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# 3rd Semester Mechanical Engineering (2013-December) Question Papers

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### 3rd Semester Mechanical Engineering (2013-December) Question Papers

1. 1. fi*.{''{,1 1OMAT31 USN Third Semester B.E. Degree Examination, Dec.2013 lJan.2Dl4 Engineering Mathematics - Time: 3 hrs. lll Max. Marks:100 Note: Answer FIVEfull questions, selecting at least TWO questions from each part PART _ A 1 ',u, Find the Fourier series (J *2@r il o o o. b. o o 6 lFh ,,, n' = c. r{} * } * +. u'3'5') (06 Marks) f(x)=(*-1)'intheinterval 0<x<1 Obtainthehalf-rangecosineseriesforthefunction, L ^ (.)X hence deduce that I '- ura n.n.. show that ! .9 f(x) = lxl in Gn,x), B 3(2n-1)r' L 6 expansion of the function ,,,,,,,, } (07 Marks) Compute the constant term and first two harmonics of the Fouripr series of (x) given by, (07 Marks) J' F6 NV x fi 0 50" ioo J Fl .=N f(x) .B+ Y o.) Oi eO -'o> a_o= 2n.,,. 2a. b. 1.0 1.9 ;J J r.4 4x .,.....fi 1.7 ,,,1 5n 2n t.2 1.0 ;J .5 CENfRAL LIBRAflY tru for* of f(x) = -L. l+x' h- *'for lxl < I Find the Fourier translorm of f r x) i Obtain the Fourier cosine = a= LV oc) lMarks; I o forlxl >t (07 Marks) -! c. -L 3a. of (07 Marks) ,;* oX >'1 sd b. Obtain the various possible solutions of two dimensional Laplace's equation, u,* *u,, by the method of separation of variables. ad E6 'ia or= aa Find the inverse Fourier sine transform S (07 Marks) ' o_i 6V o= . _.. Solve the one-dimensional wave equation, C' conditions (i) , u(0, t) : 0: 0 ,, , u(1, r2 r2 o-u j=-, o-u 6x' A' (ii) (iii) LO 5.e > (ts o- ao c or.) o= ;(x.0) tr> u(x. 0) =o 5! ^5 t< * 4 a. a.I a_) Z o a c. : UnX ; = 0. where u6 is constant (07 Marks) c."' Obtain the D'Almbert's solution of the wave equation u,, o.B 0 < x < / under the following u(x, 0) 4l! €; =0 : (x) una \$1*.0) a"' =0 - C'r** subject to the conditions (06 Mar,Iq) Findthe best values of a, b, c, if the equation y=a+bx+cx2 is to fit most closely to the fo llo wing observations. (07 Marks) x 1 2 5 4 -) v 10 t2 13 t6 t9 Solve the following by graphical method to maximize z = 50x + 60y subject to the constraints, 2x+3y<1500, 3x+2y <1500, 0( x<400 and 0<y<400. (06Marks) By using Simplex method, maximize P=4xr -2xr-x, subject to the constraints, xr +x2*X: (3,2xr+2xr*X., ( 4,xt-x, <0, X,)0 and xz )0. (07Marks)
2. 2. 5a. b. 1OMAT31 PART _ B Using Newton-Raphson method, find a real root of xsin x + cosx = 0 nearer to n, carryout three iterations upto 4-decimals places. (07 Marks) Find the largest eigen value and the corresponding eigen vector of the matrix, lz -1 ol l-, 2 -11 Io -r ,) By using the power method by taking the initial vector as [t t t]' carryout 5 -iterations. (07 Marks) c. Solve the following system of equations by Relaxation method: l}x+y+z=31 ; 6 a. . b. (06 Marks) A sulvey conoucteo m a slum locallty reveals tne lollowlns mlormatron as c lassified below, nducted in locali ls the followins info Income per dav in Ruoees 'x' Under 10 10 -20 20-30 30-40 40-50 Numbers of persons 'y' 20 45 115 115 210 Estlmate the probable number of persons in the income group lU b 25. Estimate tne pr0DaDle numDel oI rn tne mcome 2A to"/.5. (07 Marks) Determine (x) as a polynomials in x for the data given below by using the Newton's divided diflerence formula. (07 Marks) x f(x) c. 2x+8y-z=24; 3x+4y+l0z=58 2 4 t0 96 5 Evaluate [. +dx jl+x 8 10 868 1746 6 t96 350 by using Simpson's H' rule by taking 6 - equal strips and of log. 2. ) ^ ^) 7a. Solve the wave equation, + = 4+, subject to u(0, t) : ol- dx' u(x. 0) : x(4 - x) by taking h : l. K : 0.j upto 4-steps. deduce an approximate value Solve numerically the equatio" 'A0x' t)0 (06 Marks) 0, u(4, t) : 0, u1(x, 0) 0 and (07 Marks) subject to the conditions. u(0. u(x,0): s.innr, 0< x <1, carryout : the computation t):0: utl. t.1. fortwo levels taking h =1 l. K: + . (07 Marks) 36 Solve u,o * u, = 0 in the following square region with the boundary conditions as indicated in the Fig. Q7 (c). (06 Marks) and c. and + =* hence 500 I 00 100 50 tt1 Fig. Q7 (c) ?n 8a. b. c. 0000 Find the z-transform o[ (i) (ii) coshnO n0 222 +32 Find the inverse z-transform or" ' Solve the difference sinh (z+2)@-a) equation, y n+2 * 6y,*r * 9y , - )n with yo = yr = 0 by using z-transform. *rk*rk>k (xr) n- (07 Marks) (06 Marks) (07 Marks)
3. 3. TOME/AU32B USN Third Semester B.E. Degree Examination, Dec.2013 lJan.20l4 Mechanical Measurements and Metrology Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting at least TWO questions from each part. c) () (.) CB o. a. b. (.) (.) ! 8e c. 6v 7r' -t o0' =oo .: c.l PART _ A De{ine metre in terms of wavelength standards. List the advantages of wavelength standards over itaterial standards. (06 Marks) Describe with a neat sketch: i) Imperial standard yard ii) Wringing phenomena of slip gauges (08 Marks) Four length bars of basic length 100 mm are to be calibrated,using a calibrated length bar of 400 mm whose actual length is 399.9992 mm. It was also found that length of bars B, C and D in comparison to A are +0.0002 mm. +0.0004 mm and -0.0001 mm respectively and the length of all the four bars put together in comparison to standard calibrated bar is +0.0003 mm longer. Determine the actual dimensions of all the four end HOO oJtr =o 71. a. - a: b. oO o0c c. -€ Differentiate between: i) Hole basis and shaft basis system of tolerances ii) Interchangeability and selective assembly. Write notes on: i) Compound tolerances ii) Marks) Gauge tolerance. Determine the dimensions of hole and shaft for a fit 30H8f7. The given data arc: i:0.45Dr/r + 0.001D. IT8 :25i.1T7: l6i. Fundamentaldeviation for shaft'f is -5.5D0+r. 30 mm diameter lies in the diameter step of 18-30 mm. Sketch the fit and comment on the same. (08 Marks) or= p-A o'' o_i o= 3a. b. c. AE Explain with a neat sketch, the working of Solex pneumatic gauge, (08 Marks) Explain with a neat sketch, the construction and working of LVDT. (08 Marks) Show the arrangement of angle gauges, with a neat sketch by selecting minimum number of gauges for the angles 32'15'33" and54o36'42". ',,. (04 Marks) G; :9 v, ^: -40 o= qo tr> Xo o rJ< -i c.i o o Z L 4 a. , b. c. What is the best size wire? Derive an expression for the same in terms of the pitch and angle of the thread. (06 Marks) Explain 3-wire method of measuring effective diameter of screw thread. (08 Marks) Explain the principle of interferrometry. Write a note on optical flat. (06 Marks) PART -B 5 a. With a neat block diagram, explain the generalized measurement system with an example to each stage. (08 Marks) b. Distinguish between: c. Define the following terms with reference to measurement system: i) Calibration ii) Sensitivity iii) Hysterisis iv) Threshold value i) Primary and secondary transducers ii) Active and passive transducers (06 Marks) (06 Marks)
4. 4. .. t ,,r,,:,r, 1.t) 2 of2
5. 5. MATDIP3Ol USN Third Semester B.E. Degree Examination, Dec.2013 Advanced Mathematics -I Time: 3 hrs. ,:.,i d o o Max. Marks:100 , 1 ' ;. L /Jan.20l4 Note: Answer any (1 Express the complex number + i)(1 + FIVEfull 3i) 1+ 5i questions. ,' in the form x + iy. (06 Marks) ..,"'.'.,......,'.. J ' b. r ----.-,:---r- -. (3Find the modulus and amplitude of c. Expand coso 0 in a series of cosines multiples of 0. (07 Marks) Find the nth deiivative of sin(ax + b). If y: (sin-l x)2, Showthat (1-x')y,*, (06 Marks) a o C) oX d= j=h bol troo 2a. b. c. .=N o:u otr aO o2 a: tr -(2n+l)xy,*, -n'.yn=fl Findthenthderivativeof ^[ I r +,. -3t2 Il. i'[51x-ll (?-tf2x+3)J Using Taylor's theorem, express the polynomial 2xr +7x2 +x b. Using .vtaclaurrn's series. expand tan x upto the term containing usmg Maclaurin's senes, ran rhe contammg c. lf z =r' + y'' (07 Marks) (07 Marks) - 6 in powers of (x - a. o(.) botr (07 Marks) - 3axy then prove ,1'ru, AyAx :t: - "-"- 9'l = axav ovox AxAy 1). (06 Marks) (07 Marks) x;,3g;:{gN(0, "t.r'6 Y ''^y c) Marks) iY ,,il cetur*:: Sqi "Er.r{E&t lE t 4a. b. e If x' + y3 + 3xy = I . find l|. r9 1 l6ElAF' J ' '3[--- '",CI2 0z .. .. ' z: (x, y) and x=eo +e-u andy=e-'-e', provethat:--=* -?o OE o-A c. If u = x+3y2 oj o= ao atE ',... ,,,,': 5a. !O 5.Y >'! uov iou o= o. li tr> =o 5L c. o o '7 o D(u.v.w) at (1, -1, 0). A(x.Y-z) for 1r ? xdx f sin" x dx . - : (06 Marks) A l----. J lt i.!." Evaluate I If ., -" + 6a. lll Evaluate [ |. [.''' J J J_ (07 Marks) ) )dydx (07 Mark\$) ''dxdydz. (06 Marks) eY 000 t, L o. Marks) l3 J< -N E'v'aluate find the value of iZ- 0z ;-Vfi.t0l (07 Marks) Obtain ihe reduction formula - b. ' .) ^) " -23, y = 4x2yz, w = 222 -xy, {,fr*Marks) ,frrgpp_-_ b. c. r rrru rr,! vqru! vr Find the rurr. or l[f) l(rL_ Prove that B(m,n) = g)]q. l(m + n) (07 Marks) (07 Marks)
6. 6. MATDIP3Ol 7 a. Solve 9 -.'*-" +x' .e-" dx b. Solve 4,Y =*' -y' which is homogeneous (06 Marks) . .'tr dx 4a:^, Solve dv V = e'* (x + 1) ,. :,,,.{., r c. - ,. ., * 'SL* .,.m, in x and y. xy (07{arks) . -.%,*" ,,,':1''"r" (o6 Marks) &L (07 Marks) (07 Marks) s ,s_. \$o*d* t' {< {< * * {' .. ' : / t { {u j'hn .:: ::::::;, ==il;..= ..'1 '::: :a .=' * &d' lud ,* tuill' S .:::''"':" i ":1J' . ' nl'S ,::":l :::,,,,":'13' 2 of2
7. 7. IOME/AUITL33 USN Third Semester B.E. Degree Examinationo Dec.2013 lJan.2014 Basic Thermodynamics Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting ut lesst TWO questionsfrom each pait. iJ o () o. E o o L b. 3e. c. oo, -l =co .= cn Y{r o< -A 3* a:: 2 a. b. o() 50i -L a6 c. 3.J 5i, iq o'! ().-i o: !o 5.Y > (F boo cb0 o= go =<d tr> o lr< :- 3 a. o. E For a non-flow system, show that the heat transferred is equal to the change in enthalpy of a system. f o o Does heat transfer inevitably causes a temperature rise? What is the other cause for rise in (02 Marks) With a neat p-V diagram, derive an expression for workdone in each case of the following: i) Isochoric process. ii) Isobaric process. iii) Isothermal process and iv ) Polytropic process. (10 Marks) A piston device contains 0.05m3 of a gas initially at 200kPa. At this state, a linear spring having a spring constant of 150 kN/m is touching the piston but exerling no force on it. Now heat is transferred to the gas. causing the piston to rise and to compress the spring until the volume inside the cylinder doubles. If the cross-sectional area of the piston is 0.25m2, determine: i) a final pressure inside the cylinder; ii) the total work done by the gas and iii) the fraction of work done against the spring to compress it. (08 Marks) temperature? (04 Marks) b. A gas undergoes a thermodynamic cycle consisting of the following processes: i) Process 1-2: constant pressure P:1.4 bar, Vr:0.028m3, Wr2:10.5kJ; ii) Process 2-3: compression with pV: constant, U:: Uz and iii) Process 3-1: constant volume, Ur * U: : -26.4 kJ. There are no significance change in KE and PE. i) Calculate the net work for the cycle; ii) Calculate the heat transfer for the process 1 - 2; ii) Show that (J Z PART _ A Distinguish between: i) Microscopic and macroscopic point of view. ii) Temperature and thermal equilibrium and iit) Intensive and extensive properties. Classify the following into open, closed and isolated system: i) Evaporator; ii) Thermoflask; iii) Passenger's train when stop at platform; iv) Refrigerant in a refrigerator; v) Pressure cooker; vi) I.C. engine during compression/expansion stroke; vii) Boiler and viii) Throttle valve. (08 Marks) Define a Quasi-static process. A platinum wire is used as a resistance thermometer. The wire resistance was found to be lOohm and 16ohm at ice point and steam point respectively, and 3Oohm at sulphur boiling point of 444.6"C. Find the resistance of the wire at 750'C, if the resistance varies with temperature by the relation. R: Ro (1 + oct + pt'). (06 Marks) Q= cycle c. f W , and iv) Sketch the cycle on p-V diagram. (08 Marks) cycle In a certain stea{y flow process, 12 kg of fluid per minute enters at a pressure of 1.4bar, density 25 kglm3, velocity 120 ntls and internal energy 920 kJlkg. fne Rula properties at exit are 5.6bar, density 5 kg/m3, velocity 180 m/s, and internal energy 72OkJlkg. During the process, the fluid rejects 60 kJ/s of heat and rises through 60m. Determine work done during the process in kW. (08 Marks)
8. 8. lOME/AU/TL33 a. b. c' State the limitations of first law of thermodynamics. Illustrate with examples. (04 Marks) Prove that Kelvin-Plank and Clausius statements of second law of thermodynamics are equivalent. (06 Marks) A heat pump working on the Carnot cycle takes in heat trom a reservoir at 5oC and delivers heat to a reservoir at 60oC. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at 840'C and rejects heat to a reservoir at 60'C. The reversible heat engine also drives a machine that absorbs 30kW. If the heat pump extracts lTklls from the 5oC reservoir, determine: i) the rate of heat supply fromthe 840"C source and iil the rate of heat rejection to the 60"C sink. (10 Marks) PART - B a. Prove that whenever a system executes a compete cyclic process, the quantit, b. c. Explain principle of increase of entropy. In a shell and tube heat exchanger 45kg of water per minute is heated fi"om 30.C hot gases which enter the heat exchanger at 225"C.If the flow rate of gases is find the net change of entropy of the universe. a. b. {* = , tort*ururr (06 Marks) to g5oC by 90 kg/min, (06 Marks) Draw the phase equilibrium diagram for a pure substance on'I-S plot with relevant constant property lines. (05 Marks) What is the main objective of quality measurement? With a neat sketch, explain throttling calorimeter (07 Marks) c' What do you understand by degree of superheat? Steam initially at 1.5Mpa, 300.C expands reversibly and adiabatically in a steam turbine to 40'C. Determine the ideal work output of the turbine per kg of steam. (08 Marks) a. Derive Clausius Clayperon's equation for evaporation of liquid and explain the significance. b. Distinguish betweEn: i) Ideal gas and real gas and c. (04 Marks) 0.5 kg of air is compressed reversibly and adiabatically from 80kPa,50oC to 0.4Mpa and is then expanded at constant pressure and to the original volume. St<etctr tttese processes on the p-V and T-s planes. Compute the heat transfer and work transfer for the whoie path. ii.y Perfect.gas and semiper*.t|!'*X"*' (10 Marks) a. b. c' Explain the following: i) Generalizedcompressibilitychart. ii) Law of corresponding states and iii) compressibility factor. (06 Marks) Derive Vander Waal's constants in terms of critical properties. iot *".u.i Determine the pressure exerted by CO2 in a container of 1.5m3 capacity when it contains 5kg at 27oC. i) Using ideal gas equation and ii) Using Vander Waal's equation. (06 Marks) ) nf )
9. 9. 10ME/AU32B USN Third Semester B.E. Degree Examination, Dec.2013 lJan.2Dl4 Mechanical Measurements and Metrology Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting --'l---*---""'*-----'-'D - --__ -^-J---at least TWO questions from eoch part. () o o L g PART_A I a. Define metre in terms of wavelength standards. List the advantages of wavelength b. () 6 (.) ! 8e c. yl de ;r, troo .=N (o+ Eil. otr saJ 2 a. 3s 6= b. o() (o0 b0i c. standards over material standards. (06 Marks) Describe with a neat sketch: i) Imperial standard yard ii) Wringing phenomena of slip gauges (08 Marks) Four length bars of basic length 100 mm are to be calibrated using a calibrated length bar of 400 mm whose actu.al length is 399.9992 mm. It was also found that length of bars B, C and D in comparison to A are +0.0002 mm. +0.0004 mm and -0.0001 mm respectively and the length of all the four bars put together in comparison to standard calibrated bar is +0.0003 mm longer. Determine the actual dimensions of all the four end bars. (06 Marks) Differentiate between: i) Hole basis and shaft basis system of tolerances ii) Interchangeability and selective assembly. Write notes on: i) Compound tolerances ii) Gauge tolerance. Determine the dimensions (08 Marks) 7 (04 Marks) of hole and shaft for a fit 30H8li. ihe given data are: i:0.45Dr'+0.001D. IT8:25i.1T7:16i. Fundamentaldeviarion lorstratt't is-5.5D0ar. 30 mm diameter lies in the diameter step of l8-30 mm. Sketch the f-rt and comment on the same or= =)Y ^X o.! o_a oi; 3a oE og Marks) ?. b. c. Explain with a neat sketch, the working of Solex pneumatic gauge. (08 Marks) Explain with a neat sketch, the construction and working of LVDT. (08 Marks) Show the arrangement of angle gauges, with a neat sketch by selecting minimum number of gauges for the angles 32o15'33" and 54o36'42". (04 Marks) 1 a. What is the best size wire? Derive an expression for the same in terms of the pitch and angle of the thread. (06 Marks) Explain 3-wire method of measuring effective diameter of screw thread. (08 Marks) Explain the principle of interferrometry. Write a note on optical flat. (06 Marks) LO >'k eo0 AE tr> :o VL o- U< :' o o Z P b. c. 5 a. PART _ B With a neat block diagram, explain the generalized measurement system with an example to each b. a c. stage. Distinguish between: i) Primary and secondary transducers ii) Active and passive transducers Define the following terms with reference to measurement system: i) Calibration ii) Sensitivity iii) Hysterisis iv) Tkeshold value (08 Marks) (06 Marks) (06 Marks)
10. 10. lOME/AU32B a. b. c. With a neat sketch, explain the working principle of a CRO. State the advantages of electrical signal conditioning elements. (08 Marks) (06 Marks) Explain with a neat sketch, Ballast circuit diagram. (06 Marks) ""':""" :'',,d, ', ',,: a. b. for pressure measurement. los"tudrts) principle of proving ring. a neat sketch, explain the working (06 Marks) *.-,,,.t*Olain with a suitable diagram, the working of hydraulic dynamometer. (06 Marks) With With a neat sketch, describe the Pirani gauge used ,:_,,,,.,,,,,, 8 a. b. Sk@,an0 explain the working principle of optical Desciibe-=the steps gauges. pyrometer. (0s Marks) to be taken for the preparation of specimen and mounting of strain (06 Marks) ' ,,:,"";-.,,,: ,1,,, i.'l"t ,,,,% ' :"'.. t :' ::: ,= ,:::, ,::,:, .. -. 1 ::.."" :::._ ,:.. :j:., a: :t ,,. 0".,,".i I I 'i ,; ::: 1 :::::::: ir't;::" :' j.:.. :"-"!,; -'",...,,,-" .= iru -l 1r ',il\$E " t"tttt'tttt" ' :i,[ ,,'',, ':t,, .;. 't"""'ttt' i: " ,r,1,' . )jl( . .1 :ia :, ,I l,, ,..tt,,,,,,.' 'il 2 of2
11. 11. lOME/A.U35 USN Third Semester B.E. Degree Examination, Dec.20L3 /Jan.2ol4 Manufacturing Process - I Time: 3 hrs. Max. Marks:100 Note: Answer FIVEfull questions, selecting at least TWO questions from each part. d) o o a PART la. b. c. -A List and briefly explain the different steps involved in a casting process. Discuss in detail the different materials used in making a pattern. Briefly dis,gqss the importance of binders and additives used in sand.moulding. (08 Marks) (06 Marks) (06 Marks) o 6) 3e 2a. b. c. *oo List the types of moulding sand. Discuss the desirable prop With neat sketch. explain jolt type moulding List casting defects. Discuss any two. :of moulding turd,o, Marks) machine. (07 Marks) (05 Marks) I Eoo .=N cO+ 5*u (Jtr .Eo) 3a. b. 4 a. a: oO b. With neat sketches, describe the,shell mouldingprocess. List advantages of the process. (10 Marks) What is die-casting? With a neat, and lateled sketch, explain cold chamber diecasting process. (10 Marks) With neat sketch, show the construcJion details of a Cupola furnace. Also indicate different zones and write the reactions taking place in each of the zones. (10 Marks) With neat sketch. explain the working of a direct arc electric firrnace. 0 Marks) ooi c!.6 9= 26 -o(B 5 a. 3(] o.= ^X trao.v o.a o: 6,i b. 6 a. GH !o 5.v >,h bocbo tr> o- U< -N o o Z L o b. PART Explain the following, D iD Submerged arc *ith - ). B .illi neat sketches: welding. , Oxy-acegllene welding. and their fiekl of applications. With neat sketch" explain forward and backward welding methods. {/ "/ ":- / (08 Marks) With neat sketches, explain the following: D Seam welding ":" (12 Marks) ii) Projectionwelding. With a sketch, explain the electron beam welding process and mention its applications, (08 fuarks) 7a. b. 8a. b. With neat sketch, explain heat affected zone (HAZ) and its various regions. Explain the different welding defects, their causes and remedies. "111'lii (10 Maiks),; (10 Marks) What is non-destructive testing? Explain with neat sketch ultrasonic inspection and its application areas. (10 Marks) With neat sketch, explain fluroscent particle inspection process and its application areas. (10 Marks)
12. 12. lOME/AU36B USN Third Semester B.E. Degree Examination, Dec.2013 /Jan.2O14 Fluid Mechanics Time: 3 hrs. Max. Marks:100 Note: Answer FIVE full questions, selecting at least TWO questions from euch part. o o () PART * A (.) o L 3e a. d. Define the following terms and mention their SI units: i) Capillarity. iil Dynamic viscosity. iii) Weight density. (06 Marks) iv) Bulk modulus. Explain the effect of temperature variation on viscosity of liquids and gasses. (04 Marks) Two large plane surfaces are 2.4cm apart. The space between the surface is filled with glycrene. What force is required to drag a very thin plate of surface area 0.5 square meters between the two large plane surfaces at a speed of 0.6 m/s, if the thin plate is at a distance of 0.8cm from one of the plane surface? Take p : 8.1 t 10-rN-s/m2. (07 Marks) Derive an expression for surlace tension of a soap bubbie. (03 Marks) a. Define the following: (!= 7h ;, =q .=N d+ 9[i oi b. c. -O o> a2 ;! oO =l 50tr -oE >d 6'O cg 3o 'Xa OE 5.e > (F ^^o cco *o E> v9 (08 Marks) A Caisson for closing the entrance to dry dock is of trapezoidal form 16m wide at the top c. 6tE L(j Gauge pressure. Vaccum pressure. il ;;:.;ri*il*;; b. o-X oi d= it ii) and 10m wide at the bottom and 6m deep. Find the total pressure and centre of pressure on the Caisson if the water on the outside is just level with the top and dock is empty. (08 Marks) (04 Marks) What is a manometer? How they are classified? potential flow, the velocity potential is given by 0 : x(2y - 1), determine the velocity at point P(4, 5). Determine also the value of stream function at the point P. (10 Marks) Derive an expression for metacentric height of a floating body using analytical method. a. If for a two-dimensional b. (10 Marks) ^O a- lr< *c.] o '7 o a E 4a. b. c. Derive Euler's equation of motion for an ideal gas. (08 Marks) (02 Marks) State Bernoulli's theorem for steady flow of an incompressible fluid. A pipe line carrying oil of specific gravity 0.87, changes in diameter from 200mm diameter at a position A to 500mm diameter at a position B which is 4 meters at a higher level if the pressures at A and B are 9.81 N/cm2 and 5.886 N/cm2 respectively and the discharge is 200 litres/s determine loss of head and direction of flow. (10 Marks) I of2
13. 13. IOMEiAU36B PART 5a. b. c. 7a. b. 8a. B Derive an expression for the discharge over a triangular notch in terms of water over the (08 Marks) crest of the notch. A 30cm x 15cm venturimeter is provided in a vertical pipe line carrying oil of specific gravity 0.9, the flow being upwards. The difference in elevation of the throat section and entrance section of the venturimeter is 30cm. The differential U-tube mercury manometer shows a gauge deflection of 25cm. Calculate: i) The discharge of oil; ii) the pressure difference between the entrance section and the throat section. Take coefficient of meter as (09 Marks) 0.98 and specific gravity of mercury as 13.6. What are the methods of dimensional analysis? Describe Buckingham's n-theorem for dimensional a. b. - analysis. (03 Marks) Derive an expression for the loss of head due to sudden enlargement of a pipe. (10 Marks) Determine the difference in the elevations between the water surfaces in the two tanks which are connected by a horizontal pipe of diameter 300mm and length 400m. The rate of flow through the pipe is 300 litres/sec. Consider all losses and take f : 0.008. Also draw HGL and (10 Marks) TEL. (10 Marks) Derive an expression for Hagen Poiseullie formulae. An oil of viscosity 0.1 N-s/m2 and relative density 0.9 is flowing through a circular pipe of diameter 50mm and length 300m. The rate of flow of fluid through the pipe is 3.5 litres/sec. Find the pressure drop in a length of'300m and also the shear stress at the pipe wall. Define terms: i) Drag; ii) :' Lift; iii) Displacement thickness ; iv) Boundary layer ltlff::l (10 Marks) b. ;:i.t:ffi:, e ror raminar boundary rayer nows given as +=r(*)-1rr;r.'.,", an expression for boundary layer thickness (61. Shea, stress (t6) interms of Reynold's number. (10 Marks) 2 of2