USN

Time:3 hrs.

la.

b.

c.

2a.b.

c.

3a.

b.

O6ME46B

(04 Marks)

- D tlow in the torm

flow and incompressible

(10 Marks)out the velocity and its

(06 Marks)

Fourth Semester B.E. Degree Examination, December 20llFluid Mechanics

d.

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Max. Ivlarks:100Note: Answer any FIW full questions, selecting

at least Tlllo qaestions from each part.

PABT -ADefine the following properties of a fluid and mention the phenomena associated with eachproperty i) Capillarity and ii) Surface tension. (04 Marks)Define compressibility. Derive an expression for the bulk modulus of elasticity for a perfectgas, undergoing the isothermal process. (06 Marks)Calculate the capillary effect in mm in a glass tube of 3mm diameter, when, immersed inmercury. The value of the surface tension for mercury at 20oC in contact with air is0.51 N/m. Contact angle for mercury : 130o. Also sketch the mercury surface inside andoutside the tube indicating the angle of contact clearly. (06 Marks)If the equation of velocity profile over a flat plate is V : 2f/3 where 'v' is the velocity inm/s and'y' is the distance in m, determine shear stress at y: 75 mm. Take p: 8.35 poise.

(04 Marks)

Define : i) Buoyancy and centre of buoyancy ; ii) Metacentre and metacentric height.(04 Marks)

Show that the centre of pressure lies below the centre of gravity of the vertical surfae*submerged in a liquid. (08 Marrrs)As shown in the Fig.Q.2(c), pipe M contains carbon tetrachloride of specific gravity 1.594under a presstre of 1.05 bar and pipe N contains oil of specific gravity 0.8. If the pressure inthe pipe N is 1.75 bar and the manometric fluid is mercury, find the difference x between thelevels of mercury. (08 Marks)

Fig.Q.2(c)

Differentiate between :

i) Lagrangian approach and Eulerian approach.ii) Steady flow and uniform flow.Derive with usual notations, the continuity equation tbr 3

+. ryq * 49") +

a(l*) = 0. Modiry the equation for steady0t&qAz

flow.Sketch the streamlines represented by V : x2 + y'. Also finddirection at the point (1,2).

I of2

4a.b.

c.

5a.

b.

6a.

b.

c.

8a.b.

a=VD'f[ H'l'D)

WhereV:velocityofflow,D:Depthatthethroat,H:Fleadofwater,g=Accelerationdue to gravlty. (10 Marks)

PART _ E

State Bernoulli's theorem for the steady flow of an incompressible fluid. Derive an

expression for Bemoulli's equation from the first principles. (10 Marks)

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 between30cm 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 Bernoulli's equation and the equation of continuity, find the rate of flow.Neglect the losses between tappings. (10 Marks)

Expiain how veiocity of flow at any point in a pipe or a channel can be measured, with apitot tube. (06 Marks)

At a sudden enlargement of a water line from 240 mm to 480 mm diameter pipe, thehydraulic gradient rises by 10 mm. Estimate the rate of flow. (08 Marks)

An orifice meter with orifice diameter 10cm is inserted in a pipe of 20 cm diameter. Thepressure gauges fitted upstream and downstream of the orifice meter give readings of19.62 N/cm2 and 9.81 N/cm2 respectively. Co for the meter is 0.6. Find the discharge ofwater 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 thedifference 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 viscousflow. Derive the expressions governing shear stress and velocity profile. (14 Marks)

O6ME468Explain the dimensional homogeneity, with an example. (04 Marks)

Define the following dimensionless numbers and mention their significance in fluid flowproblems:i) Reynold's no. ; ii) Froude's no. ; iii) Mach no. (06 Marks)

Prove that the discharge over a spillway is given by the relation using Buckingham'sII - theorem.

Derive an expression for the velocity of sound in terms of bulk modulus (k). (06 Marks)

Define the following :

i) Boundary layer thicknessii) Displacement thicknessiii) Momentumthickness.A flat plate 1.5m x 1.5m moves at 50 km/hr in stationary air of densityefficients of drag and lift are 0.15 and 0.75 respectively, determine :

i) The lift forceii) The drag forceiii) The resultant forceiv) The power required to keep the plate in motion.

***!S*

2 of2

@v

(06 Marks)

1.15 kg/m3.If the co-c.

(08 Marks)

USN O6ME46B

Time: 3 hrs.Note: Answer any FIW full qaestions, selecting

at least TWO questionsfrom each part.

PART _ A

I a. Define the foliowing terms and mention their SI units:i) Specific weight ii) Dynamic viscosity iii) Kinematic viscosityiv) Surface tension v) Capillarity.

Fourth semester B.E. Degree Examination, June/July z0llFluid Mechanics

Max. Marks:100

(10 Marks)

(05 Marks)

(05 Marks)

ooii

o()

Y? q.r

o,;&scra.o .,'oo rl

c,a

:oots()()E:

a:ou

ooccd a3

>.86-'O cd

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orvo,i

o:3i;atE

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tr50

=(d:i9

5L->.U<dN

o

z

Lo

b. A differential U-tube manometer is used to rneasure the pressure difference between twopoints in a horizontal water pipe line. If the manometer shows a difference in mercury levelsas 25 cm, find the pressure difference between the points in bar. (10 Marks)

2 a. State and prove Pascal's law. (08 Marks)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 that'l' cannot exceed A.7715 d for the cylinder tofloat with its longitudinal axis vertical. (0E Marks)

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 Cartesianco-ordinates. i10 Marks)

b" The stream function fcrr a 2-D floN,is given by V : gxy. Calculate the velocity at a pointP(4, 5). Find also the velocity potential firnction. (10 Marks)

4 a. State and explain Buckingham n theorem.

b. Explain kinematic and dynamic similarity.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,.Using Buckingharn's n theorern show that

v: /zgH4i#,*) (10 Marks)

PART _ B

5 a. Derive Euler's equation of motion along a stream line and hence reduce Bernoulli,sequation. (lo Marks)b. A vertical pipe currying oil of specific gravity 0.8 tapers uniformly from 20 cm diameter at

the lower section to 10 cm diameter atJhe upper r.oiiorr. The vertical distance between thesections is 1,m. The pressure gauges installed at the lower and upper sections read 6 Nlcmiand 8 N/cm' respectively, when the discharge is 30 litres/sec. Calculate the loss of headbetween the two sections and determine the direction of flow. (r0 Marks)

I of2

c. Derive Darcy's equation for loss of head between the two sections. Determine the directionof flow. (0S Marks)

7 a. Derive Hagen Poiselli's 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 itskinematic viscosity 20 stokes. Find the power required to pump oil. (08 Marks)

6 a. With the help of a neat sketch, explain how a pilot tubeopen channel.

b. Derive the expression for discharge through a venturimeter.

I a. Explain the following :

i) Liftii) DragiiD Displacement thicknessiv) Mach numberv) Isentropic flow.

b. A flat plate 1.8mxtr.8m moves at 36 km/lr in a stationary air of mass densitythe coefficients of drag and lift are 0.15 and 0.75 respectively" Detenuine

D Drag forceii) Lift forceiiD Resultant forceiv) Power required to keep the plate in motion.

O6ME46B

is used to find the velocity in an(04 Marks)

(08 Marks)

(10 Marks)

1.2 kglm3. lf

(I0 Marks)

{.r}:tr}*

2 of2

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i (,)

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a.atro-5(!

9.d5t)olE

EO=

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0)

zadEo.

Fourth Semester B.E. Degree Examination, December 2010Fluid Mechanics

Time:3 hrs. Max. Marks:100Note: 1. Answer any FIVE full qaestions, selecting

at leost TWO questions from each part.2. Assume suitable data, if required.

PART _ AI 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 :

i) Viscosity changes with temperature rise.ii) Mercury (Hr) is preferred as a manometric liquid.iii) Free surface of water in a capillary tube is concave.iv) Light weight objects can float on the free surface of liquids.v) Metacentric height is positive for stable equilibrium of floating bodies. (10 Marks)

c. Derive the relation for capillary rise of water in a glass tube. (03 Marks)d. A liquid bubble of 2cm radius has an internal pressure of 12.95 Pascals. Determine the

surface tension of the liquid film. (04 Marks)

2 a. Derive the relations for hydrostatic forces on a curved surface, which is immersed in a liquidof specific weight'W'. (06 Marks)

b. With a neat sketch, explain the working of an inverted u - tube manometer. (06 Marks)c. A wooden block of size 6m x 4m x 2m floats on fresh water. Depth of immersion of the

wooden block is 1.2 m. A concrete block is placed centrally on the surface of the woodenblock, so that,i) The top surfbce of the wooden block touches the ftee surface of,waterii) 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 eachcase. (08 Marks)

3 a. Derive the continuity equation for a three dimensional flow, in Cartesian co-ordinates.(08 Marks)

b. Show that the streamlines and equipotential lines are orthogonal to each other. (04 Marks)c. A stream function represents 2-D fluid flow, y : 2xy.Find the velocity at a point P(3, 4).

USN

4a.b.

c.

O6ME46B

(08 Marks)

(02 Marks)

Check whether the flow is rotational. Find the velocity potential function $.

Mention the applications of model similitude.Explain the significance of non - dimension numbers.

D Mach number ; ii) Froude's number ; iii) Weber number ; iv) Reynolds' number.

using Buckingham ,, - Y**7*o*

that the velocity of fluid flow throu*, f'"X[Borifice is given by v =,l2gi (*,#r) , *r,.r"

H: Head of fluid flow ;

p = Dynamic viscosity of the fluid ;g = gravitational acceleration.

D: Diameter of the orificep: Density of the fluid.

I of2

(10 Marks)

O6ME46B

PART - Ba. Derive the Bernoulli's equation for a steady, incompressible fluid flow. List the

assumptions' Mention the significance of each term in Bernoulli's equation. (10 Marks)b. Pipeline AB carries oil of specific gravity 0.90. Diameter of the pipe at A is 250 mm andthat at B is 500 m{, lnd B.of t}re pipe is 6 meters above the end a. rfr" pressue intensitiesat 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 watermanometer shows a deflection of 12 mm of water. If the coefficient of pitot tube is 0.9g, findvelocity of air flow and mass flow rate of air. Assume specific *eight of air as f O N/mLDiameter of the duct is 500 mm. (06 Marks).c. Oil of specific gravity 0.90 flows through an inclined venturimeter. lnlet and throatdiameters 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. AssumeC6 = 0.98 for the venturimeter.

(10 Marks)

a. Derive a relation for the discharge through a circular pipe of diameter D, for the viscousflow. (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 andsecond sections are 25 mm and 50.mm_respectively. If the friction coefficient of pipematerial is 0.005, determine the velocity of waier flowtkough the two sections and the rateof water flow in litres/sec. Represent TEL and HGL. (r2 Marks)

a. Define drag force and 1ift force.b. Define and explain :

i) Boundary layer thicknessii) Mach cone, Mach angleiii) Subsonic flow.

c. A projectile travels in air of pressure 1.011500 km/hour. Determine the Mach numberR:287 J/kg k.

x 10s N/m2 at l0oC.and the Mach angle.

(04 Marks)

(08 Marks)Speed of projectile isAssumek:1.4and

(08 Marks)

**:t*'1.

2 of2

USN O6UIE468

Fourth semester B.E. Degree Examination, MaylJune 2010Fluid Mechanics

Time:3 hrs. Max. Marks:100Note: Answer any FIVEfull questions, selecting

at least TWO questions from each part.

1 a. Define the following terms *,rn,n"[f;,rtf, ^i) CapillarityiD Surface tensioniii) Mass densityiv) Pressure intensityv) Kinematic viscosity. (10 Marks)

b. Derive the relation for pressue intensity and the surface tensile force, in case of soapbubble. (04 Marks)c. A steel shaft of 30 mm diameter rotates at 24A rpm, in a bearing of diameter 32 mm.Lubricant oil of viscosity 5 poise is used for lubricanl of shaft in the bearing. Determine thetorque required at the shaft and power lost in maintaining the lubrication. Lingth of bearingis 90 mm" (06 Marks)

2 a. State and prove Pascal's law.b. Show that, for a submerged plane surface, the centre of pressure, lies below 6rt[m?t

gravity of ttre submerged surface. (08 Marks)c. A differential rnercury manometer is used for measuring the pressgre difference betweentwo pipes A and B. Pipe A is 500 mm almve the pipe B and deflection in Hg manometer is200 mm- Pressure intensity in pipe A is greater than pipe B. pipes carry oil of specificgravity 0.90. Find the pressure difference between the two pipes. Sp.gr. olmercury = t:.0.

(08 Marks)

Explain the importance of metacentre with stability of floating bodies. (04 Marks)A wooden block (barge) 6 mts in length, 4 mts in width and 3 mts deep, floats in fresh waterwitn

-aef$ of immersion 1.5 rnts. A concrete block is placed centrally on the surface of thewooden block, so that the depth of immersion with concrete is 2.8 mts. Find the volume ofthe concrete block placed centrally, if the specific gravity of concrete is2.75. Find also thevolume of water displaced. (08 Marks)Differentiate between :

i) steady flow and uniform flow ii) Laminar and turbulent flowii) Sheamline and streakline iv) Rotational and irrotational flow. (08 Marks)

Show that streamlines and equipotential lines are orthogonal to each other. (04 Marts)Torque developed by a disc of diameter D, rotating at a speed N is dependant on fluid

viscosity op' and fluid density 'p'. obtain an expression for torque, 1= pN2D5 -[#r]

aioD

E

()€6d)

3eQ:s

Eabo rl

coo.= a.l(!.sfxaogootr_c()eEHLv53sBgbU=!o.(,40trdcd!Ba66r!o(d

-a" B

6 -lJ

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o=BUia tEa.,

E()

3P>' 9:bDecboo=E8=oULcho<r c.t

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oF

3a.b.

c.

4a.b.

c. Foratwo dirnensional fluidflow, velocitypotential is g = y+ * ->?.Fi"dJljHHfunction and velocity at apoint P (2,3). Check irrotationality oino*. (0E Marks)

I of2

O6ME468

PART - Brl

a. Derive Bernoulli's equation and state the assumptions made. Mention the statement of(10 Marks)Bernoulli's equation.

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. Elevationdifference 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

6a.b.

also loss of head between the two sections.

Sketch and derive the relation for actual discharge through an orifice meter.

,*****

(10 Marks)

(08 Marks)

(08 Marks)(04 Marks)

(06 Marks)

(10 Marks)

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, finddeflection in mercury manometer connected across the pitot - tube. Detemine the mass rate

7a.b.

Derive the relation for the pressure drop in a viscous flow through a circular pipe. 1to Marks)Sketch the total energy line and the hydraulic gradient line for a pipeline connecting tworeservors. (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.

of water flow.c. List the types of losses, with a neat sketch and equations for head losses.

Coefficient of friction for pipe material is 0.01.

a. Explain following terms :

i) Liftii) DragiiD Boundary layer separationiv) Momentum thicknessv) Displacementthickness.

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

USN

3a.

O6ME46B

Max. Marks:100

(06 Marks)

(05 Marks)

(04 Marks)

(08 Marks)

(06 Marks)(08 Marks)

Fourth Semester B.E. Degree Examination, Ilec.09-Jan.10Fluid Mechanics

b.

oooE_gGEt,(E

oo.((tU'O(, .!=

g_HvZE3(5-toor?.L ooC+'=N:vso(,,Ld)(l)-5E!i:u>a-aQ.=onfr9AEhc<oEPKobt(Egrroo3rAb.et^_E(s=d)Fo-Eo_8(E---U';u-Yg6ae(UeL(ufroo'->EPorEGao)E>:occo<-ni"!,oz$oOL

E

Time: 3 hrs-

Note: Answer any FIVE full questions, selectingat least TWO questionsfrom each part.

PART _ A

I a. Distinguish between :

i) Mass density and specific weightii) Newtonian and non-Newtonian fluidiii) Absolute and l(inematic viscosity.

Calculate the pressure of water in the pipe.

2 a. Define the terms :

i) Total pressure ii) Centre of pressure

b. An oil film of thickness 2mm is used for lubrication between a square plate of size

0.9m x 0.9m on an inclined plane having an angle of inclination 30o. The weight of the

square plate is 350N and it slides down the plane with a uniform velocity of 0.3mlsec. Find(06 Marks)

c. f;Jr'irH"y;ffir:X,f #::- absorute, sause and atmospheric pressures with a simplesketch. (03 Marks)

d. A U-tube manometer containing mercury is connected to a pipe in which water is flowing.Water lend in the limb connected to pipe is 0.5m below centre of the pipe and the. free

surface mercury in the other limb (open to atmosphere) is 0.8m below the ceritre of the pipe,

An annular plate 3m external diameter and i.5m intemal diameter is immersed in water withits greatest and least depths below water surface at 3.6m and l.Zm respectively. Determinethe total pressure and the position of centre of pressure on one face of the plate. (08 Marks)

A solid cylinder 15cm diameter and 60cm long consists of two parts made of differentmaterials. The first part at the base is l.2cm long and of speeific gravity 5. The other part ofthe cylinder is rnade of the material having specific gravity 0.6. State if it can float vertically

b.

c-

in water.

Distinguish between :

i) Steady and un-steady flowi0 Uniform and non-uniform flowiii) Laminarand turbulent flow"Derive an expression for continuity equation for a three dimensional flow.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 at

the point {2,3). (06 Marks)

4 a. State Buckingham's ru theorem. Why this theorem is considered superior over the Rayleigh'smethod for dimensional analysis?

I nf?

(05 Marks)

54.b.

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

the viscosity of the fluid p. Show using the Buckingham's theorm that, the discharge can be

represented bY

Q=ND3f[(#}[#)] (loMarks)

c. what is meant by geometric, kinematic and dynamic similarities? (05 Marks)

head and direction of flow. (06 Marks)

PART _ B

Define Euler's equation of motion. Deduce Bemoulli's equation from the same. (08 Marks)

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

are 20N/cm2 and 15N/.*) ,.rp."tively and discharge is 150 litreslsec, determine the loss of

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

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'

Take f = 0.02 and neglect minor losses.

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. (04 Marks)

b. Derive Hagen-Poiseuille equation with usual notations. (08 Marks)

c. An oil of viscosity O.lNslm2 and relative density 0.9 is flowing through a circularpipe ofdiameter 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 lVlarks

8 a. Define the terms :

i) Boundary layer ii) Boundary layer thickness iii) Drag

iv) Life v) Momentum thickness.

Define the terms : sub sonic flow, sonic flow and supersonic flow'

Ca = 0.98. (06 Marks)

(08 Marks)(04 Marks)

(10 Marks)(06 Marks)

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

b.

c.

USNO6ME46B

Max. Marks:100

(08 Marks)

(06 Marks)

Fourth Semester B.E. Degree Examination, Dec.09-Jan.10Fluid Mechanics

b.

c.

d.

c.

oo()Eo6EooE(,

.ou, 0)o .:=

Peo-s.v.ZE3(g60srf,= co

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BEp+oo-ohc<oEH'K1,b56Sf,E(oaB'3eo_=(5=d,Fo-CO8N

-e-9Eo=;EaLcLO5'Eo'->EPor:(Eao)F>59cco<-Fi3'oz(UEonE

Time:3 hrs.

la.

2a.

b.

Note: Answer any FIVE full questions, selectingat least TWO questionsfrom each part.

PART - A

Distinguish between :

D Mass density and sPecific weightii) Newtonian and non-Newtonian fluidiii) Absolute and Kinematic viscosity. (06 Marks)

An oil fi}m of thickness 2mm is used for lubrication between a square plate of size

0.9m x 0.9m on an inclined plane having an angle of inclination 30o. The weight of the

square plate is 350N and it slides down the plane with a uniform velocity of 0.3mlsec. Find

the viscosity of the oil in poise. (06 Marks)

Establish a relationship among absolute, gauge and atmospheric pressures with a simple

sketch' (03 Marks)

A U-tube manometer containing mercury is connected to a pipe in which water is flowing.

Water lend in the limb connected to pipe is 0.5m below centre of the pipe and the. free

surface mercury in the other lirnb (open to atmosphere) is 0.8m below the centre of the pipe,

Calculate the pressure of water in the pipe. (05 Marks)

Define the terms :

i) Total pressure ii) Centre of pressure (04 Marks)

An annuiar plate 3m extemal diameter and 1.5m intemal diameter is immersed in water with

its gteatest and least depths below water surface at 3.6m and 1.2m respectively. Determine

theiotal pressure and 1}1g position of centre of pressure on one face of the plate. (08tlarks)

A solid tylinder 15cm diameter and 60cm long consists of two parts made of diflerent

materials. The first part at the base is 1.2cm long and of specific gravity 5. The other part ofthe cylinder is made of the material having specific gravity 0.6. State if it can float vertically

in water.

a. Distinguish betw'een :

i) Steady and un-steady flowi0 Uniform and non-uniform flowiii) Laminar and turbulent flow.

b. Derive an expression for continuity equation for a three dimensional flow. (08 Marks)

c. If for a two dimensional potential flow, the velocity potential is given by 0 = 4x(3y - 4) ,

determine the velocity at the point (2,3). Determine also the value of stream function y at

the point (2, 3). (06 Marks)

a. State Buckingham's r theorem. Why this theorem is considered superior over the Rayleigh's

method for dimensional analysis? (05 Marks)

I nf )

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 Buckingham's theorm that, the discharge can be

represented bY

Q=ND3f[[#),[ffi_)]c. What is meant by geometric, kinematic and dynamic similarities?

(10 Marks)

(05 Marks)

(08 Marks)(04 Marks)

PART * B

S a. Define Euler's equation of motion. Deduce Bernoulli's 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 ofhead and direction of flow. (06 Marks)

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

Co = 0'98. (06 Marks)

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.

Take f = 0.02 and neglect minor losses.

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)

Derive Hagen-Poiseuille equation with usual notations. (08 Marks)_

An oil of viscosity 0.1Ns/m2 and relative density 0.9 is flowing through a circularpipe ofdiameter 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

**{.**

2 ofZ

b.c.

the plane. (04 Marks)

USN

Time:3 hrs.

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.

b. Define following terms with their units.

O6ME468

(05 Marks)

(05 Marks)

(10 Marks)

(05 Marks)(05 Marks)

Fourth Semester B.E. Degree Examination, June-July 2009Fluid Mechanics

Max. Marks:100Note: Answer any F(YE full questions choosing at least two

questions frr* each uniL

PART _ A

c. The space between two square flat parallel plates is filled with oil. Eaeh side of the plates is800 mm. Thickness of the oil film is 20 mm. The upper plate moves at a uniform velocity of3.2rn/sec when a force of 50 N applied to upper plate. Determine :

i) Shear stressii) Dynamic viscisity of oil in poiseiii) Power absorbed in moving the plateiv) Kinematic viscosity of oil if specific gravify of oil is 0.90.

i) Specific weight ;

iv) Specific gravity ; v) Capillarity

Show that streamlines and equipotential lines are orthogonal to each other.Explain Model Similitude and Non-dimensional numbers.

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 thevolume of concrete block placed on the wooden block, so as to completely submerge thewooden 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 streamfunction. (08 Marks)

4a.b.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 Buckingham's theorem, show that the relation for pressure difference Ap is given

by Ap=pv2r(*,*)

I of2

(10 Marks)

06M[468

PART _ B

a. State and prove Bernoulli's equation for a fluid flow. Mention assumptions made inderivation. (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.b.c.

7a.b.

Explain with neat sketch, working of pitot-static tube.Differentiate between Orificemeter and venturimeter with neat sketches.

horizontal pipeline. Take F0.01 for material of pipeline.

a. Explain terms :

i) Liftii) Dragiii) Displacement thicknessiv) Momentum thickness

A horizontal venturimeter with 50cm diameter at inlet and 20cm throat diameter is used formeasuring rate of water flow, if the pressure at inlet is 1.8 Bar and vaccum pressure at thethroat is 30cm of mercury, find the rate of flow. Assume 10% differential pressure head islost between the inlet and throat section. Assume coefEcient of discharge is 0.96. (10 Marks)

Derive Hagen-poiseulle's equation for viscous flow through a circular pipe. (10 Marks)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 forremaining length. Find the elevation difference between the two reservoirs connected by the

(05 Marks)(05 Marks)

(10 Marks)

(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

USN 2AO2 SCHEME ME45

and direction ofresultant hydrostatic force on a curved(10 Marks)

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 cohesionii) Cohesion is more then adhesionShow 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)

fi'=

Uig.Q.2(b).

2 a. Explain clearly how the magnitudesurface is determined.

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)

3 a. Define metacentric height of a floating body. Obtain an expression for metacentric height ofa 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 ofmanometer 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

4a.

b.

5a.

ME45

State the continuity principle. Derive three dimensional continuity equations in differentialform for a general fluid flow situation. Simpli$z it to two dimensional steady,incompressible flow and one dimensional unsteady flow cases. (10 Marks)For a two dimensional flow, the stream function is given by V: Zxy. Calculate the velocityeomponents at a point (3, 6). Show that velocity potential exists for this case. Determine thevelocity potential firnction. (10 Marks)

State Buckingham rc theorem. The input power of a centrifugal pump is found to depend ondiameter of impeller D, discharge Q, density of liquid p, rotational speed N, and specificener$Y of liquid gH. Using Buckingham ru theorem, obtain the relevant ,r terms governingthe pumping operation. (10 Marks)Water flows upwards through ataperedpipe as shown in Fig.Q.5(b). Find the magnitude anddirection of deflection h of the differential mercury manombter corresponding to a dischargeofaJ2m3/s. Thefrictioninthepipecanbecompletelyneglected, - :

(t0Marks)

b.

6a.b.

Derive an expression for discharge *""#??'rtt

of oil flowing through the pipe and .

Define Lift and Drag. Distinguish between skin friction drag and form drag.

(10 Marks)

(10 Marks)(05 Marks)

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 dischargethrough the tube when the height of oil level of the tank is 0.8 m above the pipe inlet. Theflow 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 flowthroilgh a horizontal round pipe and hence show that discharge Q througir this pipe is given

by O = -91 tp where dp is the pressure gradient D is the diarneter and p is the viscosity128pr dx dx )

b.

A television transmitter antenna consists of a vertical pipe 0.2 m diameter and 30 m high ontop 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 asCI"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 -+ 6.Calculate the displacementu -(o/ [a./ -.- J

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, writeIoP

down the continuity equation and equation of motion and show that d4 =

du fi4, _1):

A U'* * * * *

(loMarks)

USN.

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 cohesionii) Cohesion is more then adhesionShow 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

]t'tilig.Q.2(b).

2OO2 SCHEME ME45

(10 Marks)

hydrostatic force on a curved(10 Marks)

resistance when the shaft is rotated at a speed of 240 tpm.

2 a. Explain clearly how the magnitude and direction of resultantsurface is determined.

3a.

Fis.Q.3(b).I of2

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)

Define metacentric height of a floating body. Obtain an expression for metacentric height ofa 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)

If the pipe shown in Fig.Q.3ft) contains water and there is no flow, calculate the value ofmanometer reading h. If manometer reading h = 50 mm when water is flowing through thepipe, calculate the pressure difference Pe. - Ps in kPa. (10 Marks)

b"

4a.

b.

ME45

State the continuity principle. Derive tfuee dimensional continuity equations in differentialform for a general fluid flow situation. Simpliff it to two dimensional steady,incompressible flow and one dimensional unsteady flow cases. (10 Marks)For a two dirnensional flow, the stream function is giverr by V: Zxy. Calculate the velocitycomponents at a point (3, 6). Show that velocity potential exists for this case. Determine thevelocify potential function. (10 Marks)

5 a. State Buckingham rc theorem. The input power of a cerrtrifugal pump is found to depend ondiameter of impeller D, discharge Q, density of liquid p, rotational speed N, and specificenergy of liquid gH. Using Buckingham rc theorem, obtain the relevant n terms governingthe pumping operation. (10 Marks)Water flows upwards through a tapered pipe as shown in Fig.Q.5(b). Find the magnitude anddirection of deflection h of the differential mercury manometer corresponding to a dischargeof A J2m3 /s. The friction in the pipe can be completely neglected,

- - (10 Marks)

b.

5a.b.

Derive an expression for discharge *"rf;??ltl; (10 Marks)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 dischargethrough the tube when the height of oil level of the tank is 0.8 m above the pipe inlet. Theflow 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 flowthrough 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 viscosity128p 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 as0.2. (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 the displacementu -(0,/ [aJ -- J

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, writeloP

down the continuity equation and equation of motion and show that d4 =

u, (Jr, -r)'A U'* * * * *

(lo*rarks)

USNO6ME468

09Fourth Semester B.E. Degree Examination, Dec 08 / JanFluid Mechanics

Time:3 hrs. Max. Marks:100

Note z Answer FIVE fult questions, selecting atleast TWOquestions from each part.

PART - Aa. 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 auniform 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 ofthe 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 itsvolume is submerged in mercury and remaining in water. Estimate the density of the metal.

(04 Marks)

b.

Prove that the equipotential lines and the stream lines are always intersect orthogonally.

Given the velocity field, V : 5x3 i - 15x2 yj, obtain the equation of the str."*rrrrJllffilTlabove given veiocity field, check for the continuity and irrotationality. (08 Marks)

^t

The velocity potential function is given by the expression, 0 = -+ - *' * *i'

+ y233i) Find the velocity components in x and y directions.

(06 Marks)ii) Show that { represents a possible case of flow.

What do you mean by : i) Geometric simiiarity ii) Kinematic similarity iii) Dynamicsimilarity iv) Dimensional homogeneity. (04 Marks)

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)

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.

L ot.- (06 Marks)

c.

b.

c.

1a.b.

O6ME46B

PART. BDerive Euler's equation of motion along a stream line and hence obtain the Bernoulli'sequation for incompressible fluids. (06 Marks)

b. Using the Euler's equation of motion, derive the Bemoulli's 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 (Vt -Y)2 l2r, where V1 and Vz are the velocities of fluid (S : 0.8) flow at the upper

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 fromthe 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 dailysupply 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 asection ll,l#:flpressure 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)

Derive Hagen Poiseuille equation for a laminar flow in a circular tube. (10 Marks)

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)

We know that the velocity of sound wave is the square root of the ratio of change ofpressure to the change of density of a fluid. Using this definition, derive the expressions fora velocity of sound in a compressible fluid when it undergoes a process i) Isothermal and

a.

ii) Reversible adiabatic.b. Define the following and write their equations :

i) Dragii) Liftiii) Displacementthicknessiv) Momentumthickness.

(06 Marks)

(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 velocityof 25mls. Find the weight of the man if the weight of parachute is 9.81N. Take Co:0.6

*r<rr**

and density of air : l.25kglm3

) n€1

(08 Marks)

,USN. ME45

(10 Marks)

a static fluid either(08 Marks)

its greatest and least

(08 Marks)(04 Marks)

Fourth Semester B.E. Degree Examination, June / July 08Fluid Mechanics

Time: 3 hrs. Max. Marks:100Note z Answer any FIVE full questions.

1 a, State Newton's 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. Takeo' : 0.075 N/m and o = 60" fcir water. What will be the percentage increase in the value ofheight, 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 is60 cms. The thickness of the oil film is 12.5 mm. The upper plate, which moves at2.5 mlsrequires 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.

2 a. Show that the centre of pressure, for a plane surface immersed invertically or inclined, lies always below the centre of gravity.

b. A circular plxe 4.5 m in diameter is submerged in water such thatdepths below the water surface are 3 m and 1.5 m respectively" Findi) Total pressure on the top face of the plate.ii) The position of centre of pressure.

c. State hydrostatic law- and derive an expression for the same.

3 a. Define meta centre of a floating body. Describe the analytical method of determining themetacentric height. (10 Marks)

b. State the condition for stable equilibrir:,m of a floating body and expiain how this is takencare 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 is6a 6v 5w

glven oY, 6,

* Sy

* 5, = U. (08 Nlarks)

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 pointP(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 thepipe D, length of pipe L, the velocity V, viscosity p and density p. Using Buckingham'stheorem 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 to0.5 m2 area. Find the magnitude and direction of the force required to hold the duct inposition 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

b.

M8,45

Derive an expression for the discharge through an inclined Venturimeter for an upwardflow. (08 Marks)A reservoir has been built 4 km away from a town having a population of 5000. Water is tobe supplied from the reservoir to the town. The per capita consumption of water per day is200 litres and half of this daily supply is to be pumped within 10 hrs. The loss of head dueto 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.

c. Write a note on Energy gradient line and hydraulic gradient.(08 Marks)(04 Marks)

(10 Marks)

(06 Marks)

1500 km/hr.(04 Marks)

b.

c.

a. Derive an expression for the ioss of head due to friction for laminar flow through a roundpipe. 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 processii) Adiabatic processJustifu 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 ofdrag and lift are 0.i8 and 0.9 respectively. Determine

D Drag forceii) Lift forceiii) Resultant force andiv) Power exerted by air stream on the plate.

Take density of air : 1.15 kg/m3.Define the following:0 Boundary layer thickness.ii) Displacementthickness.iii) Momentumthickness.A projectile travels in air of pressure 10.1043 N/cm2 at i0"C, at a speed ofFind the Mach number and Mach angle. Take y: 1.4 and R:287 J/kg'K.

,<****

2 of}

USNME45

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 S'I. 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 20'C 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 fi'ee surface. Find the(05 Marks)force and center ofpressure

i cm and 60 cm ofc. Measurements of pressule at the base and top of a mountain ate 74

mercury respectively. Calculate the height of the mountain if air has a specific weight of1

(05 Marks)l.ZTkglm".

3 a. Define the following:i) Buoyancy.ii) Absolute pressure.

iii) Metacentre.iv) Gauge pressure.

v) Centre of pressure (10 Marks)

b" A'block 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 ofthe 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

5 a. Using Buckingham'sl^ ,T"rem, show that the velocity through a'circular 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

ME45'

due to gravrty. (10 Marks)

Derive the Euler's equation of motion for steady flow and obtain Bernoulli's equation fromit. State the assumptions made in the derivation of Bemoulli's equation. (10 Marks)

Explain a venturimeter. Drive an expression for discharge. Why venturimeter is better than

orifice meter? (10 Marks)

Derive Darcy-Weisbach formula to calculate the frictional head loss in pipe in terms offriction factor. (10 Marirs)

Explain:i) Mach number.ii) Subsonic flow.iii) Supersonic flow.iv) Laminar flow.v) Turbulent flow. (10 Marks)

Water at 15"C flows between to large parallel plates at a distance of 1.6 mm apart.

a.

b.

ta-

b.Determinei) The maximum velocityii) The pressure drop per unit length andiii) 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.

a. Definei) Drag.iil i,ift.iii) Boundary layer thickness.iv) DisplacemeRt tiiickness.v) Momentum thickness.

(05 Marks)

(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[ + l-t + I where u is the velocity at a distance yo u v \6/ \61from the plate and u: U at

"p = 6 , where 6 is the boundary layer thickness. (05 Marks)

2 ofZ

Petge Nri... I ME45

USN

NEW SCHEME

Fourth Semester B.E, Degree Examination, JuIy 2007Mechanical En gineering

Fluid MechanicsTime: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 densityii) Kinematic viscosity and dynamic viscosityiii) Compressibility and bulk modulusiv) 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 thepower lost in the bearing for a sleeve length of 90 mm. The thickness of the oil filmis 1.5 mm. io, Marks)

a. State and prove hydrostatic law.b. write u rrot. on differential manometers.

(06 Marks)

c' The right limb of a simple u-tube manometer containing mercury l, "ptXTlTlatmosphere while the left limb is connected to a pipe in which 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 is20 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:l1frilTfsG 0.8 is filled on the top of water upto lm height. calcuiate

, Total pressure on one side of the tankii) 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 potentialii) Stream line and streak lineiii) Rotational and irrotational flow.

b. Obtain an expression for continuity equationcoordinates.

c. The velocity components in a two dimensionalare as follows

3

u=f +2x-x2y and v=xy23', -zv -*3/' ,/-1

(08 Marks)Contd.... 2

(06 Marks)for a 3 dimensional flow in Cartesian

(06 Marks)flow field for an incompressible fluid

Obtain an expression for the stream function r.pr.

Page No... 2

a. State Buekingham's n theorem. (02 Marks)b. Find the expression for the power developed by a pump (P) when it depends upon the

head (FI), d.ischarge (Q) and specific weight (w) of the fluid. (08 Marks)i. Derive an expression for discharge through an orifice. (07 Marks)

d. Why coefficient of discharge (C6) of venturimeter is higher than that of anorificemeter? (03 Marks)

a. State Bernaulli's theorem for steely flow of an incompressible fluid and derive an

expression for the same. State the assumptions for such a derivation. (10 Marks)b. Find the diarneter of a pipe of length 2000 m when the rate of flow of water through

pipe is 200lts/sec and the head lost due to friction is 4 m. Take the value of C = 50 in

ME45

Chery's farmulae.

a. What is Hagen Poiseuille's formula? Derive an expression for the same.b. Obtain an expression for velocity of the sound wave in a compressible

ofchange in pressure and change ofdensity.c. Define Mach number, Mach angle and Mach cone.

a. Differentiate betweeni) Strearuline body and bluff bodyii) Friction drag and pressure drag.

C6 : 0.5 and p for air 0.00125 gmlcc and y: 0.015 stoke.c. Define displacement thickness and momentum thickness.

&JJJJ

b. A man weighing 981 N descends to the ground from an aeroplane with the help of aparachute against the resistance of air. The shape of the parachute is hemispherical of2 m diameter. Find the velocity of the parachute with which it comes down. Assume

(10 Marks)

(06 Marks)fluid interms

(08 Marks)(06 Marks)

(08 Marks)

(08 Marks)(04 Marks)

Page No... I ME45

i]SN

NEW SCITEME

Fourth Semester B.E. Degree Examination, Dec. O6 I Jan. O7ME/IP/IM/MA/AU

Fluid MechanicsTime:3 hrs.l [Max. Marks:100

Note : I. Answer any FIVE fwll questions.2. Draw neat sketches wherever necessary.

1, a. Define compressibility and derive an expression for bulk modulus of elasticity for aperfect gas undergoing isentropic process. (06 Marks)

b. Define surface tension and show that the gauge pressure within a liquid droplet variesinversely with the diameter of the droplet. (06 Marks)

c. A shaft of 0.1 m diameter rotates at 60 rpm in a A.2 m long bearing. Taking that thetwo surfaces are uniformly separated by a distance of 0.5 mm and taking linearvelocity distribution in a lubricating oil having dynamic viscosity of 4 CP, find the

2a.b.

power absorbed in the bearing.

Sketch and explain hydrostatic paradox.Define metacentre and derive an expression for a floating body forheight.

(08 Marks)

(04 Marks)its metacentric

(08 Marks)

3a.b.

c. A cargo ship weighing 4000 tonnes has a draft of 7 m in seawater (Sp.gr. 1.035).After discharglng cargo of 510 tonnes its draft reduces by 0.5 m. What will be itsdraft in a fresh water harbour after further discharging a cargo of 300 tonnes?Assume no change in cross sectional area for depth under consideration. (0g Marks)

Explain potential function and flownet. (06 Marks)The velocity in a flow field is given by u: 3 m/s, v = 6 m/s. Determine the equationof the stream line passing through the origin and the one passing through a point(2 m, 3 m), (06 Marks)

c. A velocity potential in2-D flow is (D : y + x2 - f. finA the stream function for thisflow. (08 Marks)

4 a. The losses *r", unit length of pipe in a turbulent flow through a smooth pipet'depend upon velocity V, diameter D, gravity g, dynamic viscosity p and density p.With dimensional analysis determine general form of the equation for the losses.

(06 Marks)b. Derive the Euler's equation of motion for real fluids and hence deduce Bernoulli's

equation of motion. Mention the assumptions made. (08 Marks)c' A pipe gradually tapers from a diameter of 0.3 m to 0.1 m over the length as shown

in Fig. a(Q. It conveys kerosene (Sp.gr. 0.80) at 50 l/s. The pressure at bottom end is200 kN/m'. If the pressure at upper end is not to fall below 100 kN/m2, find the valueof Z. (Neglect losses).

Fig. a(c)

(06 Marks)

Page No""" 2 ME45

a' In a 100 mm diameter horizontal pipe a venturimeter of 0.5 contraction ratio has beenfitted. The head of water on the meter when there is no flow is 3 m of water. Find therate of flow for which the throat pressure will be 2 m of water. The co-efficient of themeter is 0.97. _ (08 Marla)b' Derive an expression for a flow through a triangular notch in terms of head overnotch.

(06 Marks)c' A pitot static probe is used to measure the flow of water in a 5 cm diameter pipe. Ifthe mean velocity is 5 m/s, and the pitot static tube is connected across a mercgryfilled differential manometer, what should be the level difference in the mercurycolumn?

(06 Marks)

a' Derive Darcy-Weisbach equation and deduce itto Chezy's equation. (08 Marks)b' Show that the energy transmitted by a long pipe is maximum when one third of theenergy put into the pipe is lost in fiiclion.-One hundred kW is to be transmittedthrough a pipe, the pressure at the inlet of the pipe being 70 bar.If the pressure dropper kilometer is to be 0'44 bar and if f : 0.02; nnd the?iameter ortrr"'fip. and theefficiency of transmission for 16 lan. (12 Marks)

a' Derive an expressiol for velocity and average velocity for viscous flow between twostationery parallel plates.b. Explain b Arembert paradox. (06 Marks)

(04 Marks)c' A teievision transmitter antenna consists of a vertical pipe 20 cm diarneter and 30 mhigh on top of tall structure. Determine the total drag on the antenna and the bendinsmoment about the base in a 30 m/s wind at NTP. fake density of air

^t t.zi-iehr|

and viscosity as I .79x10's NS/m2, Cp : 0.2. (10 Marks)

a. Explaini) Boundary layer thicknessii) Displacementthicknessiii) Momentum thickness.The velocity profile in a laminar boundary layer is approximated by a parabolic

profire #=r(#)-(#)' where a is the vetocity at yand u-+(rasy-+d.

. calculate displacement thickness and momentum thickness. (r0 Marks)b' Dttermine the velocity of a bullet fired in the air if the mach angle is observed to beJU". Given that the temperature of air is 220c, density 1.2 kg/nl. Take y = 1.4 andR:287 J,&gK. Derive the equation used. (r0 Marks)

!krr ***