() Class Test Solutio (OCF + Hdrolog) -5-6 Aswer ke. (a). (a). (). (a) 5. () 6. (d) 7. (b). () 9. (d). (b). (b). (d). (). () 5. (b) 6. (d) 7. (d). (b) 9. (a). (). (d). (b). (). () 5. (b) 6. (a) 7. (). (b) 9. (). (a). (b). (). (b). () 5. () 6. (d) 7. (). (b) 9. (a). (b). (). (b). (). (d) 5. (a) 6. (a) 7. (). (b) 9. (d) 5. (a) 5. () 5. (d) 5. (a) 5. (b) 55. (b) 56. (b) 57. (d) 5. (a) 59. (b) 6. (a) 6. (a) 6. () 6 (a) 6. (b) 65. (d) 66. () 67. () 6. (a) 69. (b) 7. () 7. (d) 7. (b) 7. (d) 7. () 75. (d) 76. () 77. () 7. (b) 79. (d). (d). (a). (d). (a). () 5. (a) 6. (d) 7. (). (d) 9. (a) 9. (d) 9. (b) 9. (a) 9. (d) 9. () 95. (d) 96. (d) 97. (d) 9. (b) 99. (d). (d)
. (a) Here, T 5 ears p q..9 p,.9.55. (a). () Maximum average depth 6 mm 5. The probabilit of a hr raifall equal to or greater tha mm ourrig at Kolkata atleast oe i ears p,.55.55. Tpial DAD urve 5 hrs hrs Area (km ) The water budget equatio for the athmet i a time t is R P L where L Losses Water ot available to ruoff due to ifiltratio, evaporatio, traspiratio ad surfae storage. I the preset ase, t duratio of hrs P Iput due to preipitatio m Ruoff/raifall ratio. Ruoff. m. m ha.m Average stream flow rate at the outlet i the period of hrs m /s 6.667 m /s m /mit. (a) Raifall of mm/h itesit over the watershed for a duratio of 6h 6 mm m Measured diret ruoff volume i the stream m Preipitatio ot available to ruoff i this ase 9 m 9.9 m 9 m m 5. () Total area of the athmet km. Zoe Area (km ) Aual ruoff (m) (km ) m A B C 6. (d) 6 9 5 Total ruoff 55 km.m 7 6 6 Aual average ruoff from athmet 55 5. m Class A pa evaporatio.5 m/da Assumig pa oeffiiet C P for the pa.7 Lake evaporatio C P Pa evaporatio.7.5 m/da.5 m/da Total evaporatio from the aal durig the moth
() 7. (b).5 5 6 m Raifall itesit m/h for h. () Total raifall 6 m Surfae ruoff.6 Mm.6 6 6. m m loss due to ifiltratio 6 6 m Average ifiltratio apait durig the storm 6.75 m/h Horto s equatio is K t f p h f f f e o t ad F P f p t dt K t f t fo f e dt h As t, t Kht e dt K For large t values, F P f t 9. (d) h f o f Here, F P m, f o m/h, f m/ h ad t 9 h K h ( 9) + ( )/K h K h h f o mm/h f 5 mm/h K h.5 h Horto s equatio is. (b) ad F P K t f p h f f f e t p o f (t) dt K t f t fo f e dt h For large value of t, Time (da) 5. (b). (d) F P fo f f t K h 5 5.5 + 5 mm Raifall (m) 6 9 5 t -idex (m/da) Exess raifall (m/da) 6 Total ruoff from the athmet m. u 5 km/h u 9? u h Ch /7 where u h Wid veloit at a height h above the groud C Costat u 9 /7 5 9 u 9 6. km/h Usig the oveae ad slope urves, the disharge at a stage is alulated as K Sf where K AR / Maig s roughess A Area of ross-setio R Hdrauli radius
(). () A ad R are futios of the stage, the value of K is also a futio of stage. Sf S ad. () f S S f f 6. m /s m v.d.6 m/s v.d. m/s d.9 m Average veloit of flow at the setio v v v.d.d.5 m/s Disharge through the hael,.9.5.5 m /s 5 m /s h h h DRH Cathmet area km Volume of surfae ruoff 6 5 6 5 Raifall exess, ER 6 5. (b) Volume of surfae ruoff 6. (d) 6 m ER m Area of athmet 6 596.6 6 m 596.6 km ER of h UH m.5 m 5 m Volume of ruoff Area uder h UH 6 5 5 5, m Time (h) () 5 6 7 7. (d) Cathmet area represeted b this UH Ordiate of h UH (m /s) () 5 Ordiate of h UH lagged b h () 5 5, 5. 6 m 5. km Ordiate of h UH lagged b h () 5 Total raifall of h storm 7 m Loss @.5 m/h for h m ol. + ol. + ol. (5) 7 Effetive raifall of the storm 7 6 m Peak ordiate of h UH m /s Peak ordiate of h DRH 6 m /s Ordiate of h UH (ol. 5)/ (6).67.67..
(5). (b) 9. (a). () Base flow m /s Peak of the flood disharge due to the storm + 5 m /s For total depth of raifall of 7. m Loss @.5 m/h for h. m Effetive raifall 7.. 5 m Peak flow of flood hdrograph m /s Peak flow of DRH due to 5 m exess raifall m /s Peak flow of DRh due to m exess raifall /5 6 m /s For total depth of raifall of 9.5 m of h duratio, loss @.5 m/h for h. m Effetive raifall 9.5. 7.5 m Peak flow of DRH due to 7.5 m exess raifall 6 7.5 m /s Base flow m /s Peak flow of flood hdrograph due to 9.5 m of raifall + m /s. % of flood peak % Area of athmet A 6 km Duratio of uit hdrograph h Equilibrium disharge of S-urve S.77 A/D m /s 6.77 5. m /s The equivalet ruoff oeffiiet, C e.7. 5.... (d) Area of watershed, A 9 ha.9 km Ruoff oeffiiet, C. i t,p.5 m/h 5 mm/h Usig Ratioal formula for peak disharge, P. (b). (). (). Cit,p A 5.9.5 m /s.6.6 Volume of water lost 6..5 Mm here Speifi ield.5 Porosit,.5 Volume of saturated olum aquifer m Volume of water stored i the saturated olum.5.5 m Iitial apait of the reservoir Mm Fial apait of the reservoir 6 Mm Aual sedimet ield. ha m. Mm Trap effiie, t.9 Aual apait loss of the reservoir with sedimet.9..6 Mm No. of ears required to fill 6 Mm reservoir apait 5. (b) 6.6 6.67 ears 7 ears The Probabilit desit futio satisf the oditio that f(x)dx 6. (a) 6 Kx dx K( x) dx 6 7 k + 7 k k Ratioal formula is P CiA has to
(6) 7. () V N s P doesot deped o time ad if itesit, i is same, the P i.e., peak flow does t hage. Equatio of urret meter V an s + b... (i) Here, Stream veloit at the istrumet loatio i m/s Revolutios per seod of the urret meter a, b Costat of urret meter From ().5 a 5.6 a 5 From () & () From (i) + b... (ii) a.5, b. + b... (iii) V.5 N s +..5 5 6 +..6 m/s. (b) Legth of ju mp 6.9 ( ) [experimetall] L 6.9 (.). m 5/ / 9. () A /pw.6. The most effiiet triagular setio has a 9 agle ad : side slopes. (a) d d d,p A.d, d 5/ / d /.d.6, d.6m V q/ /.5. m/s F r V / g F r. / 9.7.5.5 w. (b). (). (b). () 5. () / + F r / /.5 + [ + () (.5) ] /.6 m V V (.) (.5) (V ) (.6) V.9 m/s F r.9 / 9.7.6.96 Loss, E j ( ) / (.6.5) / [() (.6) (.5)].6 m E + v / g.5 +. / [() (9.7)].5 m Peretage dissipatio E j /E.6/.5. or. peret C g 9. 9. 9. m/s Veloit of wave movig upstream C V 9. 6. m/s. kg Rs RSl m siº. Froude umber, of flow at miimum depth, Fr V. gl 9. Depth of flow before ad after Jump, + Fr +..9
(7).9.9.9 m 6. (d) Disharge itesit, Bed slope, q m / s / m S..5 Chael is ver wide so hdrauli radius, R Usig Maig s Equatio, q R S / / / ( ).5. Normal depth of flow,.7 m Critial depth of flow, q g / 6 9. /.m Sie, slope is steep.7m m.7m Steep CDL NDL At a ertai setio flow depth is m < meas i regio So, profile is S 7. () de S S f dx f de S S dx E x S S f Depth of mid-poit.9.95m At this poit, q (S ) Sf.7 E E 5/ / f q g + 9..6 m q g.9 + 9..9.97 m x.6.97..7 5. m {( ve) meas upstream}. (b) Disharge per meter width q m /s/m Eerg loss, E L m For retagular hael q g ( ).5...() 9. EL...() Solvig b trial ad error Chekig optio (a). m Puttig i equatio (). (. + ).5...5.9..9 m E L
() 9. (a). (b).9...9. m Chekig optio (b). m Puttig i equatio ()..9.5.55 m E L.55...55 Hee O.k disharge (m /s) () Time 6.96 m m /s 5 m /s 6 time (hours () Ordiate of 6h UH 5 () lagged b 6h 5 () Additio ol()+ol() 5 5 (5) Ordiate of h UH ol() ol() 5.5 7.5 Peak disharge of h UH.5 m /s Average raifall Ifilteratio 6 m..5 6 m Raifall exess 6 6 m Hee peak disharge of DRH peak disharge of h UH.5 5 m /s. () Depth of raifall Area of athmet. (b) Area uder UH 6 A 97 m. A Time Iterval 97 hetare Raifall (mi) (mm).7 +.. +.. +.5 7 5.5 +. 7 6. +. 5 Maximum raifall i mi 7 mm Itesit 7.5mm / mi. () For most effiiet trapezoidal setio, b 6 / For miimum wetted perimeter, 6. Hdrauli radius, R b Area Wetted Parameter b + b + b +
(9). (d) R 5. (a) b + + 6 + Width of top of liquid surfae b + + Hee width at top is two times the legth of slopig sides. Hee the oditio for most eoomial setio is maximum disharge for a give ross-setio. This is ahieved b maximum hdrauli radius ad miimum wetted perimeter. T 5 h The oditio for ritial depth i.e. miimum speifi eerg. A...(i) g T A h T h h h T h g h 6 5 h h h g /5 () I hdrauli Jump, the flow trasforms from super-ritial to sub-ritial i.e. froude umber harge from more tha oe to less tha oe. 6. (a) () It is assumed that the flow is uiform before ad after the Jump. The pressure distributio is hdrostati before ad after. () Hdroli Jump is assoiated with loss of eerg due to edd aid turbulees. 7. () Sie the first storm produes m et ad the seod storm produes m, divide all ruoffs b two. Offset the seod storm b hr. (b) hour first seod storm storm total 5 5 7.5 7.5 6 5 56 5 6 75.5 5.5 7.5 7.5 6 5 5 5..5 hee the peak is 75 m /s peak disharge m /s h hdrograph peak disharge m /s measured peak disharge m /s hdrograph disharge at h m /s From the illustratio, at h the disharge is 6 m /s ad the gagig statio measures 5 m /s. The uit hdrograph shows the peak ourrig at 6 h with a disharge of 6 m /s. h h m m 6 5 s s 5 m /s m 6 s
() 9. (d) Peak of iflow hdrograph, m /hr Peak of outflow hdrograph, m /hr Time base of iflow hdrograph 96 hours. (m /hr),, O E H 96 G Iflow hdrograph Outflow hdrograph A () B () C (96) D Time (hrs.) 9 Chael storage after hour (Total iflow hr Total outflow i hr) (Area of OEA Area of OAH) Time at whih peak of outflow hdrograph ours 95 (,,) + 9, hours Ordiate of H, m /hr m /hr. Storage after hour, m. Chael storage after hour, m. 5. (a) Maximum storage will our i the hael at the time of itersetio of iflow ad outflow hdrograph. Beause, till this poit iflow i the hael is greater tha the outflow ad beod this poit, outflow is more tha the iflow ad hee hael storage will derease beod this poit. Hee, Maximum storage will our at t hours, from the startig. Maximum storage (Area of OEGB) (Area of OGB) (Area of OEA + Area of AEGB) Area of OGB,, (,,) 9 (5, + 7,), 96, m Maximum storage 96, m. 5. () Hdrauli gradiet, i Differee i head Legth Disharge veloit, 5 5 v k i.5 m/da 6 Seepage veloit, v Disharg e veloit Porosit.5 m / da.5 6 Time of travel of iert traer from oe well to aother t Dista e betwee wells Veloit 5 75 das 5. (d) Hdrauli flood routig equatio is I I t t S S Noe of the optios is orret t 5. (a) Kirpih equatio is a empirial equatio used for the estimatio of the time of oetratio.
() 5. (b).5 55. (b) R R. m.5 RS (9. ).. E E z Flow u/s will irease Flow u/s will irease 59. (b) 56. (b) 57. (d) 5. (a). N/m * shear veloit.67 m/s. C / d g (x ) Head (x ) q Cd g (x ) F F / q q F g g g F or F F F F F V. Hr < g 9.. iitial flow is subritial (v) g.95 m / E C. m E E (.)..9 m g z E Flow is hoked s + s r. +.. porosit Total groud water storage. 6.5.5 Mm Available groud water storage. 6.5.5 Mm where s speifi ield s r 6. (a) Piezometri head 6. (a) 6. () h speifi retetio h h h L x where h piezometri head at the u/s ed ad at a distae x from u/s ed the head is h. h piezometri head at a distae L from u/s ed This is the equatio of the hdrauli lie, whih is show to var liearl from h to h. Give diameter, d m Slope, S. m
() 6. (a) Give: Width, full half A R A R F r AR AR B 5. m / / S / / / full / half Disharge, m /s Let depth of flow be We kow that F r S full half d d / d d d d V g Agai V Disharge Area / / full half...(i) [V veloit of flow] (5.) Puttig value of V i equatio (i), we get 6. (b) m.5 m /s. g. m.99 S. Normal depth of flow betwee.76 m to. m. If prevailig ormal depth of flow is ot exreded, there must ot be hokig of the i.e., setio or there must be just hokig. Thus the width of the setio should be suh that for the prevailig sp. eerg there should be ritial flow at the otrated setio q g Bmi g / / E E iitial E iitial Let is ow alulate E iitial / / AR S.7 m E iitial + Bmi g () / / g Bmi / () (.).5 / B mi / q g.7 9. (.7).79 m.79.79.6 m 65. (d) Variatio of disharge wrt ormal depth i a wide retagular hael (where hdrauli radius ormal depth) i.e. R is give b, / / V R S () S Disharge, V A 5/. / / B / / S Normal depth is ireased b %, the /
() %age hage i disharge is give b, 5/ 5/ (.) () 5/ () peretage hage i disharge, 5/ (.) 7.6%. 66. () Disharge per meter width, q 9 m /s/width I retagular hael, ( ).6 (.6 ).6 m q g 9 9..6 5.99 5.766, 6. 5.766 m 5.77 m 67. () For hdrauliall effiiet hael wetted perimeter should be miimum dp d A B. e (Area Costat) P B + e P e A e e e A A B. e e e e B B e B Top width, B e e Perimeter, P B + e Hdrauli radius e + e e Hdrauli depth A P B. e e e. e A T e e B. e B 6. (a) Width of retagular hael, B 6. m Disharge, 6 m /s Normal depth,.6 m Maig s.5 From Maig s equatio; e / / AR s Area, A B. 6.6 9.6 m Perimeter, P B + 9. m R A P. 6 / / AR S S.59 69. (b) Veloit, v A 6 9.6 E / /.(9.6).(.) S.5 5 m/s v (5 / ) g.6 9.
() F r.7 m v (5 / ) g 9..6. < subritial flow Without affetig the upstream oditio E E + Z Z E E Z will be maximum whe E is miimum (ritial speifi eerg at setio-) Z max E E C q E g.7.95 m. m 7. () E.7 m / (6 / 6) 9. / If upstream oditio is ot affeted, E E Flow is subritial so as we otrat the width at setio () depth of flow will derease whe the depth at setio () is equal to ritial depth, flow at setio will be ritial flow, beod this further otratio will affet the upstream oditio E E C E q g /.7.7 q.9 m /s/m B.9 B.9 6.9. m. m 7. (d) Disharge per meter width q m /s Bed slope, S.. / / AR s For wide retagular hael,.. R s q / 5/.6 m ritial depth of flow > Hee, slope is steep q g /.7 m 9. 7. (b) Disharge, m /s. Flow depth, B.B. g F r.5 v g.5.5.. g.5.5 9..5 /
(5).6 m Perimeter, P B +. m Area, A B..9 m R A.m P From Maig s equatio, / / A R s.9.. S S. / / 7. (d) Width ad flow depth are same. So, R. m Slope S. Average boudar shear stress, 7. () grs 9... 7. N/m Bed slope, S 6 Maig s oeffiiet,. 5 m /s Area, A Perimeter, P Hdrauli radius, R A P Usig Maig s Equatio 75. (d) We kow that 5 / / AR s / /. 6 / 5.9 m V w V V V w C V Where V w Absolute veloit of surge? Give.6 m, V. m/s We kow that C g C.6 C V w..6 m/s7. (a) Chael is steep so ritial depth will our at etrae speifi eerg at setio () speifi eerg at setio (). m.. m Reservoir we kow. m Steep hael CDL NDL
(6) q g /.m q. m /s/m. m /s Whe hael slope is ireased b %, the also ritial depth will our at the etrae hee disharge will ot hage i hael. 76. () Pressure fore, P pressure at C.G. Area P P x 9 Area. Fore i x diretio Rate of hage of mometum i x diretio P P (v v ) Give,.5 m A A m /s 9 N/m.5 9.5.5 7 7 7. Solvig b trial ad error,.7.m 77. () F F r F r..5 m? F? r. m Now,. r 7. (b) Critial depth, 79. (d) r ( Fr ). [ Fr ].5 [ Fr ] F.9. q g /.67 m Give.5 m < S > S C Hee slope is steep Chage i storage s s iflow outflow x + z () 9. 6 6 m ( 6 )m + ( 6.)m 5 6. 6 E E.6 6m 6 m m /
(7). m. (d) (P ) t R Ruoff m /s 6 (x) E ( ) m km km (). m km ( ) 5 m /s 6. (d) Give data: hr, m raifall has a retur period of 5 ears i.e. T 5 rs. The probabilit of ouree of a evet, r times i suessive ears Where, P q C r r rp q (z) Probabilit of ouree of a evet T Probabilit of o-ouree p The probabilit of the hr, m raifall or m ore, ouri g i ea h of t wo suessive ears C p q C p q 5.. (a) Both the storms have same ifiltratio idex. (P ) t R Ruoff where P is raifall itesit (. ) 5. 5. m/hr where P is raifall itesit (p.). p...5 m/hr. (a) We kow that,. () Area of UH Cathmet area m 6 Disharge (m /s) 6 A A. km 5 6 Time (hours) Area of uit hdrograph m athmet area 6 6. A 6 m. A A 7.9 6 m 7.9 km 5. (a) Duratio of storm is differet from duratio of uit hdrograph (UH) So, we have to overt h UH ito h UH (duratio of UH equal to storm duratio) Storm duratio m duratio of UH h m h
() () Time hr As m is ot a iteger so usig S urve method () Ordiate of h UH () S urve additio () S urve ordiate (5) S urve lagged b h (6) ol () - ol (5) (7) Ordiate of h UH ol (6) / _ 5 6 7 6 9 9 9 9 5. 5.. Peak of h UH 6 m /s Effetive raifall of storm 6.6. 6 m Peak flow due to storm 6 peak of h UH + base flow 6 6 + 5 m /s 6. (d) O KI K I KO K K K O 7. () Aordig to give oditio - flow is subritial A B Flow C Depth of flow E E q q Subritial Superritial Speifi eerg q > q as width of the hael ireases, disharge per uit width dereases ad hee flow depth for dereased disharge/width ireases f or subritial flow. while it will fall for superritial flow.. (d) Water surfae slope equatio for graduall varied flow is give b - where,s S f F r d dx S Sf F Chael bed slope slope of eerg gradiet Froude Number Hee, d dx..5. Hee, orret optio is (d). r..5.6 9. (a) I ase of egative suge (surge movig dowstream) depth dereases ad veloit ireases. v V w v o applig otiuit equatio betwee () ad () (V V w ) (V V w ) (7.56 V w ).6 (.7 V w ). V w +. m/s
(9) 9. (d) Give. m ad. m 9. (b) Head loss i the jump H L.....6 m.5 m.6 m m. m m A.5 ( +.) m.665 m..5.. m A.5 ( +.6). m.76 m.6.577.6 Chage i magitude of the seod term, A (A A ) 9. (a) {.76.9577.665 5.5} NDL 9.5 kgf. x M HJ CDL M z M NDL Sill Sie NDL is above CDL, so bed slope is mild M urve is followed b hdrauli jump. Due to sill depth will irease ad hee the profile after HJ will be M. 9. (d) Disharge i river, from Maig s equatio / / AR S For ostat stage (depth) S S S 6 5 m /s 9. () From Dar W eisbah equatio h f flv gd From Chez s equatio V C RS where R is hdrauli radius h f A C P L h f V L C D from equatio (i) ad (ii) V C D L C flv gd g f 95. (d) From Chez's equatio AV A.C RS here A B. m... (i) h f D C D L... (ii) R A P B. B (.5) ( ) 6. m /se.5 96. (d) Critial depth i retagular hael q g / ( / B) g / (.5 / 5) 9. /
() (.67) / (.6) / 97. (d) M : Bak water profile (all the urves i regio have positive slopes ad are ommol kow as bak water urves. H : S : A 9. (b) Froude No. LC followed b hdrauli jump Hdrauli drop ours (all the urves i regio have egative slope ad referred as drawdow urves so i S profile hdrauli drop ours) : upward slope i the diretio of flow V gl harateristi legth for retagular hael F F V g, V L (depth of flow) C q g For Retagular hael / q / g / q F g / F 99. (d) Area m Top width m T ga B. / F q F g q g q / /...(i)... (ii) for ritial flow oditio m m g m m 5/ for triagular hael q g / B / q Area B m Retagular hael B B m B m B T B m g B m C (Z) / m (Sie for ritial flow, ad for shallow paraboli hael m T ga ). (d) For most effiiet triagular hael setio. 5 i.e., : m : Perimeter P
() x x m 5 P P. For most effiiet trapezoidal hael setio. m 6º B Side slope legth Top width if 6 l B P ( l l l ) l si 6.6 l