Fluid mechanics Question papers

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 and
O'E
y- outside the tube indicating the angle of contact clearly. (06 Marks)
6V
5r ll d. If the equation of velocity profile over a flat plate is V :2f/3 where 'v' is the velocity in
ro
co9 m/s and'y' 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)
tsE
bd 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 in
ot
bod the pipe N is 1.75 bar and the manometric fluid is mercury, find the difference x between the
.g (s
1rh levels of mercury. (08 Marks)
,ts
G{
'C, 63

aB
ko
.oP
a8.
tro-
6d
Oj Fig.Q.2(c)
o=
go
ia tE
=#
E {ll
3E
o'i
>' l!
boo
co0
o=
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 incompressible
o
z
E
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)
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O6ME468
4a. Explain the dimensional homogeneity, with an example. (04 Marks)
b. Define the following dimensionless numbers and mention their significance in fluid flow
problems:
i) Reynold's no. ;ii) Froude's no. ; iii) Mach no. (06 Marks)
c. Prove that the discharge over a spillway is given by the relation using Buckingham's
II - theorem.

a=VD'f[ @ 'D)
H'l
v
WhereV:velocityofflow,D:Depthatthethroat,H:Fleadofwater,g=Acceleration
due to gravlty. (10 Marks)

PART _ E

5a. 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)
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 Bernoulli's 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

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 Pascal's 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 that'l' 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 Buckingharn's n theorern show that
o:
3i;
atE v: /zgH4i#,*) (10 Marks)
qo
o":
},qr
tr50 PART _ B
=(d
:i9
5L
5 a. Derive Euler's 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 at
o the lower section to 10 cm diameter atJhe upper r.oiiorr. The vertical distance between
the
z sections is 1,m. The pressure gauges installed at the lower and upper sections read
6 Nlcmi
L and 8 N/cm' respectively, when the discharge is 30 litres/sec. Calculate the loss of
o head
between the two sections and determine the direction of flow. (r0 Marks)

I of2

O6ME46B

6 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 Darcy's equation for loss of head between the two sections. Determine the direction
of 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 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

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 weight'W'. (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 each
i (,)
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)
cbO
'o=
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) Froude's number iii) Weber number ; iv) Reynolds' number.
-.:
0) c. using Buckingham ,, - that the velocity of fluid flow throu*, f'"X[B
z 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

O6ME46B

PART -B
a. Derive the a
Bernoulli's equation for 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 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 :
ii) Mach cone, Mach angle
iii) Subsonic flow. Marks)
(08
c. 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

USN O6UIE468

Fourth semester B.E. Degree Examination, MaylJune 2010
Fluid Mechanics
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 Pascal's 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 :
bDe
cbo
o=
i) steady flow and uniform flow ii) Laminar and turbulent flow
E8 ii) Sheamline and streakline iv) Rotational and irrotational flow. (08 Marks)
UL
=o
ch
o< 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
(,
o
F 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

O6ME468

PART -B
rl
a. Derive Bernoulli's equation and state the assumptions made. Mention the statement of
Bernoulli's 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

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
t,
(E
o
o PART _ A
.((t
U'O
(, .!=
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;Jr'irH"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.
9A
Eh Water lend in the limb connected to pipe is 0.5m below centre of the pipe and the. free
c<
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)
ob
t(E
gr
roo
3rA 2 a. Define the terms :
b.e
t^_
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 with
Fo-
=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)
Por
EG
ao)
E>
:o 3a. Distinguish between :
cc i) Steady and un-steady flow
o< 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 at
o
OL the point {2,3). (06 Marks)
E

4 a. State Buckingham's theorem. Why this theorem is considered superior over the Rayleigh's
ru
method for dimensional analysis? (05 Marks)

I nf?

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 Buckingham's theorm that, the
represented bY

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

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

PART _ B

Define Euler's equation of motion. Deduce Bemoulli's 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 lVlarks

8 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

O6ME46B
USN

Fourth Semester B.E. Degree Examination, Dec.09-Jan.10
Fluid Mechanics
o
o
()
oE Note: Answer any FIVE full questions, selecting
6
E
o
o
E
(, PART -A
.o
u, 0)
o .:=
Pe
o-s
la. Distinguish between :
.v.Z
E3 D Mass density and sPecific weight
(g
60 ii) Newtonian and non-Newtonian fluid
srf
,=
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)
BE
p+ 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. free
c<
oE surface mercury in the other lirnb (open to atmosphere) is 0.8m below the centre of the pipe,
H'K (05 Marks)
1,b Calculate the pressure of water in the pipe.
56
Sf,
E(o
aB
'3e
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 with
Fo-
=d,
CO
8N 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 diflerent
aLc 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 vertically
LO
5'E
o'-
>E in water. (08 Marks)
Por
:(E
ao)
F>
59 a. Distinguish betw'een :
cc i) Steady and un-steady flow
o< 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)
o
z c. If for a two dimensional potential flow, the velocity potential is given by 0 = 4x(3y - 4) ,
(U
E determine the velocity at the point (2,3). Determine also the value of stream function y at
o (06 Marks)
n the point (2, 3).
E

a. State Buckingham's theorem. Why this theorem is considered superior over the Rayleigh's
r
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_)] (10 Marks)

c. What is meant by geometric, kinematic and dynamic similarities? (05 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 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 = 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 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

USN O6ME468

Fourth Semester B.E. Degree Examination, June-July 2009
Fluid Mechanics
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 Buckingham's theorem, show that the relation for pressure difference Ap is given
by Ap=pv2r(*,*) (10 Marks)

I of2

06M[468

PART _ B

a. State and prove Bernoulli's 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-poiseulle's 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

USN 2AO2 SCHEME ME45

Fourth Semester B,E. Degree Examination, June-July 2009
Ftuid Mechanics
Time: 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

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)
*****

USN. 2OO2 SCHEME ME45

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

]t't

3a.
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

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)
*****

USN
O6ME468

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

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.-

O6ME46B

PART. B
Derive Euler's equation of motion along a stream line and hence obtain the Bernoulli's
equation 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 -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

,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 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. 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 Buckingham's
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

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/kg'K. (04 Marks)

,<****

2 of}

ME45
USN

Fourth semester B.E. Degree Examination, Dec. 07 / Jan. 08
Fluid Mechanics
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
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" 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 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

ME45'

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

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

Page No... 2 ME45

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 an
orificemeter? (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
Chery's farmulae. (10 Marks)

a. What is Hagen Poiseuille's formula? Derive an expression for the same. (06 Marks)
b. Obtain an expression for velocity of the sound wave in a compressible fluid interms
ofchange in pressure and change ofdensity. (08 Marks)
c. Define Mach number, Mach angle and Mach cone. (06 Marks)

a. Differentiate between
i) Strearuline body and bluff body
ii) Friction drag and pressure drag. (08 Marks)
b. A man weighing 981 N descends to the ground from an aeroplane with the help of a
parachute against the resistance of air. The shape of the parachute is hemispherical of
2 m diameter. Find the velocity of the parachute with which it comes down. Assume
C6 : 0.5 and p for air 0.00125 gmlcc and y: 0.015 stoke. (08 Marks)
c. Define displacement thickness and momentum thickness. (04 Marks)

&JJJJ

Page No... I ME45
i]SN

NEW SCITEME
Fourth Semester B.E. Degree Examination, Dec. O6 I Jan. O7
ME/IP/IM/MA/AU
Fluid Mechanics
Time: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 a
perfect gas undergoing isentropic process. (06 Marks)
b. Define surface tension and show that the gauge pressure within a liquid droplet varies
inversely 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 the
two surfaces are uniformly separated by a distance of 0.5 mm and taking linear
velocity distribution in a lubricating oil having dynamic viscosity of 4 CP, find the
power absorbed in the bearing. (08 Marks)
2a. Sketch and explain hydrostatic paradox. (04 Marks)
b. Define metacentre and derive an expression for a floating body for its metacentric
height. (08 Marks)
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 its
draft 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)
3a. Explain potential function and flownet. (06 Marks)
b. The velocity in a flow field is given by u:
3 m/s, v = 6 m/s. Determine the equation
of 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 this
flow. (08 Marks)

4 a. The losses *r", unit length of pipe in a turbulent flow through a smooth pipe
t'
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 is
200 kN/m'. If the pressure at upper end is not to fall below 100 kN/m2, find the value
of Z. (Neglect losses). (06 Marks)

Fig. a(c)

Page No""" 2
ME45

a' In a 100 mm diameter horizontal pipe a venturimeter of 0.5 contraction
ratio has been
fitted. The head of water on the meter when there is no flow is 3 m
of water. Find the
rate of flow for which the throat pressure will be 2 m of water.
The co-efficient of the
meter is 0.97.
b' _
Derive an expression for a flow through a triangular notch in terms
(08 Marla)
of head over
notch. (06 Marks)
c' A pitot static probe is used to measure the flow of water in a 5 cm diameter pipe.
If
the mean velocity is 5 m/s, and the pitot static tube is connected
across a mercgry
filled differential manometer, what should be the level difference in the mercury
column? (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 the
energy put into the pipe is lost in fiiclion.-One hundred
kW is to be transmitted
through a pipe, the pressure at the inlet of the pipe being
70 bar.If the pressure drop
per kilometer is to be 0'44 bar and if f : 0.02; nnd
the?iameter ortrr"'fip. and the
efficiency of transmission for 16 lan.
(12 Marks)

a' Derive an expressiol for velocity and average velocity for
viscous flow between two
stationery parallel plates.
(06 Marks)
b. Explain b Arembert paradox.
(04 Marks)
c' A teievision transmitter antenna consists of a vertical pipe 20 cm
diarneter and 30 m
high on top of tall structure. Determine the total drag
on the antenna and the bendins
moment about the base in a 30 m/s wind at NTP. fake
and viscosity as I .79x10's NS/m2, Cp : 0.2.
density of air t.zi-iehr|
^t (10 Marks)
a. Explain
ii) Displacementthickness
iii) Momentum thickness.
The velocity profile in a laminar boundary layer is approximated
by a parabolic
profire where a is the vetocity at yand u-+(rasy-+d.
#=r(#)-(#)'
calculate displacement thickness and momentum thickness.
.
b' Dttermine the velocity of a bullet fired in the air if the mach
(r0 Marks)
angle is observed to be
JU". Given that the temperature of air is 220c, density
1.2 kg/nl. Take y = 1.4 and
R:287 J,&gK. Derive the equation used. (r0 Marks)

!krr ***

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