial depth for a give disharge is the depth orrespodig to whih the ross-setioal area A ad top width T of the hael setio are suh that the value of A T A T g Z g is give b A A T Z where setio f ator f or ritial f low A omputatio, Z A for a hael setio T at the ritial state of flow is equal to /g. For a prismati hael, the setio fator Z is a futio of the depth of flow. Surfae profile i mild-sloped haels; I a mild sloped hael, there will be three zoes viz; > Y >, > >, ad > > i whih M, M ad M omes will be formed. Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org

13 PERT (CPM & OCF) CLASS TEST CIVIL ENGINEERING () 7. (a) ostat ostat F P P 7. (d) P E Speifi eerg urve E ga Chael is ver wide so R. m As per strikler s equatio, / d Atual dia of grai dm 000 d mm Wrog value used b egieer wrog (000 d) / d orret orret wrog 000 As per maig s equatio q S 5/ observed ( ) wrog / / 5/ / ( orret ) 5/ orret ( orret ) orret m 5/ / (.) 5/ 7. (a) 75. (b).8 m F P Speifi fore urve F ga 0. m Az V w.7 m/se 7.5 m/se.8(.7 V w ) 0.(7.5 V w ) (.7 V w ) 7.5 V w. 7.5 V w.8 m/se V w The eters of the irles move at urret V ; hee, x V (smaller irle) 0 0 x 9 9 V (larger irle) 0 0 Subtratig these equatios, 9 0 5V, V 9 0 / 5, 0 g m/s, V (9)(.98)/5 7.5 m/s. Regd. offie : F-, (Upper Basemet), Katwaria Sarai, New Delhi-00 Phoe : 0-00 Mob. : , ies_master@ahoo.o.i, ifo@iesmaster.org