ESE (Prelims) - Offline Test Series MECHANICAL ENGINEERING SUBJECT: FLUID MECHANICS AND TURBO MACHINERY SOLUTIONS

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1 ES I: 0 ESE- 09 (Prelis) - Offline est Series est- 0. Ans: (a) MECANICAL ENGINEERING SUBJEC: FLUI MECANICS AN URBO MACINERY SOLUIONS Fro Newton s Law of viscosity: du dy = du for a ie dr d r = u ax dr R r u ax = u ax r R R Straigt line variation assing troug origin. us, = 0 at r = 0 and u ax for r = R R ence, figure given in otion (a) is correct. 0. Ans: (b). In reaction turbines te ressure dro occurs in bot fixed and oving blades. erefore, bot fixed and oving blades act as nozzle.. e use of initial Curtis stage reduces te nuber of stages required. us, te lengt of te rotor is reduced.. In Rateau staging ressure dro is divided equally aong stages. Pressure dro occurs only in nozzles. ere is no ressure dro wile te stea flows troug blades. Sortcut: Stateent is wrong. Insecting te otions given one can eliinate all otions containing. us, otion (b) is correct. 0. Ans: (c) (F ) water and (F ) oil act in oosite directions. e oint of alication of (F ) oil is te centroid of te volue of oil being suorted by te curved surface. is is found to be at a distance vertical line assing troug O. R fro te F R 80 yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata v oil oil = kn er eter widt of te gate.

2 : : Mecanical Engg._ est _ Solutions 0. Ans: (b) NPS = a s v fs 05. Ans: (d) Let = = =. a () be te bq caracteristic curve of te u at N = N r. By siilarity laws N u 60 N N () N Siilarly Q N N N Q N () Q N Substituting values of & Q fro () and () into equation () i.e. But, a b Q a bq () a bq (5) (Given) Coaring () and (5) and a = a b = b a bq 06. Ans: (c) P d d d P = 07. Ans: (c) = 0.07 N/ It is known tat Wz GM W.d were, W = 00 kn, W = 700 kn, =.8 d = 0. & z = GM Ans: (d) e effect of suersaturation is to reduce te entaly dro sligtly during te exansion. e final dryness fraction and entroy are also increased. ry saturated Wilson line e ass flow rate wit suersaturated is greater tan ass flow wit isentroic flow. P P s P yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

3 : : ESE - 09 (Prelis) Offline est Series 09. Ans: (b) Wen te tank artially filled wit water is accelerated wit constant acceleration in orizontal direction, te water level surface will ove u at te rear and ove down at te front. 0. Ans: (a) Wen an array of arrows indicating te agnitude and direction of a vector roerty at an instant is lotted, it is called vector lot.. Ans: (a) Given: u = xy + and v = y 0.6 e sear strain rate is given by: xy u v = (x + 0) = x y x xy, = = s v u y x z = x 0 = x z, = rad/s. Ans: (b) S = 00 K, = 500 K = 000 K, =? = 600 k 500 Back work ratio =. Ans: (b) W W W = = C = 0.67 e velocity rofile (given) is linear, i.e., ax y K.E. Correction factor is given by, Kinetic energy of flow er second based on actual velocity Kinetic energy of flow er second based us, A on average velocity da A. da A ax = da dy A 0 ax y / / 8 8 = y dy 0 yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

4 : : Mecanical Engg._ est _ Solutions. Ans: (b) Q annulus = Q ie 0 i i 0 i i 0 i 0 i 0 i 5. Ans: (a) Rajet engine cannot oerate under static conditions as tere will be no ressure rise in te diffuser. Rajet consists of bot suersonic and subsonic diffuser. Air enter te engine wit suersonic seed wic ust be reduced to subsonic value. is is necessary to revent blow out of te flae in te cobustion caber. ey are ost efficient at ig velocities of about k/ and at very ig altitudes. ue to te fact tat a turbine is not used to drive te ecanical coressor, te axiu teerature wic can be allowed in rajet is very ig, about 000C as coared to about 900C in turbojets. 6. Ans: (a) Q A in in Q in out A A out tank d dt out A tank d dt in in = 0-7. Ans: (b) in in =. /s Alying Bernoulli s equation to inside te balloon and te nozzle exit, we get Pinside were is te velocity of fluid jet leaving te nozzle. Pinside Alying oentu equation in x- direction F = A = Ans: (c) Air Water = = 0.8 N () 00 kpa Party oen valve () yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

5 : 5 : ESE - 09 (Prelis) Offline est Series Alying energy equation for oints () and (), we write P P Z Z K g g were, = 0, P = P at = 0, = 0 /s Z = 8, Z = K L g L = 5 ( + K L ) 8 K L Ans: (c) Lift is te su of te coonents of te ressure and wall sear forces in te direction noral to te flow. 0. Ans: (d) urbulent boundary layer consists of lainar sub-layer, overla layer and outer turbulent layer.. Ans: (c) Loss in ressure rise due to flow searation on blade is called stalling. Unsteady eriodic flow reversal wen coressor is oerated on ositive sloe region of caracteristic curve. Wen velocity of flow becoes equal to sonic seed, ass flow rate cannot be increased in converging ortion. is enoenon is called coking. ecrease in wirl velocity at exit of centrifugal coressor due to relative eddy is called sli.. Ans: (a) ead loss at entry to te ie = 0.5 g = = 0. fl ead loss due to friction = g 0.00 = us, figure given in otion (a) is correct.. Ans: (d) For creeing flow over a sere,. Ans: (c) F = (as sere is considered as one of te tree diensional objects) ence, te density is not te factor on wic te aerodynaic drag on suc a body deends in creeing flow. () () Pu d = 0 s = 5 yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

6 : 6 : Mecanical Engg._ est _ Solutions e anoetric ead reresents net outut of a u. i.e. energy added by te u to fluid. 5. Ans: (c) P Z g g P Z g g = = 8 Entrance lengt for fully develoed lainar flow in a ie is given by L e 0.05Re L e = Ans: (c) = 0.6 = 60 c Given L =.88 k, actual = 0 s, Critical tie, c = L C = /s, C = /s 88 s Since, C < actual, te valve is gradually closed. ence, Pressure rise, 7. Ans: (a) P gradual L actual kpa 0 dp e ressure gradient, in te direction of dx flow for a orizontal ie is negative. e lower critical Re for a flow in ie is sae for different fluids. 8. Ans: (a) Soeties actual discarge in a recirocating u is ore tan teoretical discarge ALN / 60. is aens wen acceleration ead in suction ie is ig as coared to acceleration ead in delivery ie. is causes delivery valve to oen before coletion of suction stroke. 9. Ans: (d) Pitot-static tube is used to easure te fluid velocity using a differential anoeter. Rotaeter is used to easure flow rate of liquids. ot wire aneoeter is used to easure te fluctuating coonents of velocity in turbulent flow. Nozzle eter is used to easure flow rate of fluids. 0. Ans: (c) Power required, P = F F P N us, stateent () is correct. For equilibriu condition in vertical direction F = W + F sear F sear = F W = = 50 N us, Stateent () is also correct. yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

7 : 7 : ESE - 09 (Prelis) Offline est Series yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

8 Ans: (d) For radial blade, = 90 u = w = 00 /s = P in u w 90 0 = P in P in =. Ans: (b) =. 0.9 Starting fro oint A using anoetric equation: P A +.5 w 0.8 w w ( ) = P B P B P A =.5 w 0.8 w 0. + Liquid (S.G =.5) A B PB P w A Liquid (S.G =.5).5 w 0..5 w = w ( ) = w ( ) = 0. w 0. Oil (S.G = 0.8) : 8 : Mecanical Engg._ est _ Solutions. Ans: (c) U-ube anoeter is used to easure ressure differential. Bourd on gauge is used to easure gauge ressure. ydroeter is used to easure relative density. Baroeter is used to easure local atoseric ressure.. Ans: (d) e region outside te boundary layer is called inviscid region. us, in tis region boundary layer aroxiation does not arise as tere is no velocity variation in different layers in tis region. e boundary layer aroxiation is aroriate for wake and jet also. ese flows ave a redoinant flow direction, and for ig Reynolds nubers, te sear layer is very tin causing te viscous ters to be uc saller tan te inertial ters, just as in te case of a boundary layer along a wall. 5. Ans: (c) For iniu work inut, te otiu ressure ratio is given by, r Po P i yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad n n = nuber of stages

9 r 6 = P i = P = bar, P = bar, P = bar, P = 8 bar and P 5 = P 0 = 6 bar e ressure difference for last stage is P 5 P = 6 8 = 8 bar. : 9 : ESE - 09 (Prelis) Offline est Series were A is te cross-section area of ice block and is te eigt of te ice block below te seawater surface. ( seawater ice ) = ice 0. seawater 0. ice (. ) = Ans: (c) on-karan oentu integral equation dp for flow over a flate late 0 for dx steady, lainar or turbulent incoressible d w flow is dx U us, only stateent (iii) is correct. 7. Ans: (c) Air vessels ake te velocity in ie nearly equal to average velocity. ence, acceleration ead is reduced, wic els in reducing cavitation cances. As flow velocity is constant te ead loss due to friction is also reduced. 8. Ans: (a) Weigt of te cubic ice block = Buoyant force ice A ( + 0.) = seawater A 9. Ans: (d) Patline is define as te actual at by an individual fluid article over soe eriod of tie. 0. Ans: (a) For critical flow in a ie, Re = 000 d / s 0 us, discarge =. Ans: (b) 0 = lit / s / s raft tube converts a art of residual kinetic energy into useful work. raft tube extracts te lost otential ead equal to draft tube eigt d by reducing ressure at te turbine exit roortional to yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

10 : 0 : Mecanical Engg._ est _ Solutions draft tube eigt d. As ressure difference across turbine is increased, inut energy is increased.. Ans: (c) For turbulent flow troug roug ies, te required relation is given as: () ax. f () By Bernoulli's equation, P g g P g () g d Z Z fd P = P at ; Z Z = d P Pat d g g g raft increases cances of cavitation as fd ressure at turbine exit is reduced.. Ans: (a) Sear velocity, * o were, 0 = Wall or boundary sear stress Sear velocity is a fictious (iaginary) quantity. It is used in te analysis of lainar sub layer, and in classification of turbulent flow as ydro dynaically soot, transition, roug, etc.. Ans: (c) = = =.86 N u Q u P u 5. Ans: (c) N Q P Boundary layer tickness is te noral distance fro te boundary were velocity is 99% of free strea velocity. islaceent tickness is te distance fro te boundary by wic te ain flow can be assued to be sifted so tat otential flow teory can be used to analyze te flow. Lainar sublayer is te region near te boundary were viscous stress is also resent. e velocity rofile in tis region is linear. yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

11 : : ESE - 09 (Prelis) Offline est Series 6. Ans: (a) e velocity triangle of Kalan turbine at exit is given by tan f u f Q = constant everywere. ti ub But u = r r u is igest at ti and lowest at ub. igest at ub and lowest at ti. 7. Ans: (c) Alying linear oentu equation in x- F direction: F on water on water P A cos60 inlet guage A cos60 r f u P A inlet gauge = ( 0.5) = = 50 N =.5 kn Fro Newton s tird law of otion, F on bend =.5 kn o analyse flow troug a lawn srinkler, oent of oentu rincile is alied. Using energy equation, one can find out ressure at a oint in a ieline if required data are given. 9. Ans: (c) e gauge would read te stagnation ressure. 0 P0 P. were, P is te static ressure far ustrea of te disk were velocity is 0. us, te gauge would read a ressure greater tan 50. Ans: (a) g u w Ans: (b) Ans: (a) Since atoseric ressure acts on te control volue, te ressure forces are evaluated using gauge ressure at inlet and exit sections wen linear oentu equation is alied. Air () 9.6 () Water yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

12 : : Mecanical Engg._ est _ Solutions Given data: It is known tat P 0 P air P P 0 air g w us, w 5. Ans: (c) w = ; =.5 ; air =. kg/ air air wg w = 0 /s =.5 0 = 60 /s e resultant ydrostatic force acting on te F R gate (widt = unity) is oil oil = oil oil water water = 6 oil + water = = 68 kn Integrating w.r.t. y, we ave f = r = logx logy + f(x) ifferentiating w.r.t. x, log y f x x f(x) = 0 x v Given u = w log y x Integrating te above equation, f(x) = c us, = logx log y + c were c is constant of integration. e correct otion is (a). 5. Ans: (b) For radial blades at exit = 90 u w u g w u g k g u = = g k u = 0.65 = 8.5% 5. Ans: (a) e velocity coonents u and v are related to strea function, as: u and v y x log x us, u, y y 55. Ans: (b) wind W O yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

13 : : ESE - 09 (Prelis) Offline est Series rag force, F = C A wind = C. aking M o, we write F W C 56. Ans: (a) Given data: wind = iston = 80, cylinder = 80., wind g C wind g 0 = = 0.8 /s 0.8. = 76.5 Pa.s = Pa.s F axial = 7 N, L = 00 Oil tickness, = (80. 80)/ = 0. Let be te iston velocity. en F seer = Area = iston L Equating te axial load, F axial to sear force, F sear, F sear = F axial 57. Ans: (b) iston L 7 = 7 iston L = 5 /s c g = 080 = 60 /s v For axiu efficiency 58. Ans: (d) u = 0 /s N u 60 6 N 0 N = 00 r 60 At noral teerature (0C) Siilarly, air = /s water = /s air > water air = Pa.s water = Pa.s air < water erefore, bot te stateents are correct. Note: As te density of water is uc ore tan tat of air, te denoinator causing kineatic viscosity is iger for water. yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

14 : : Mecanical Engg._ est _ Solutions yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

15 : 5 : ESE - 09 (Prelis) Offline est Series 59. Ans: (a) Inside diffuser of a centrifugal coressor kinetic energy is converted into static ressure. ence, static ressure increases along te direction of flow. owever, te stagnation ressure Po P reains constant. 60. Ans: (c) orque convertor is a device wic odifies torque. It acts like a gear box. N and N Fluid couling transfers torque fro one saft to oter. N N couling N N 6. Ans: (c) e given exression for sear stress is indeed valid for bot lainar and turbulent steady incoressible flow in a ie. Pressure gradient does deend on te nature of flow. P For Lainar flow : L d For turbulent flow: P g f fl d 6. Ans: (d) P f L d elocity rofile in Couette flow is affected by te ressure gradient iosed wic can be concluded fro u y P y x y were is te vertical distance between te two lates and is te velocity of te to late. Stateent (II) is correct. 6. Ans: (a) urbine and generator are connected to eac oter troug gear box or tey are ounted on sae saft. Frequency of A.C. voltage roduced deends uon generator seed. were, NP f 60 P = Pairs of oles in generator, N = Generator saft seed ariation in A.C. frequency can daage electronic coonents ence it is undesirable. erefore, to aintain constant A.C. frequency te turbine seed ust be ket constant. yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

16 : 6 : Mecanical Engg._ est _ Solutions 6. Ans: (b) Stateent (I) is correct. is ay be furter exlained wit te exale of a Golf ball. A soot golf ball (iaginary ball) would aintain a lainar boundary layer on its surface and te boundary layer would searate fairly easily, leading to large aerodynaic drag. Golf balls ave diles (a tye of surface rougness) in order to create an early transition to a turbulent boundary layer. Flow will searate fro te golf ball surface furter downstrea in te boundary layer resulting in significantly reduced aerodynaic drag. Stateent (II) is also correct but it is not te correct exlanation of stateent (I). e turbulent boundary layer as ig energy. ence, it as better ability to overcoe adverse ressure gradients. 65. Ans: (c) As seen above te velocity wit te long ie being ore, it takes less tie for draining reservoir coared to tat of flow troug orifice. Stateent (I) is correct. owever, Stateent (II) is wrong as seen fro te above equations. Note: owever, as lengt of drain ie is large, frictional losses are ore along wit inor losses (entry and exist loss). ence, te actual velocity troug te long drain ie ay be less and ence ay take ore tie, ractically. 66. Ans: (a) For gas turbine intended for use in veicles, it is desirable to oerate near te coressor ressure ratio tat yields axiu net work er unit ass so as to kee engine weigt sall. If coressor ressure ratio for te axiu teral efficiency is used ten to develo te sae net ower outut a larger ass flow rate would be required and tus igt dictate a larger syste. rain wit long ie elocity of flow at Outlet of ie g = l rain troug orifice elocity of flow troug orifice = g 67. Ans: (b) At te oint of searation te value of du dy y0 du is zero. erefore. 0. dy But te zone of forward flow & reverse flow doesn t ily tat te sear stress is zero. yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

17 : 7 : ESE - 09 (Prelis) Offline est Series 68. Ans: (a) In te resent roble, Air is blowing over te reservoir. ence, tere is an interface between te two fluids. e velocity of water in te reservoir can be assued to zero. We know, At te interface of two different fluids, te velocities of two fluids are equal. ence te velocity of air at te interface also becoes zero. As te flowing air as certain free strea velocity, tis velocity can be acieved in a certain narrow region above te reservoir called boundary layer. ence te boundary layer fors in te air only, as reservoir is assued to te static. air 0 w = 0 air Boundary layers in air Reservoir (assued to be static) 70. Ans: (a) F L U w ig velocity, low ressure Low velocity, ig ressure Because of rotation of cylinder unsyetric velocity distribution is resent around te surface of cylinder, wic leads to unsyetric ressure distribution causing lifting force. 7. Ans: (a) Wake is indeed unsteady due to vortex sedding and tis creates oscillatory forces. ese forces cause structural vibration wic can lead to failure wen te structure s natural frequency is closely atced to te vortex sedding frequency. us, bot stateents are correct and stateent (II) is te correct exlanation of stateent (I). 69. Ans: (d) ydraulic ra is used in illy region were it takes water fro ustrea of river, discards soe water at downstrea of river and reaining water is sent at iger elevation. In ydraulic ra ig ressure is generated in downstrea caber due to water aer effect. 7. Ans: (a) Under oologous condition, geoetry and velocity triangles are siilar. e efficiency of Francis turbine after neglecting frictional effects is given by u w g u u w w yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad

18 : 8 : Mecanical Engg._ est _ Solutions By siilarity laws: All velocities Entaly P = constant u and w u c w c u c Entroy w c c c c c = 7. Ans: (a) In lainar flow troug a ie ead loss is L 8QL given by f f Q, keeing oter araeters constant. P = Power consution = Q f P Q If discarge is doubled, ten te ower consution increases to four ties. 7. Ans: (d) Polytroic efficiency of coression rocess is ore tan overall efficiency and for exansion rocess is less tan overall efficiency. As constant ressure lines diverge fro eac oter, su of isentroic work of eac successive sall stage is ore tan isentroic work in overall stage. ence, sall stage efficiency for coression rocess is ore tan isentroic efficiency. yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad ci i c i > i c > ci 75. Ans: (b) Caillary deression for g is given by cos g g d Fro te above relation, deends on and. us, stateent(i) is correct. For g, varies between 0 to 50. us, stateent (II) is also correct. owever, stateent (II) is not te correct exlanation of stateent (I).

19 : 9 : ESE - 09 (Prelis) Offline est Series yderabad eli Boal Pune Bubaneswar Lucknow Patna Bengaluru Cennai ijayawada izag iruati Kukatally Kolkata Aedabad