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Fluid mechanics Question papers

1. 1. USN O6ME46B Fourth Semester B.E. Degree Examination, December 20ll Fluid Mechanics Time:3 hrs. Max. Ivlarks:100 Note: Answer any FIW full questions, selecting at least Tlllo qaestions from each part. PABT -A o () o la. Define the following properties of a fluid and mention the phenomena associated with each property i) Capillarity and ii) Surface tension. cd o. (04 Marks) d b. Define compressibility. Derive an expression for the bulk modulus of elasticity for a perfect I gas, undergoing the isothermal process. (06 Marks) () 6 c. Calculate the capillary effect in mm in a glass tube of 3mm diameter, when, immersed in o mercury. The value of the surface tension for mercury at 20oC in contact with air is E9 0.51 N/m. Contact angle for mercury : 9p- 130o. Also sketch the mercury surface inside andOEy- outside the tube indicating the angle of contact clearly. (06 Marks) 6V5r ll d. If the equation of velocity profile over a flat plate is V :2f/3 where v is the velocity inroco9 m/s andy is the distance in m, determine shear stress at y: 75 mm. Take p: 8.35 poise..= a] 6J sl (04 Marks) hoo tsa) ()tI-c !) 2a. Define : i) Buoyancy and centre of buoyancy ; ii) Metacentre and metacentric height.oi (04 Marks)EE b. Show that the centre of pressure lies below the centre of gravity of the vertical surfae* submerged in a liquid. (08 Marrrs)tsEbd c. As shown in the Fig.Q.2(c), pipe M contains carbon tetrachloride of specific gravity 1.594(Bo under a presstre of 1.05 bar and pipe N contains oil of specific gravity 0.8. If the pressure inotbod the pipe N is 1.75 bar and the manometric fluid is mercury, find the difference x between the.g (s1rh levels of mercury. (08 Marks),ts G{C, 63aBko.oPa8.tro-6dOj Fig.Q.2(c)o=goia tE=#E {ll3Eoi> l!booco0o=o. h;F>Xt)3k 3a. Differentiate between :ch i) Lagrangian approach and Eulerian approach.L.)< r^i ii) Steady flow and uniform flow. (04 Marks)o b. Derive with usual notations, the continuity equation tbr 3 - D tlow in the torm +. ryq * 49") + a(l*) = 0. Modiry the equation for steady flow and incompressibleozE 0t&qAz& flow. (10 Marks) V:tr Sketch the streamlines represented by x2 + y. Also find out the velocity and its direction at the point (1,2). (06 Marks) I of2
2. 2. O6ME4684a. Explain the dimensional homogeneity, with an example. (04 Marks) b. Define the following dimensionless numbers and mention their significance in fluid flow problems: i) Reynolds no. ;ii) Froudes no. ; iii) Mach no. (06 Marks) c. Prove that the discharge over a spillway is given by the relation using Buckinghams II - theorem. a=VDf[ @ D) Hl v WhereV:velocityofflow,D:Depthatthethroat,H:Fleadofwater,g=Acceleration due to gravlty. (10 Marks) PART _ E5a. State Bernoullis theorem for the steady flow of an incompressible fluid. Derive an expression for Bemoullis equation from the first principles. (10 Marks) b. Gasoline : (sp.gr 0.8) is flowing upwards through a vertical pipe, which tapers in diameter from 30cm to 15 cm. A gasoline mercury differential manometer is connected between 30cm and l5cm pipe section to measure the rate of flow. The distance between the manometer tapping is 1m and gauge reading is 50 cm of mercury. i) Find the differential gauge reading in terms of gasoline head. ii) Using Bernoullis equation and the equation of continuity, find the rate of flow. Neglect the losses between tappings. (10 Marks)6a. Expiain how veiocity of flow at any point in a pipe or a channel can be measured, with a pitot tube. (06 Marks) b. At a sudden enlargement of a water line from 240 mm to 480 mm diameter pipe, the hydraulic gradient rises by 10 mm. Estimate the rate of flow. (08 Marks) c. An orifice meter with orifice diameter 10cm is inserted in a pipe of 20 cm diameter. The pressure gauges fitted upstream and downstream of the orifice meter give readings of 19.62 N/cm2 and 9.81 N/cm2 respectively. Co for the meter is 0.6. Find the discharge of water through the pipe. (06 Marks)7 a. There is a horizontal crack 40 mm wide and 2.5 mm deep in a wall of thickness 100 mm. Water leaks through the crack. Find the rate of leakage of water through the crack, if the difference of pressures between the two ends of the crack (fixed plates) is 0.02943 N/cm. Take the viscosity of water equal to 0.01 poise. (06 Marla) b. Sketch the shear stress and velocity profile across a section of a circular pipe, for the viscous flow. Derive the expressions governing shear stress and velocity profile. (14 Marks)8a. Derive an expression for the velocity of sound in terms of bulk modulus (k). (06 Marks) b. Define the following : i) Boundary layer thickness ii) Displacement thickness iii) Momentumthickness. (06 Marks) c. A flat plate 1.5m x 1.5m moves at 50 km/hr in stationary air of density 1.15 kg/m3.If the co- efficients of drag and lift are 0.15 and 0.75 respectively, determine : i) The lift force ii) The drag force iii) The resultant force iv) The power required to keep the plate in motion. (08 Marks) ***!S* 2 of2
3. 3. USN O6ME46B Fourth semester B.E. Degree Examination, June/July z0ll Fluid Mechanics Time: 3 hrs. Max. Marks:100 Note: Answer any FIW full qaestions, selecting at least TWO questionsfrom each part. PART _ A o o ii I a. Define the foliowing terms and mention their SI units: i) Specific weight ii) Dynamic viscosity iii) Kinematic viscosity iv) Surface tension v) Capillarity. (10 Marks) o b. A differential U-tube manometer is used to rneasure the pressure difference between two () points in a horizontal water pipe line. If the manometer shows a difference in mercury levels Y? q.r as 25 cm, find the pressure difference between the points in bar. (10 Marks) o,; &s cra 2 a. State and prove Pascals law. (08 Marks) .o ., oo c,a rl b. A wooden cylinder having specific gravity 0.7 is required to float in water. If the diameter of the cylinder is d and the length /. Show thatl cannot exceed A.7715 d for the cylinder to :oo float with its longitudinal axis vertical. (0E Marks) ts() ()E: c Differentiate between stable, unstable and neutral equilibrium of a floating body. (04 Marks) 3 a. Det-tne contindty equation and derive the same fcr a 3-dimensiorral fluid flow in Cartesian a: co-ordinates. i10 Marks) ou b" The stream function fcrr a 2-D floN,is given by V :gxy. Calculate the velocity at a point ooc cd a3 P(4, 5). Find also the velocity potential firnction. (10 Marks) >.8 6- 4 a. State and explain Buckingham n theorem. (05 Marks)O cd b. Explain kinematic and dynamic similarity. (05 Marks) OE ?C) c Yelocity of fluid flow through a circular orifice, is dependent ori head of flow oH,, orifice diameter D, absolute viscosity op, mass density p and gravitatiorral acceleration .g,. 14 c- orv o,i Using Buckingharns n theorern show thato:3i;atE v: /zgH4i#,*) (10 Marks)qoo":},qrtr50 PART _ B=(d :i95L 5 a. Derive Eulers equation of motion along a stream line and hence reduce Bernoulli,s->.U< equation. (lo Marks)dN b. A vertical pipe currying oil of specific gravity 0.8 tapers uniformly from 20 cm diameter ato the lower section to 10 cm diameter atJhe upper r.oiiorr. The vertical distance between thez sections is 1,m. The pressure gauges installed at the lower and upper sections read 6 NlcmiL and 8 N/cm respectively, when the discharge is 30 litres/sec. Calculate the loss ofo head between the two sections and determine the direction of flow. (r0 Marks) I of2
4. 4. O6ME46B6 a. With the help of a neat sketch, explain how a pilot tube is used to find the velocity in an open channel. (04 Marks) b. Derive the expression for discharge through a venturimeter. (08 Marks) c. Derive Darcys equation for loss of head between the two sections. Determine the direction of flow. (0S Marks)7 a. Derive Hagen Poisellis equation for laminar flow through a circular pipe. (12 Marks) b. Fuel is pumped up in a 30 cm diameter and 15 km long pipeline at the rate of 750 kg/min. The pipe is laid at an upgrade of 1:300. The specific gravity of fuel oil is 0.95 and its kinematic viscosity 20 stokes. Find the power required to pump oil. (08 Marks)I a. Explain the following : i) Lift ii) Drag iiD Displacement thickness iv) Mach number v) Isentropic flow. (10 Marks) b. A flat plate 1.8mxtr.8m moves at 36 km/lr in a stationary air of mass density 1.2 kglm3. lf the coefficients of drag and lift are 0.15 and 0.75 respectively" Detenuine D Drag force ii) Lift force iiD Resultant force iv) Power required to keep the plate in motion. (I0 Marks) {.r}:tr}* 2 of2
5. 5. l USN O6ME46B Fourth Semester B.E. Degree Examination, December 2010 Fluid Mechanics Time:3 hrs. Max. Marks:100 Note: 1. Answer any FIVE full qaestions, selecting at leost TWO questions from each part. 2. Assume suitable data, if required. () o o d PART _ A d I a. Differentiate between gauge pressure and absolute pressure. Represent positive and negative gauge pressures on a chart. (03 Marks) (€ (:) b. Give reasons for the following : d o i) Viscosity changes with temperature rise.3e ii) Mercury (Hr) is preferred as a manometric liquid. iii) Free surface of water in a capillary tube is concave.69 iv) Light weight objects can float on the free surface of liquids. ao"-il v) Metacentric height is positive for stable equilibrium of floating bodies. (10 Marks) coo=+.= c.l c. Derive the relation for capillary rise of water in a glass tube. (03 Marks) cd+ x al) d. A liquid bubble of 2cm radius has an internal pressure of 12.95 Pascals. Determine the E(J OE surface tension of the liquid film. (04 Marks)-c 0) oB 2 a. Derive the relations for hydrostatic forces on a curved surface, which is immersed in a liquid E* of specific weightW. (06 Marks) od b. With a neat sketch, explain the working of an inverted u - tube manometer. (06 Marks) bU c. A wooden block of size 6m x 4m x 2m floats on fresh water. Depth of immersion of the (Bo wooden block is 1.2 m. A concrete block is placed centrally on the surface of the wooden aotr c6 .6!b block, so that, >P 6< i) The top surfbce of the wooden block touches the ftee surface of,water ii) Both wooden block and concrete block submerge completely in water. Assume specific gravity of concrete : 2.5. Find the volume of the concrete block in eachi (,) eO case. (08 Marks) a.a tro- 5(! 3 a. Derive the continuity equation for a three dimensional flow, in Cartesian co-ordinates. 9.d (08 Marks) 5t) olE b. Show that the streamlines and equipotential lines are orthogonal to each other. (04 Marks)EO-!,o.-= qr c. A stream function represents 2-D fluid flow, y : 2xy.Find the velocity at a point P(3, 4).>bDo Check whether the flow is rotational. Find the velocity potential function \$. (08 Marks)cbOo= oii tr> 4a. Mention the applications of model similitude. (02 Marks) =o UL b. Explain the significance of non - dimension numbers.Q< e.i ; ; D Mach number ii) Froudes number iii) Weber number ; iv) Reynolds number.-.: 0) c. using Buckingham ,, - that the velocity of fluid flow throu*, f"X[Bz Y**7*o*E ad orifice is given by v =,l2gi (*,#r) , *r,.r" o. H: Head of fluid flow ; D: Diameter of the orifice p = Dynamic viscosity of the fluid ; p: Density of the fluid. g = gravitational acceleration. (10 Marks) I of2
6. 6. O6ME46B PART -B a. Derive the a Bernoullis equation for steady, incompressible fluid flow. List the assumptions Mention the significance of each term in Bernoullis equation. (10 Marks) b. Pipeline AB carries oil of specific gravity 0.90. Diameter of the pipe at A is 250 mm and that at B is 500 m{, B.of t}re pipe is 6 meters above the end a. rfr" pressue intensities lnd at A and B are 200 kN/mz and 120 kN/m2 respectively. Discharg. of oil is 450 litlsec. Determine : i) Loss of head and ii) Direction of oil flow. (10 Marks) a. Differentiate between a venturimeter and an orificemeter. (04 Marks) b. A pitot - tube is used for measuring the velocity of air flow through a duct. A u tube water - manometer shows a deflection of 12 mm of water. If the coefficient of pitot tube is 0.9g, find velocity of air flow and mass flow rate of air. Assume specific *eight of air as f O N/mL Diameter of the duct is 500 mm. (06 Marks). c. Oil of specific gravity 0.90 flows through an inclined venturimeter. lnlet and throat diameters are 30 cm and l5cm respectivelyand the throat is 30cm above the inlet section. Pressure intensity at the inlet is 150 kPa and deflection in mercury manometer is 25 cm. Determine the rate of oil flow in lts/sec and also the pressure intensiiy at the throat. Assume C6 = 0.98 for the venturimeter. (10 Marks)a. Derive a relation for the discharge through a circular pipe of diameter D, for the viscous flow. (08 Marks)b A 100 meters long pipeline connects two reservoirs. The difference in waterlevels is 15 meters. The pipeline has two equal sections of 50 meters each. Diameters of first and second sections are 25 mm and 50.mm_respectively. If the friction coefficient of pipe material is 0.005, determine the velocity of waier flowtkough the two sections and the rate of water flow in litres/sec. Represent TEL and HGL. (r2 Marks)a. Define drag force and 1ift force. (04 Marks)b. Define and explain : i) Boundary layer thickness ii) Mach cone, Mach angle iii) Subsonic flow. Marks) (08c. A projectile travels in air of pressure 1.01 x 10s N/m2 at l0oC. Speed of projectile is 1500 km/hour. Determine the Mach number and the Mach angle. Assumek:1.4and R:287 J/kg k. (08 Marks) **:t*1. 2 of2
7. 7. USN O6UIE468 Fourth semester B.E. Degree Examination, MaylJune 2010 Fluid Mechanics Time:3 hrs. Max. Marks:100 Note: Answer any FIVEfull questions, selecting at least TWO questions from each part. ai o D 1 a. Define the following terms *,rn,n"[f;,rtf, ^ E i) Capillarity iD Surface tension () iii) Mass density € 6 d) iv) Pressure intensity 3e v) Kinematic viscosity. (10 Marks) Q:s b. Derive the relation for pressue intensity and the surface tensile force, in case of soap bubble. (04 Marks) Ea c. rl A steel shaft of 30 mm diameter rotates at 24A rpm, in a bearing of diameter 32 mm. bo coo Lubricant oil of viscosity 5 poise is used for lubricanl of shaft in the bearing. Determine the .= a.l (!.sf torque required at the shaft and power lost in maintaining the lubrication. Lingth of bearing xao go otr is 90 mm" (06 Marks) _c() eE HL v5 3s 2 a. State and prove Pascals law. b. Show that, for a submerged plane surface, the centre of pressure, lies below 6rt[m?t Bg gravity of ttre submerged surface. (08 Marks) bU c. A differential rnercury manometer is used for measuring the pressgre difference between =! two pipes A and B. Pipe A is 500 mm almve the pipe B and deflection in Hg manometer is o.(, 40tr dcd 200 mm- Pressure intensity in pipe A is greater than pipe B. pipes carry oil of specific!B a6 gravity 0.90. Find the pressure difference between the two pipes. Sp.gr. olmercury = t:.0. 6r!o(d (08 Marks)-a" B 6 -lJ 3a. Explain the importance of metacentre with stability of floating bodies. (04 Marks) a8_ b. A wooden block (barge) 6 mts in length, 4 mts in width and 3 mts deep, floats in fresh water trit oj witn of immersion 1.5 rnts. A concrete block is placed centrally on the surface of the -aef\$ o= wooden block, so that the depth of immersion with concrete is 2.8 mts. Find the volume of BU ia tE a., the concrete block placed centrally, if the specific gravity of concrete is2.75. Find also the E() volume of water displaced. (08 Marks)3P> 9: c. Differentiate between :bDecboo= i) steady flow and uniform flow ii) Laminar and turbulent flowE8 ii) Sheamline and streakline iv) Rotational and irrotational flow. (08 Marks)UL=ocho< 4a. Show that streamlines and equipotential lines are orthogonal to each other. (04 Marts)r c.t b. Torque developed by a disc of diameter D, rotating at a speed N is dependant on fluid:o viscosity op and fluid density p. obtain an expression for torque, 1= -[#r]z pN2D5(,oF c. Foratwo dirnensional fluidflow, velocitypotential is g = y+ * ->?.Fi"dJljHH function and velocity at apoint P (2,3). Check irrotationality oino*. (0E Marks) I of2
8. 8. O6ME468 PART -B rl a. Derive Bernoullis equation and state the assumptions made. Mention the statement of Bernoullis equation. (10 Marks) b. A pipe gradually tapers from a diameter of 0.4 mts to diameter 0.25 mts at the upper end. The pipe carries oil of specific gravity 0.90 and rate of flow is 45 kg/sec. Elevation difference between two sections is 5.0 meffes. If the pressure intensities at the bottom and the upper sections are225 kN/m? and 105 kll/m2 respectively, find the direction of flow and also loss of head between the two sections. (10 Marks)6a. Sketch and derive the relation for actual discharge through an orifice meter. (08 Marks) b. A pitot static probe measures the velocity of water flow through a pipe of diameter 7.5 cm. If the mean velocity of water flow is 6.5 m/sec and coefficient of pitot tube is 0.98, find deflection in mercury manometer connected across the pitot - tube. Detemine the mass rate of water flow. (08 Marks) c. List the types of losses, with a neat sketch and equations for head losses. (04 Marks)7a. Derive the relation for the pressure drop in a viscous flow through a circular pipe. 1to Marks) b. Sketch the total energy line and the hydraulic gradient line for a pipeline connecting two reservors. (04 Marks) c. A pipeline 50 m long, connects two reservoirs, having water level difference of 10m. Diameter of the pipe is 300 mm. Find rate of water flow, ionsidering all the losses. Coefficient of friction for pipe material is 0.01. (06 Marks) a. Explain following terms : i) Lift ii) Drag iiD Boundary layer separation iv) Momentum thickness v) Displacementthickness. (10 Marks) b. Derive a relation for the velocity of sound in a compressible fluid. (06 Marks) c. Find the velocity of a bullet fired in the air, if the Mach angie is 30o. Temperature of air is : : z2"C,density of air is 1.2 kg/rn. Assume T 1.4 and R 287 J/kg K. (04 Marks) ,***** 2 of2
9. 9. O6ME46B USN Fourth Semester B.E. Degree Examination, Ilec.09-Jan.10 Fluid Mechanics o Time: 3 hrs- Max. Marks:100 o o E _g Note: Answer any FIVE full questions, selecting G E at least TWO questionsfrom each part. t, (E o o PART _ A .((t UO (, .!= g_H I a. Distinguish between : vZ E3 (5- i) Mass density and specific weight to ii) Newtonian and non-Newtonian fluid or? .L oo C+ iii) Absolute and l(inematic viscosity. (06 Marks) =N :vs b. An oil film of thickness 2mm is used for lubrication between a square plate of size o(,, Ld) 0.9m x 0.9m on an inclined plane having an angle of inclination 30o. The weight of the (l)- 5E square plate is 350N and it slides down the plane with a uniform velocity of 0.3mlsec. Find !i: (06 Marks) u> a- aQ.=o c. f;JrirH"y;ffir:X,f #::- absorute, sause and atmospheric pressures with a simple sketch. (03 Marks) nfr d. A U-tube manometer containing mercury is connected to a pipe in which water is flowing. 9AEh Water lend in the limb connected to pipe is 0.5m below centre of the pipe and the. freec<oE surface mercury in the other limb (open to atmosphere) is 0.8m below the ceritre of the pipe,PK Calculate the pressure of water in the pipe. (05 Marks)obt(Egrroo3rA 2 a. Define the terms :b.et^_ i) Total pressure ii) Centre of pressure (04 Marks)E(s b. An annular plate 3m external diameter and i.5m intemal diameter is immersed in water withFo-=d)Eo_ 8(E its greatest and least depths below water surface at 3.6m and l.Zm respectively. Determine --- U; u-Y the total pressure and the position of centre of pressure on one face of the plate. (08 Marks) g6 A solid cylinder 15cm diameter and 60cm long consists of two parts made of different ae (Ue materials. The first part at the base is l.2cm long and of speeific gravity 5. The other part of L(u fro o- the cylinder is rnade of the material having specific gravity 0.6. State if it can float vertically >E in water. (08 Marks)PorEGao)E>:o 3a. Distinguish between :cc i) Steady and un-steady flowo< i0 Uniform and non-uniform flow-ni iii) Laminarand turbulent flow" (06 Marks)"!,o b. Derive an expression for continuity equation for a three dimensional flow. (08 Marks)z c- If for a two dimensional potential flow, the velocity potential is given by 0 = 4x(3y - 4) ,\$ deterrnine the velocity at the point (2, 3). Determine also the value of stream function ry atoOL the point {2,3). (06 Marks)E 4 a. State Buckinghams theorem. Why this theorem is considered superior over the Rayleighs ru method for dimensional analysis? (05 Marks) I nf?
10. 10. O6ME46B Assuming that the rate of discharge Q of a centrifugal pump is dependent upon the mass density f of fluid, pump speed N(rp*), the diameter of the impellor D, the pressure P and discharge can be the viscosity of the fluid p. Show using the Buckinghams theorm that, the represented bY Q=ND3f[(#}[#)] (loMarks) c. what is meant by geometric, kinematic and dynamic similarities? (05 Marks) PART _ B Define Eulers equation of motion. Deduce Bemoullis equation from the same. (08 Marks)54. b. A pipe line carrying oil of specific gravity 0.8 changes in diameter from 300mm at position A io 500mm diameter at poiition B which is 5m at a higher level. If the pressure at A and B loss of are 20N/cm2 and 15N/.*) ,.rp."tively and discharge is 150 litreslsec, determine the (06 Marks) head and direction of flow. A horizontal venturimeter with inlet diameter 20cm and throat diameter 10cm is used to pressure measure the flow of water. The pressure at the inlet is 17.658N/cm2 and the vacuum Take at the throat is 30cm of mercury. Find the discharge of water through the venturimeter- (06 Marks) Ca = 0.98.6 a. What are the energy losses that occur in pipes? Derive an expression for loss of head due to friction in pipes. (08 Marks) b. A pipe of dia 30cm and length 1000m connects two reseryoirs having difference of water levels as l5m. Determine the discharge through the pipe. If an additional pipe of diameter 30cm and length 600m is attached to the last 600m length, find the increase in discharge (08 Marks) Take f = 0.02 and neglect minor losses. (04 Marks) Write a note on Hydraulic gradient and total energy lines. c. a. Sketch the velocity and shear stress distribution across the section of the pipe for viscous flow through it. Marks) (04 Derive Hagen-Poiseuille equation with usual notations. (08 Marks) b. c. An oil of viscosity O.lNslm2 and relative density 0.9 is flowing through a circularpipe 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 (0S lVlarks8 a. Define the terms : i) Boundary layer ii) Boundary layer thickness iii) Drag iv) Life v) Momentum thickness. (10 Marks) b. Define the terms : sub sonic flow, sonic flow and supersonic flow (06 Marks) c. An aeroplane is flying at a height of 15km where the temperature is -50oC. The speed of the plane is cott".pot ding to M : 2.0. Assuming K : 1.4 and R : 287JkgK, find the speed of (04 Marks) the plane. {.**:t* 2 of2
11. 11. O6ME46B USN Fourth Semester B.E. Degree Examination, Dec.09-Jan.10 Fluid Mechanics Time:3 hrs. Max. Marks:100 o o () oE Note: Answer any FIVE full questions, selecting 6 E at least TWO questionsfrom each part. o o E (, PART -A .ou, 0) o .:= Pe o-s la. Distinguish between :.v.Z E3 D Mass density and sPecific weight (g60 ii) Newtonian and non-Newtonian fluidsrf,= co iii) Absolute and Kinematic viscosity. (06 Marks)E\$ b. An oil fi}m of thickness 2mm is used for lubrication between a square plate of size E- oo) Lo 0.9m x 0.9m on an inclined plane having an angle of inclination 30o. The weight of the o-!g square plate is 350N and it slides down the plane with a uniform velocity of 0.3mlsec. Find o= the viscosity of the oil in poise. (06 Marks) oq c. Establish a relationship among absolute, gauge and atmospheric pressures with a simple.=O sketch (03 Marks)BEp+ d. A U-tube manometer containing mercury is connected to a pipe in which water is flowing.oo-oh Water lend in the limb connected to pipe is 0.5m below centre of the pipe and the. freec<oE surface mercury in the other lirnb (open to atmosphere) is 0.8m below the centre of the pipe,HK (05 Marks)1,b Calculate the pressure of water in the pipe.56Sf,E(oaB3e 2a. Define the terms :o_ i) Total pressure ii) Centre of pressure (04 Marks)=(5 b. An annuiar plate 3m extemal diameter and 1.5m intemal diameter is immersed in water withFo-=d,CO8N its gteatest and least depths below water surface at 3.6m and 1.2m respectively. Determine -e-9E theiotal pressure and 1}1g position of centre of pressure on one face of the plate. (08tlarks)o=;E c. A solid tylinder 15cm diameter and 60cm long consists of two parts made of diflerentaLc materials. The first part at the base is 1.2cm long and of specific gravity 5. The other part of the cylinder is made of the material having specific gravity 0.6. State if it can float verticallyLO5Eo->E in water. (08 Marks)Por:(Eao)F>59 a. Distinguish between :cc i) Steady and un-steady flowo< i0 Uniform and non-uniform flow-Fi iii) Laminar and turbulent flow. (06 Marks)3 b. Derive an expression for continuity equation for a three dimensional flow. (08 Marks)oz c. If for a two dimensional potential flow, the velocity potential is given by 0 = 4x(3y - 4) ,(UE determine the velocity at the point (2,3). Determine also the value of stream function y ato (06 Marks)n the point (2, 3).E a. State Buckinghams theorem. Why this theorem is considered superior over the Rayleighs r method for dimensional analysis? (05 Marks) I nf )
12. 12. O6ME46B b. Assuming that the rate of discharge Q of a centrifugal pump is dependent upon the-mass density j of fluid, pump speed N(rpm), the diameter of the impellor D, the pressue P and the viscosity of the fluid p. Show using the Buckinghams theorm that, the discharge can be represented bY Q=ND3f[[#),[ffi_)] (10 Marks) c. What is meant by geometric, kinematic and dynamic similarities? (05 Marks) PART * BS a. Define Eulers equation of motion. Deduce Bernoullis equation from the same. (08 Marks) b. A pipe line carrying oil of specific gravity 0.8 changes in diameter from 300mm at position A to 500mm diameier at position B which is 5m at a higher level. If the pressure at A and B are 20N/cm2 and 15N/.# ,.rp""tively and discharge is 150 litres/sec, determine the loss of (06 Marks) head and direction of flow. c. A horizontal venturimeter with inlet diameter 20cm and throat diameter 10cm is used to measure the flow of water. The pressure at the inlet is 17.658N/cm2 and the vacuum pressure at the throat is 30cm of mercury. Find the discharge of water through the venturimeter. Take (06 Marks) Co = 098.6 a. What are the energy losses that occur in pipes? Derive an expression for loss of head due to friction in pipes. (08 Marks) b. A pipe of aia 30cm and length 1000m connects two reservoirs having difference of water levels as 15m. Determine the discharge through the pipe. If an additional pipe of diameter 30cm and length 600m is attached to the last 600m length, find the increase in discharge. (08 Marks) Take f = 0.02 and neglect minor losses. (04 Marks) Write a note on Hydraulic gradient and total energy lines. c.7 a. Sketch the velocity and shear stress distribution across the section of the pipe for viscous flow through it. (04 Marks) b. Derive Hagen-Poiseuille equation with usual notations. (08 Marks)_ c. An oil of viscosity 0.1Ns/m2 and relative density 0.9 is flowing through a circularpipe of diameter 50mm and length 300m. The rate of flow of fluid through the pipe is 3.5 litresisec. Find the pressure drop in a length of 300m and also the shear stress at the pipe wall. (08 Marks a. Define the terms : i) Boundary layer ii) Boundary layer thickness iii) Drag iv) Life v) Momentum thickness. (10 Marks) b. Define the terms : sub sonic flow, sonic flow and supersonic flow. (06 Marks) c. An aeroplane is flying at a height of 15km where the temperature is -50oC. The speed of the plane is corresponding to M :2.0. Assuming K : 1.4 and R = 287JikgK, find the speed of the plane. (04 Marks) **{.** 2 ofZ
13. 13. USN O6ME468 Fourth Semester B.E. Degree Examination, June-July 2009 Fluid MechanicsTime:3 hrs. Max. Marks:100 Note: Answer any F(YE full questions choosing at least two questions frr* each uniL PART _ A I a. Give reasons : i) Viscosity of liquids varies with temperature. i0 Thin objects float on free surfaee of static liquid. iii) Metacentric height determines stability of floating body. iv) Rise of water Ltt a Calillary tube. v) Mercury is used as Manometric liquid. (05 Marks) b. Define following terms with their units. i) Specific weight ; iv) Specific gravity ; v) Capillarity (05 Marks) c. The space between two square flat parallel plates is filled with oil. Eaeh side of the plates is 800 mm. Thickness of the oil film is 20 mm. The upper plate moves at a uniform velocity of 3.2rn/sec when a force of 50 N applied to upper plate. Determine : i) Shear stress ii) Dynamic viscisity of oil in poise iii) Power absorbed in moving the plate iv) Kinematic viscosity of oil if specific gravify of oil is 0.90. (10 Marks)2 a. State and prove Hydrostatic law. (05 Marks) b. With neat sketch, explain working of differential u-Tube Manometsr and derive relation for measuring pressure difference between two pipes. (05 Marks) c. A wooden block of size 6m x 5m x 3m height floats in freshwater. Find the depth of immersion and determine the metacentric height. Specify gravity of wood is 0.70. Find the volume of concrete block placed on the wooden block, so as to completely submerge the wooden block in water. Take specific gravity of concrete as 3.0. (10 Marks)3 a. Explain experimental procedure to determine the metacentric height of a floating vessel. (04 Marks) b. Derive continuity equation for a three dimensional fluid flow in Cartesian co-ordinates. (08 Marks) c, Velocity potential function for a two dimensional fluid flow is given by S = x(2y -1) . Check the existence of flow. Determine the velocity of flow at a P(2,3) and the stream function. (08 Marks)4a. Show that streamlines and equipotential lines are orthogonal to each other. (05 Marks) b. Explain Model Similitude and Non-dimensional numbers. (05 Marks) c. The pressure difference Ap for a viscous flow in a pipe depends upon the diameter of the pipe D, length of pipe L, velocity of flow V, viscosity of fluid p and the density of fluid p. Using Buckinghams theorem, show that the relation for pressure difference Ap is given by Ap=pv2r(*,*) (10 Marks) I of2
14. 14. 06M[468 PART _ B a. State and prove Bernoullis equation for a fluid flow. Mention assumptions made in derivation. (10 Marks) b. Water is flowing through a taper pipe of length 150m, having diameter 500 mm at the upper end and 250 mm at the lower end. Rate of flow is 70 liters per sec. The pipeline has a slope of I in 30. Find the pressure at the lower end if the pressure at higher level is 2.5bar. (10 Marks)6a. Explain with neat sketch, working of pitot-static tube. (05 Marks) b. Differentiate between Orificemeter and venturimeter with neat sketches. (05 Marks) c. A horizontal venturimeter with 50cm diameter at inlet and 20cm throat diameter is used for measuring rate of water flow, if the pressure at inlet is 1.8 Bar and vaccum pressure at the throat is 30cm of mercury, find the rate of flow. Assume 10% differential pressure head is lost between the inlet and throat section. Assume coefEcient of discharge is 0.96. (10 Marks)7a. Derive Hagen-poiseulles equation for viscous flow through a circular pipe. (10 Marks) b. Rate of water flow through a horizontal pipe is 0.030 m/sec. Length of pipe is 1000 meters. Diameter of pipe for first half of length is 200mm and suddenly changes to 400mm for remaining length. Find the elevation difference between the two reservoirs connected by the horizontal pipeline. Take F0.01 for material of pipeline. (10 Marks) a. Explain terms : i) Lift ii) Drag iii) Displacement thickness iv) Momentum thickness (08 Marks) b. Explain Mach angle and Mach cone. (04 Marks) c. A projectile travels in air of pressure 15 N/cm2 at 100C, at a speed of 1500 km/hr. Find the Mach number and Mach angle. Assume T:1.4 and R:287 J/kgof (08 Marks) ***** 2of2
15. 15. USN 2AO2 SCHEME ME45 Fourth Semester B,E. Degree Examination, June-July 2009 Ftuid MechanicsTime: 3 hrs. Max Marks:100 Note: 7. Answer any FIVE full questions. 2. Assume any missing data suitably.L a. Define surface tension. Sketch a liquid droplet on a solid surface when i) Adhesion is more then cohesion ii) Cohesion is more then adhesion Show the angle of contact on the sketches. A glass tube of small diameter is dipped in a mercury container vertically. Sketch the mercury surface inside and outside the tube indicating the angle of contact ciearly. Obtain an expression for capitiary {se/depression that would take place in this tube in terms of densit5 of liquid, surface tension, angle of contact and local acceleration due to gravity. (L0 Marks) b. A cylindrical shaft of 90 mm diameter rotates about a vertical axis inside a fixed cylindrical" tube of length 0.5 m and 95 mm internal diameter. If the space betweeri tube and the shaft is filled by a lubricant of viscosity 0.2 Pa.s, determine the power required to overcome viscous resistance when the shaft is rotated at a speed of 240 rpm. (10 Marks)2 a. Explain clearly how the magnitude and direction ofresultant hydrostatic force on a curved surface is determined. (10 Marks) b. A hydrometer shown in Fig.Q2(b) is to be used to determine relative densities of different liquids. It has a mass of 20g. The external stem diameter is 5 mm. Find the distance between the markings corresponding to the foilowing relative densities (10 Marks) fi= U ig.Q.2(b).3 a. Define metacentric height of a floating body. Obtain an expression for metacentric height of a floating body in terms of second moment of area of its plan at water surface, submerged volume and distance between centre of gravity and centre of buoyancy of the floating body. (10 Marks) b. If the pipe shown in Fig.Q.3ft) contains water and there is no flow, calculate the value of manometer reading h. If manometer reading h: 50 rnm when water is flowing through the pipe, calculate the pressue difference Pa. - Ps in kPa. (10 Marks) Fie.Q.3O). I of2
16. 16. ME45 4a. State the continuity principle. Derive three dimensional continuity equations in differential form for a general fluid flow situation. Simpli\$z it to two dimensional steady, incompressible flow and one dimensional unsteady flow cases. (10 Marks) b. For a two dimensional flow, the stream function is given by V: Zxy. Calculate the velocity eomponents at a point (3, 6). Show that velocity potential exists for this case. Determine the velocity potential firnction. (10 Marks) 5a. State Buckingham rc theorem. The input power of a centrifugal pump is found to depend on diameter of impeller D, discharge Q, density of liquid p, rotational speed N, and specific ener\$Y of liquid gH. Using Buckingham ru theorem, obtain the relevant ,r terms governing the pumping operation. (10 Marks) b. Water flows upwards through ataperedpipe as shown in Fig.Q.5(b). Find the magnitude and direction of deflection h of the differential mercury manombter corresponding to a discharge ofaJ2m3/s. Thefrictioninthepipecanbecompletelyneglected, - : (t0Marks)6a. Derive an expression for discharge *""#??rtt (10 Marks) b. A large tank has a vertical pipe 0.7 m long and 20 mrn diameter connected to the bottom" The tank contains oii of densiry 920 kglml and viscosity 0.15 Pa.s. Find the discharge through the tube when the height of oil level of the tank is 0.8 m above the pipe inlet. The flow is laminar and friction f,actor is given by where Re is the flow Reynolds number, * (tr0 Marks) a. O-btain an expression for radial velocity distribution in a fully developed laminar flow throilgh a horizontal round pipe and hence show that discharge Q througir this pipe is given by dp O= -91 tp where dxis the pressure gradient D is the diarneter and p is the viscosity 128pr dx ) of oil flowing through the pipe and . (10 Marks) b. Define Lift and Drag. Distinguish between skin friction drag and form drag. (05 Marks) A television transmitter antenna consists of a vertical pipe 0.2 m diameter and 30 m high on top of a tall structure. Determine the total drag force on the antenna in a 30 m/s wind. Density of air is 1.22kd*and viscosity of air is 17.9 pPa.s. Take coefficient of drag as CI"z. to5 Marks)8 a. The velocity profile in a laminar boundary layer is approximated by parabolic profile +=/+)-[I]where u is veloci ty aty and u -+ U as y -+ u -(o/ -.- J 6.Calculate the displacement [a./ thickness, and the momentum thickness 0. (10 Marks) b. Define mach nurnber. Show that speed of propagation of a pressure disturbance in a compressible fluid .=-E.For dne dimensional steady compressible flow of gases, write IoP down the continuity equation and equation of motion and show that d4 du = fi4, _1): A U (loMarks) *****
17. 17. USN. 2OO2 SCHEME ME45 Fourth Semester B.E. Degree Examination, June-July 2009 Fluid MechanicsTime:3 hrs. Max. Marks:l00 Note: 7. Answer any FIVE full questions. 2. Assume any missing data suitably. I a. Define surface tension. Sketch a liquid droplet on a solid surface when i) Adhesion is rnore then cohesion ii) Cohesion is more then adhesion Show the angle of contact on the sketches. A glass tube of small diameter is dipped in a mercury container vertically. Sketch the mercury surface inside and outside the tube indicating the angle of contact clearly. Obtain an expression for capiliary fse/depression that would take place in this tube in terms of density of liquid, surface tension, angle of contact and local acceleration due to gravtty. (10 Marks) b. A cylindrical shaft of 90 mm diameter rotates about a vertical axis inside a fixed cylindrical tubi of tength 0.5 m and 95 mm internal diameter. If the space between tube and the shaft is fil1ed by a lubricant of viscosity 0.2 Pa.s, determine the power required to overcome viscous resistance when the shaft is rotated at a speed of 240 tpm. (10 Marks)2 a. Explain clearly how the magnitude and direction of resultant hydrostatic force on a curved surface is determined. (10 Marks) b. A hydrometer shown in Fig.Q2(b) is to be used to determine relative densities of different liquids. It has a mass of 20g. The external stem diameter is 5 mm. Find the distance between the markings corresponding to the following reiative densities (10 Marks) ]tt3a. il ig.Q.2(b). Define metacentric height of a floating body. Obtain an expression for metacentric height of a floating body in terms of second moment of area of its plan at water surface, submerged volume and distance between centre of gravity and centre of buoyancy of the floating body. (10 Marks) b" If the pipe shown in Fig.Q.3ft) contains water and there is no flow, calculate the value of manometer reading h. If manometer reading h = 50 mm when water is flowing through the pipe, calculate the pressure difference Pe. - Ps in kPa. (10 Marks) Fis.Q.3(b). I of2
18. 18. ME45 4a. State the continuity principle. Derive tfuee dimensional continuity equations in differential form for a general fluid flow situation. Simpliff it to two dimensional steady, incompressible flow and one dimensional unsteady flow cases. (10 Marks) b. For a two dirnensional flow, the stream function is giverr by V: Zxy. Calculate the velocity components at a point (3, 6). Show that velocity potential exists for this case. Determine the velocify potential function. (10 Marks) 5 a. State Buckingham rc theorem. The input power of a cerrtrifugal pump is found to depend on diameter of impeller D, discharge Q, density of liquid p, rotational speed N, and specific energy of liquid gH. Using Buckingham rc theorem, obtain the relevant n terms governing the pumping operation. (10 Marks) b. Water flows upwards through a tapered pipe as shown in Fig.Q.5(b). Find the magnitude and direction of deflection h of the differential mercury manometer corresponding to a discharge of A J2m3 /s. The friction in the pipe can be completely neglected, - - (10 Marks)5a. Derive an expression for discharge *"rf;??ltl; (10 Marks) b. A large tank has a vertical pipe A.7 m long arld 20 mm diameter connested to the bottom. The tank contains oil of density 92A kglm3 and viscosity 0.15 Pa.s. Find the discharge through the tube when the height of oil level of the tank is 0.8 m above the pipe inlet. The flow is laminar and friction f,actor is given by where Re is the flow Relmolds number. # (10 Marks) a. Obtain an expression for radjal velocity distribution in a iully developed laminar flow through a horizontal round pipe and hence show that discharge Q through this pipe is given by q =-{Se where !E i, the pressure gradient D is the diameter and p is the viscosity 128p dx dx of oii flowing through the pipe and (10 Marks) b Define Lift and Drag. Distinguish between skin friction drag and form drag. (05 Marks) c A television transmitter antenna consists of a vertical pipe 0.2 m diametei and 30 m high on top of a tall structure. Determine the total drag force on the antenna in a 30 mls wind. Density of air is 1.22kd*and viscosity of air is 17.9 pPa.s. Take coefficient of drag as 0.2. (05 Marks)8 a. The velocity profile in a laminar boundary layer is approximated by parabolic profile l=r[f)-[v]2where u is velocity atyand u -> U as y -+ 6.Calculate -- J the displacement u -(0,/ [aJ thickness, and the momentum thickness 0. (I0 Marks) b. Define mach nupber. Show that speed of propagation of a pressure disturbance in a compressible fluid . = E. For one dimensional steady compressible flow of gases, write loP down the continuity equation and equation of motion and show that d4 u, (Jr, = -r) A U (lo*rarks) *****
19. 19. USN O6ME468 Fourth Semester B.E. Degree Examination, Dec 08 / Jan 09 Fluid MechanicsTime:3 hrs. Max. Marks:100 Note z Answer FIVE fult questions, selecting atleast TWO questions from each part. PART - A a. Differentiate between : i) Newtonian and Non-Newtonian fluids. ii) Ideal and Real fluids. iii) Dynamic and Kinematic viscosity of fluids. iv) Vapour pressure and cavitation. (08 Marks) b. Derive an expression for capillary rise in water. (04 Marks) c. A cubical block of sides lm and weighing 350N slides down an inclined plane with a uniform velocity of 1.5 m/s. The inclined plane is laid on a slope of 5 vertical to 12 horizontal and has an oil film of 1.0mm thickness. Calculate the dynamic viscosity of oil. (08 Marks) a. Prove that the centre of pressure lies below the centre of gravity of a vertically immersed plane surface in a static fluid. (08 Marks) b. An inverted U - tube manometer is connected to two horizontal pipes A and B through which water is flowing. The vertical distance between the axes of these pipes is 30cm. When an oil (S :0.8) is used as a gauge fluid, the vertical height of water columns in the two limbs of the inverted manometer (when measured from the respective centre lines of the pipes) are found to be same and equal to 35cm. Determine the difference of pressure between the pipes. Pipe B is lying below the pipe A. (08 Marks) c. A metallic body floats at the interface of mercury (S = 13.6) and water such that 30% of its volume is submerged in mercury and remaining in water. Estimate the density of the metal. (04 Marks) Prove that the equipotential lines and the stream lines are always intersect orthogonally. b. : Given the velocity field, V 5x3 i - 15x2 yj, obtain the equation of the str."*rrrrJllffilTl above given veiocity field, check for the continuity and irrotationality. (08 Marks) ^t *i c. The velocity potential function is given by the expression, 0 = -+33 * * - + y2 i) Find the velocity components in x and y directions. ii) Show that { represents a possible case of flow. (06 Marks) What do you mean by : i) Geometric simiiarity ii) Kinematic similarity iii) Dynamic similarity iv) Dimensional homogeneity. (04 Marks) b. The thrust (T) of a propeller is assumed to depend on the axial velocity of the fluid (V), the density (p) and viscosity (p) of fluid, the rotational speed (1..1) rpm, and the diameter of the propeller (D). Find the relationship for T by using dimensional analysis. (10 Marks) c. A model of an air duct operating wittr water pioduces a pressure drop of 10kN/m2 over 10m length. If the scale raiio is i/50, pw: 1000 kg/m3, pa:.2 kg/m3, and pv: 0.001 Pu-s, trru: 0.00002P;s, estimate the corresponding pressure drop in a20m long air duct. (06 Marks) L ot.-
20. 20. O6ME46B PART. B Derive Eulers equation of motion along a stream line and hence obtain the Bernoullis equation for incompressible fluids. (06 Marks) b. Using the Eulers equation of motion, derive the Bemoullis equation for a compressible fluid under going i) Isothermal process and ii) Adiabatic process. (06 Marks) c. A conical tube is fixed vertically with its small end upwards. Velocity of flow down the tube is 4.5m/s at the upper end and 1.5m/s at the lower end. Tube is 1.5m long and the pressue at the upper end is 24.3 kPa (ab). Loss in the tube expressed as head is 0.3 -Y)2 l2r, where V1 and Vz are the velocities of fluid (S : 0.8) flow at the upper (Vt and lower ends respectively. What is the pressure head at the lower end? (08 Marks) a. Derive an expression for the actual discharge through orifice meter. (08 Marks) b. Water is to be supplied to a town of 4 lakhs inhabitants. The reservoir is 6.4 km away from the town and the loss of head due to friction is measured as 15m. Calculate the size of the supply main if each inhabitant consumes 180 litres of water per day and half of the daily supply is pumped is 8 hour. Take the coefficient of friction for the pipe, f :0.0075. c. A venturimeter is to be installed in a 180mm pipeline horizontall y at asectionll,l#:fl pressure is 110 kPa (gauge). If the maximum flow rate of water in the pipe is 0.15m3/s, find the least diameter of the throat so that the pressure at the throat does not fall below 80 kPa (vacuum). Assume that 4yo of the differential head is lost between iniet and the throat, (06 Marks)1a. Derive Hagen Poiseuille equation for a laminar flow in a circular tube. (10 Marks) b. Water at 150C flows between two large parallel plates at a distance of 1.6mm apart. Determine i) the maximum velocity ii) pressure drop per unit length and iii) shear stress atthe walls of the plates if the average velocity is 0.2 m/s. The viscosity of water at 150C is given as 0.01 poise. (10 Marks) a. We know that the velocity of sound wave is the square root of the ratio of change of pressure to the change of density of a fluid. Using this definition, derive the expressions for a velocity of sound in a compressible fluid when it undergoes a process i) Isothermal and ii) Reversible adiabatic. (06 Marks) b. Define the following and write their equations : i) Drag ii) Lift iii) Displacementthickness iv) Momentumthickness. (06 Marks) c. A man descends to the ground from an aeroplane with the help of a parachute which is hemispherical having a diameter of 4m against the resistance of air with a uniform velocity of 25mls. Find the weight of the man if the weight of parachute is 9.81N. Take Co:0.6 and density of air : l.25kglm3 (08 Marks) *r<rr** ) n€1
21. 21. ,USN. ME45 Fourth Semester B.E. Degree Examination, June / July 08 Fluid Mechanics Time: 3 hrs. Max. Marks:100 Note z Answer any FIVE full questions. 1 a, State Newtons law of viscosity and deduce the definition of absolute viscosity. (04 Marks) b. A capillary tube having an inside diameter of 4 mm is dipped in water at atmospheric temperature of 20. Determine the height of rvater, which will rise in the tube. Take o : 0.075 N/m and o = 60" fcir water. What will be the percentage increase in the value of height, if the diameter of the tube is 2 mm? (06 Marks) c. The space between two square flat parailel piates is filled with oil. Each side of the plate is 60 cms. The thickness of the oil film is 12.5 mm. The upper plate, which moves at2.5 mls requires a force of 9.81 N to maintain the speed. Determine D The dynamic viscosity of the oil in poise. ii) The kinematic viscosity of the oil, if its sp.gr. is 0.95. iii) Power absorbed in moving the plate. (10 Marks) 2 a. Show that the centre of pressure, for a plane surface immersed in a static fluid either vertically or inclined, lies always below the centre of gravity. (08 Marks) b. A circular plxe 4.5 m in diameter is submerged in water such that its greatest and least depths below the water surface are 3 m and 1.5 m respectively" Find i) Total pressure on the top face of the plate. ii) The position of centre of pressure. (08 Marks) c. State hydrostatic law- and derive an expression for the same. (04 Marks) 3 a. Define meta centre of a floating body. Describe the analytical method of determining the metacentric height. (10 Marks) b. State the condition for stable equilibrir:,m of a floating body and expiain how this is taken care of in the design of a ship. (04 Marks) c. A wooden block of sp.gr 0.75 floats in water. If the size of the block is 1 mx0.5 mx0.4 in, find its metacentric height for a roll on its longitudinal axis. (06 Marks) 4 a. Show that the continuity equation for a three dimensional steady incompressible flow is glven oY, 6a* 6v* 5w U. (08 Nlarks) = 6, Sy 5, b. Define stream function and velocity potential function and show how they are related. (06 Marks) c. The velocity potential function for a two dimensional flow is \$ = x(Zy -l). At a point P(4,5) determine: i) Thevelocity ii) Vahreof streamfunction. (06Marks) 5 a. The pressure difference AP for viscous flow in a pipe depends upon the diameter of the pipe D, length of pipe L, the velocity V, viscosity p and density p. Using Buckinghams theorem obtain an expression for AP. (08 Marks) b. State impulse momentum principle and mention its applications. (04 Marks) c. ln a 45" bend, a rectangul ar ak duct of 1 m2 cross sectional area is gradually reduced to 0.5 m2 area. Find the magnitude and direction of the force required to hold the duct in position if the velocity of flow at I m2 section is 10 m/s andpressure is 3 N/cm2. Take specific weight of air as 11.38 N/m3. (0E Marks) I of2
22. 22. M8,45 Derive an expression for the discharge through an inclined Venturimeter for an upward flow. (08 Marks)b. A reservoir has been built 4 km away from a town having a population of 5000. Water is to be supplied from the reservoir to the town. The per capita consumption of water per day is 200 litres and half of this daily supply is to be pumped within 10 hrs. The loss of head due to friction in the pipe line is 20 m and the co-effrcient of friction for the pipe line is 0.008. Calculate diameter ofthe supply main. Neglect minor losses. (08 Marks)c. Write a note on Energy gradient line and hydraulic gradient. (04 Marks)a. Derive an expression for the ioss of head due to friction for laminar flow through a round pipe. Sketch the velocity profile and shear stress profile. (10 Marks)b. Derive an expression for the sonic velocity in a compressible flow medium for, i) Isothermal process ii) Adiabatic process Justifu which of these two is correct. (10 Marks)a. On a flat plate of 2 m length and 1 m width, experiments were conducted in a wind tunnel, with a wind speed of 50 kmAr. The plate is kept at such an angle that the co-efficients of drag and lift are 0.i8 and 0.9 respectively. Determine D Drag force ii) Lift force iii)Resultant force and iv) Power exerted by air stream on the plate. Take density of air : 1.15 kg/m3. (10 Marks)b. Define the following: 0 Boundary layer thickness. ii) Displacementthickness. iii) Momentumthickness. (06 Marks)c. A projectile travels in air of pressure 10.1043 N/cm2 at i0"C, at a speed of 1500 km/hr. Find the Mach number and Mach angle. Take y: 1.4 and R:287 J/kgK. (04 Marks) ,<**** 2 of}
23. 23. ME45USN Fourth semester B.E. Degree Examination, Dec. 07 / Jan. 08 Fluid MechanicsTime:3 hrs. Max. Marks:100 Note zl. Answer any FIVE full questions. 2. Missing data if any cun be saitably ussumed. I a. Define the following and mention their SI. units: i) Density. ii) Dynamic viscosity. iii) Surface tension. iv) Vapour pressure v) Bulk modulus. (10 Marks) b. Derive an expression for capillary rise of liquid in a tube. (05 Marks) c. The surface tension of water droplet in contact with air at 20C is 0.071 N/m. If the diameter of droplet is 1.45 mm, calculate the pressure within the droplet. (05 Marks)Z a. Derive an expression for hydrostatic force on an inclined submerged plane surface and depth of centre of pressure (10 Marks) b. A circular plate of 2 m diameter is immersed in an oil of specific gravity of 0.8, such that its surface is 30" to the free surface. Its top edge is 2.5 m below the fiee surface. Find the force and center ofpressure (05 Marks) c. Measurements of pressule at the base and top of a mountain ate 74 i cm and 60 cm of mercury respectively. Calculate the height of the mountain if air has a specific weight of 1 l.ZTkglm". (05 Marks) 3 a. Define the following: i) Buoyancy. ii) Absolute pressure. iii) Metacentre. iv) Gauge pressure. v) Centre of pressure (10 Marks) b" Ablock of wood of specific gravity 0.8 floats in water. Determine the metacentric height of block if its size is 3 m long, 2 m wide and 1 m height. State whether equilibrium is stable or unstable. (05 Marks) c. The left limb of a mercury U-tube manometer is open to atmospheric and the right limb is cofinected to a pipe carrying water under pressue. The centre of the pipe is at the level of the free surface o1 *.r"rry. Find the difference in level of mercury limbs of U{ube if the absolute pressure of water in the pipe is 14.5 m of water, atmospheric pressure is 760 mm of mercury. (05 Marks) 4 a. Derive the general three-dimensional continuity equation and then reduce it to continuity equation for steady, two dimensional in compressible flow. (10 Marks) b. Explain: i) Velocity potential function ii) Stream function. Write down the relation between them (05 Marks) c. A stream function is given by the expression z=2x2-y3. Fitd the components of velocity and the resultant velocity at a point (4,2). (05 Marks) I of2
24. 24. ME455 a. Using Buckinghamsl^ ,T"rem, show that the velocity through acircular orifice is given by Y =^lZsA +l;,#], where H is the head causing flow, D is the diameter of the orifice, p is the coefficient of viscosity, p is the mass density and g is the acceleration due to gravrty. (10 Marks) Derive the Eulers equation of motion for steady flow and obtain Bernoullis equation from it. State the assumptions made in the derivation of Bemoullis equation. (10 Marks) a. Explain a venturimeter. Drive an expression for discharge. Why venturimeter is better than orifice meter? (10 Marks) b. Derive Darcy-Weisbach formula to calculate the frictional head loss in pipe in terms of friction factor. (10 Marirs)ta- Explain: i) Mach number. ii) Subsonic flow. iii) Supersonic flow. iv) Laminar flow. v) Turbulent flow. (10 Marks) b. Water at 15"C flows between to large parallel plates at a distance of 1.6 mm apart. Determine i) The maximum velocity ii) The pressure drop per unit length and iii) The shear stress at the walls of the plates if the average velccity is 0.2 m/s. The viscosity of water at 15"C is given as 0.01 poise. (s5llIarks) c. Find the velocit-v of, bullet fired in standard air if the Mach angle is -40. Take R : 287.14 Jlkg K and K : 1.4 for air. Assume temperature at 15"C. (05 Marks) a. Define i) Drag. iil i,ift. iii) Boundary layer thickness. iv) DisplacemeRt tiiickness. v) Momentum thickness. (10 Marks) b. A circular disc 3 m in diameter is heid normal to a26.4 mls wind of density 0.0012 gmlcc. What force is required to hold it at rest? Assume co-efficient of drag of disc : 1.1 . Find the displacement thickness and the momentum thickness for the velocity ,ttHtHrt? /7.,2 in the boundary layer given by L=2[ o u + l-t + I where u is the velocity at a distance y v 6/ 61 from the plate and u: U at "p = 6 , where 6 is the boundary layer thickness. (05 Marks) 2 ofZ
25. 25. Petge Nri... I ME45 USN NEW SCHEME Fourth Semester B.E, Degree Examination, JuIy 2007 Mechanical En gineering Fluid Mechanics Time:3 hrs.] [Max. Marks:i00 Note : 1. Answer ony FIYE fult qaestions. 2. Any missing data may be ussumed suitabty. a. Define and differentiate between the following : i) Weight density and mass density ii) Kinematic viscosity and dynamic viscosity iii) Compressibility and bulk modulus iv) Surface tension and capillarity (12 Marks) b The dynamic viscosity of an oil used for lubrication between a shaft and sleeve is 6 poise. The diameter of the shaft is 0.4 m and rotates at 190 rpm. Calculate the power lost in the bearing for a sleeve length of 90 mm. The thickness of the oil film is 1.5 mm. io, Marks) a. State and prove hydrostatic law. (06 Marks) b. write u rrot. on differential manometers. c The right limb of a simple u-tube manometer containing mercury l, atmosphere while the left limb is connected to a pipe in which "ptXTlTl a fluid of: SG 0.9 is fiowing The center of the pipe is !2 cmbelow the lever of merc,ry in the dght rimb. Find the pressue of fluid in the pipe if the difference of mercury level in two limbs is 20 cms. (08 Marks) a Derive an expression for total force on a cured surface submerged in a static fluid. b A tank contains water upto a height of 0.5 m above the base. An imm.isstr:l1frilTf sG 0.8 is filled on the top of water upto lm height. calcuiate , Total pressure on one side of the tank ii) The position of center of pressure for one side of the tank, which is 2 m wide. c. How will you determine the meta-centric height of a floating body ."o.lttlffi;i,? with a neat sketch? - (05 Marks) a. Differentiate between i) Stream firnction and velocity potential ii) Stream line and streak line iii) Rotational and irrotational flow. (06 Marks) b. Obtain an expression for continuity equation for a 3 dimensional flow in Cartesian coordinates. (06 Marks) c. The velocity components in a two dimensional flow field for an incompressible fluid are as follows 3 u=f +2x-x2y and v=xy2 -zv -*3/ 3, ,/-1 Obtain an expression for the stream function r.pr. (08 Marks) Contd.... 2