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Fluid Mechanic
& Fluid Machine
ContentsChapter Topic Page
No
Chapter-1 Properties of FluidsTheory at a glance( for IES, GATE, PSU)
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Problems
78
15
15
2022
22
24
25
Chapter-2 Pressure and Its MeasurementsTheory at a glance( for IES, GATE, PSU)
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2727
32
33
40
43
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46Chapter-3 Hydrostatic Forces on Surfaces
Theory at a glance( for IES, GATE, PSU)
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Chapter Topic Page No
Chapter-4 Buoyancy and FlotationTheory at a glance( for IES, GATE, PSU)Previous 20-Years GATE Questions
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72Chapter-5 Fluid Kinematics
Theory at a glance( for IES, GATE, PSU)
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90
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100Chapter-6 Fluid Dynamics
Theory at a glance( for IES, GATE, PSU)
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135Chapter-7 Dimensional & Model Analysis
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148
155
157
157
160Chapter-8 Boundary Layer Theory
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Chapter Topic Page No
Chapter-9 Laminar FlowTheory at a glance( for IES, GATE, PSU)
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191191
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201Chapter-10 Turbulent Flow in Pipes
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211Chapter-11 Flow Through Pipes
Theory at a glance( for IES, GATE, PSU)
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237Chapter-12 Flow Through Orifices and
MouthpiecesTheory at a glance( for IES, GATE, PSU)
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239
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244Chapter-13 Flow Over Notches and Weirs
Theory at a glance( for IES, GATE, PSU)
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245245
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247
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248Chapter-14 Flow Around Submerged Bodies-
Drag and Li ftTheory at a glance( for IES, GATE, PSU)
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Chapter Topic Page No
Chapter-15 Compressible FlowTheory at a glance( for IES, GATE, PSU)
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Chapter-16 Flow Through Open ChannelTheory at a glance( for IES, GATE, PSU)
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303303
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310
311
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312Chapter-17 Force Exerted on Surfaces
Theory at a glance( for IES, GATE, PSU)
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313313
315
316
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317Chapter-18 Hydraulic Turbine
Theory at a glance( for IES, GATE, PSU)
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318319
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351Chapter-19 Centr ifugal Pump
Theory at a glance( for IES, GATE, PSU)
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Chapter Topic Page No
Chapter-20 Reciprocating PumpsTheory at a glance( for IES, GATE, PSU)Previous 20-Years GATE Questions
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383Chapter-21 Miscellaneous Hydraulic
MachinesTheory at a glance( for IES, GATE, PSU)
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Indias No. 1 Properties of Fluids
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1. Properties of Fluids
Contents of this chapter
1. Definition of Fluid
2. Characteristics of Fluid
3. Ideal and Real Fluids
4. Viscosity5. Units of Viscosity
6. Kinematic Viscosity
7. Units of Kinematic Viscosity
8. Classification of Fluids
9. Effect of Temperature on Viscosity
10. Effect of Pressure on Viscosity
11. Surface Tension
12. Pressure Inside a Curved Surface
13. Capillarity
14. Derive the Expression for Capillary Rise
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Theory at a Glance (for IES, GATE, PSU)Definition of FluidA fluid is a substance which deforms continuously when subjected to external shearing
forces.
Characterist ics of Fluid
1. It has no definite shape of its own, but conforms to the shape of the containing vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo a
deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear forces
whereas a fluid suffers Rate of Strain i.e. it flows under similar circumstances.
Ideal and Real Fluids1. Ideal Fluid
An ideal fluid is one which has
no viscosity
no surface tension
and incompressible
2. Real Fluid
An Real fluid is one which has
viscosity
surface tension
and compressible
Naturally available all fluids are real fluid.
ViscosityDefinition:Viscosity is the property of a fluid which determines its resistance to shearing
stresses.Cause of Viscosity: It is due to cohesion and molecular momentum exchange between
fluid layers.
Newtons Law of Viscosity: It states that the shear stress () on a fluid element layer is
directly proportional to the rate of shear strain.
The constant of proportionality is called the co-efficient of viscosity.
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When two layers of fluid, at a distance dy apart,
move one over the other at different velocities,
say u and u+du.
Velocity gradient =du
dy
According to Newtons law du
dy
or =du
dy
Velocity Variation near a solidboundary
Where = constant of proportionality and is known as co-efficient of Dynamic viscosity oronly Viscosity
As du
dy
=
Thus viscosity may also be defined as the shear stress required producing unit
rate of shear strain.
Units of ViscosityS.I. Units: Pa.s or N.s/m2
C.G.S Unit of viscosity is Poise= dyne-sec/cm2
One Poise= 0.1 Pa.s
1/100 Poise is called centipoises.
Dynamic viscosity of water at 20oC is approx= 1 cP
Kinematic ViscosityIt is the ratio between the dynamic viscosity and density of fluid and denoted by
Mathematicallydynamicviscosity
density
= =
Units of Kinematic Viscosity
S.I units: m2/s
C.G.S units: stoke = cm2/sec
One stoke = 10-4 m2/s
Thermal diffusivity and molecular diffusivity have same dimension, therefore, by analogy,
the kinematic viscosity is also referred to as the momentum diffusivity of the fluid, i.e. the
ability of the fluid to transport momentum.
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Classif ication of Fluids
1. Newtonian Fluids
These fluids follow Newtons viscosity equation.
For such fluids viscosity does not change with rate of deformation.
2. Non- Newtonian FluidsThese fluids does not follow Newtons viscosity equation.
Such fluids are relatively uncommon e.g. Printer ink, blood, mud, slurries, polymer
solutions.
Non-Newtonian Fluid (dy
du )
Purely Viscous Fluids Visco-elastic
Fluids
Time - Independent Time - Dependent
1. Pseudo plastic Fluids
1;
= n
dy
dun
Example: Butter
3. Bingham or Ideal
Plastic Fluid
n
ody
du
+=
Example: Water suspensions
of clay and flash
1.Thixotropic Fluids
)(tfdy
dun
+
=
f(t)is
decreasing
Example: Printer ink; crude
oil
2. Rheopectic Fluids
)(tfdy
dun
+
=
f(t)is
increasing
Example: Rare liquid solid
suspension
Visco-elastic
Fluids
Edy
du +=
Example: Liquid-
solid combinations
in pipe flow.
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Fig. Shear stress and deformation rate relationship of different fluids
Effect of Temperature on ViscosityWith increase in temperature
Viscosity of liquids decreaseViscosity of gasses increaseNote: 1. Temperature responses are neglected in case of Mercury.
2. The lowest viscosity is reached at the critical temperature.
Effect of Pressure on ViscosityPressure has very little effect on viscosity.
But if pressure increases intermolecular gap decreases then cohesion increases so viscositywould be increase.
Surface tensionSurface tension is due to cohesion between particles at the surface.Capillarity action is due to both cohesion and adhesion.
Surface tensionThe tensile force acting on the surface of a liquid in contact with a gas or on the surfacebetween two immiscible liquids such that the contact surface behaves like a membraneunder tension.
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Pressure inside a Curved SurfaceFor a general curved surface with radii of curvature r1 and r2 at a point of interest
1 2
1 1p
r r
= +
a. Pressure inside a water droplet,4
pd
=
b. Pressure inside a soap bubble,8
pd
=
c. Liquid jet.2
pd
=
CapillarityA general term for phenomena observed in liquids due to inter-molecular attraction at the
liquid boundary, e.g. the rise or depression of liquids in narrow tubes. We use this term forcapillary action.
Capillary rise and depression phenomenon depends upon the surface tension of the liquidas well as the material of the tube.
1. General formula,4 cos
hd
=
2. For water and glass = 0o,4
hd
=
3. For mercury and glass = 138o ,4 cos42
= o
hgd
(h is negative indicates capillary depression)
Note: If adhesion is more than cohesion, the wetting tendency is more and the angle of
contact is smaller.
Derive the Expression for Capil lary RiseLet us consider a glass tube of small
diameter d opened at both ends and is
inserted vertically in a liquid, say water.
The liquid will rise in the tube above the
level of the liquid.
Let, d = diameter of the capillary tube.
h = height of capillary rise.
= angle of contact of the water
surface. = surface tension force for unitylength.
= density of liquid.g = acceleration due to gravity.
d
h
cohesion (Meniscus concave)
Under a state of equilibrium,
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Upward surface tension force (lifting force) = weight of the water column in the tube
(gravity force)
or2d
d. cos = h g4
or4 cosh
gd =
If2
> , h will be negative, as in the case of mercury = 138 capillary depression
occurred.
Question: A circular disc of diameter d is slowly rotated in a liquid of large
viscosity at a small distance t from the fixed surface. Derive the
expression for torque required to maintain the speed .Answer: Radius, R = d/2
Consider an elementary circular ring ofradius r and thickness dras shown.
Area of the elements ring = 2 rd r
The shear stress at ring,
= = =
du V r
dy t t
Shear force on the elements ring
= = dF area of the ring 2 r dr
Torque on the ring=dFr
= r
dT 2 r drr t
Total torque, T = = R
0
rdT 2 r dr.r
t
=
R
3
0
2r dr
t= 4R
2t
= ( )
4d
22t
4
32
dT
t
=
Question: A solid cone of radius R and vortex angle 2 is to rotate at anangular velocity, . An oil of dynamic viscosity and thickness t
fills the gap between the cone and the housing. Determine the
expression for Required Torque. [IES-2000; AMIE (summer) 2002]
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Answer: Consider an elementary ring
of bearing surface of radius r.
at a distance h from the apex.
and let r+dris the radius at h
+ dh distance
Bearing area = 2 rd l
=
dr2 r .
sin
Shear stress
= = = du V r
dy t t
Tangential resistance on the ringdF = shear stress area of the ring
=
drr 2 r
t sin
Torque due to the force dFdT=dF.r
32dT= r dr tsin
Total torque
R
3
0
2T= dT = r dr
tsin
= =
4 42 R R
t sin 4 2t sin
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OBJECTIVE QUESTIONS (GATE, IES, IAS)
Previous 20-Years GATE Questions
ViscosityGATE-1. The SI unit of kinematic viscosity () is: [GATE-2001]
(a) m2/s (b) kg/m-s (c) m/s2 (d) m3/s2
GATE-2. Kinematic viscosity of air at 20C is given to be 1.6 10 -5m2/s. Itskinematic viscosity at 70C will be vary approximately [GATE-1999]
(a) 2.210-5m2/s (b) 1.610-5m2/s (c) 1.210-5m2/s (d) 3.210-5m2/s
Newtonian Fluid
GATE-3. For a Newtonian fluid [GATE-2006; 1995]
(a) Shear stress is proportional to shear strain
(b) Rate of shear stress is proportional to shear strain
(c) Shear stress is proportional to rate of shear strain
(d) Rate of shear stress is proportional to rate of shear strain
Surface TensionGATE-4. The dimension of surface tension is: [GATE-1996]
(a) ML-1 (b) L2T-1 (c) ML-1T1 (d) MT-2
GATE-5. The dimensions of surface tension is: [GATE-1995](a) N/m2 (b) J/m (c) J/m2 (d) W/m
Previous 20-Years IES Questions
FluidIES-1. Assertion (A): In a fluid, the rate of deformation is far more important
than the total deformation itself.
Reason (R): A fluid continues to deform so long as the external forces
are applied. [IES-1996]
(a) Both A and R are individually true and R is the correct explanation of A(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
IES-2. Assertion (A): In a fluid, the rate of deformation is far more importantthan the total deformation itself. [IES-2009]
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Reason (R): A fluid continues to deform so long as the external forces
are applied.(a) Both A and R are individually true and R is the correct explanation of A.
(b) Both A and R are individually true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
ViscosityIES-3. Newtons law of viscosity depends upon the [IES-1998]
(a) Stress and strain in a fluid (b) Shear stress, pressure and velocity
(c) Shear stress and rate of strain (d) Viscosity and shear stress
IES-4. What is the unit of dynamic viscosity of a fluid termed 'poise'
equivalent to? [IES-2008]
(a) dyne/cm2 (b) gm s/cm (c) dyne s/cm2 (d) gm-cm/s
IES-5. The shear stress developed in lubricating oil, of viscosity 9.81 poise,
filled between two parallel plates 1 cm apart and moving with relativevelocity of 2 m/s is: [IES-2001]
(a) 20 N/m2 (b) 196.2 N/m2 (c) 29.62 N/m2 (d) 40 N/m2
IES-6. What are the dimensions of kinematic viscosity of a fluid? [IES-2007]
(a) LT-2 (b) L2T-1 (c) ML-1T-1 (d)ML-2T-2
IES-7. An oil of specific gravity 0.9 has viscosity of 0.28 Strokes at 380C. What
will be its viscosity in Ns/m2? [IES-2005]
(a) 0.2520 (b) 0.0311 (c) 0.0252 (d) 0.0206
IES-8. Decrease in temperature, in general, results in [IES-1993]
(a) An increase in viscosities of both gases and liquids(b) A decrease in the viscosities of both liquids and gases
(c) An increase in the viscosity of liquids and a decrease in that of gases
(d) A decrease in the viscosity of liquids and an increase in that of gases
IES-9. Assertion (A): In general, viscosity in liquids increases and in gases it
decreases with rise in temperature. [IES-2002]
Reason (R): Viscosity is caused by intermolecular forces of cohesionand due to transfer of molecular momentum between fluid layers; of
which in liquids the former and in gases the later contribute the major
part towards viscosity.(a) Both A and R are individually true and R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
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Non-Newtonian Fluid
IES-10. If the Relationship between the shear stress and the rate of shear
straindy
duis expressed as
n
dy
du
= then the fluid with exponent n>1
is known as which one of the following? [IES-2007]
(a) Bingham Plastic (b) Dilatant Fluid
(c) Newtonian Fluid (d) Pseudo plastic Fluid
IES-11. Match List-I (Type of fluid) with List-II (Variation of shear stress) andselect the correct answer: [IES-2001]
List-I List-IIA. Ideal fluid 1. Shear stress varies linearly with the rate of
strain
B. Newtonian fluid 2. Shear stress does not vary linearly with the
rate of strain
C. Non-Newtonian fluid 3. Fluid behaves like a solid until a minimum
yield stress beyond which it exhibits a linearrelationship between shear stress and the rate
of strain
D. Bingham plastic 4. Shear stress is zero
Codes: A B C D A B C D(a) 3 1 2 4 (b) 4 2 1 3
(c) 3 2 1 4 (d) 4 1 2 3
IES-12. In an experiment, the following shear stress - time rate of shear strainvalues are obtained for a fluid: [IES-2008]
Time rate of shear strain (1/s): 0 2 3 4
Shear stress (kPa): 0 1.4 2.6 4
(a) Newtonian fluid (b) Bingham plastic(c) Pseudo plastic (d) Dilatant
IES-13. Match List-I (Rheological Equation) with List-II (Types of Fluids) and
select the correct the answer: [IES-2003]
List-I List-II
A.ndydu )/( = , n=1 1. Bingham plastic
B.ndydu )/( = , n1 3. Newtonian fluid
D. 0 = + (du/dy)n, n=1 4. Pseudo-plastic fluidCodes: A B C D A B C D
(a) 3 2 4 1 (b) 4 1 2 3(c) 3 4 2 1 (d) 4 2 1 3
IES-14. Assertion (A): Blood is a Newtonian fluid. [IES-2007]
Reason (R): The rate of strain varies non-linearly with shear stress for
blood.(a) Both A and R are individually true and R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
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(c) A is true but R is false
(d) A is false but R is true
IES-15. Match List-I with List-II and select the correct answer. [IES-1995]
List-I (Properties of fluids) List-II (Definition/ Results)
A.Ideal fluid
1.Viscosity does not change with rate of
deformation
B. Newtonian fluid 2. Fluid of zero viscosity
C. / 3. Dynamic viscosity
D. Mercury in glass 4. Capillary depression
5. Kinematic viscosity
6. Capillary rise
Code: A B C D A B C D(a) 1 2 4 6 (b) 1 2 3 4
(c) 2 1 3 6 (d) 2 1 5 4
Surface TensionIES-16. Surface tension is due to [IES-1998]
(a) Viscous forces (b) Cohesion
(c) Adhesion (d) The difference between adhesive andcohesive forces
IES-17. What is the pressure difference between inside and outside of a droplet
of water? [IES-2008]
(a) 2 / d (b) 4 / d (c) 8 / d (d) 12 / d
Where ' ' is the surface tension and d is the diameter of the droplet.
IES-18. If the surface tension of water-air interface is 0.073 N/m, the gauge
pressure inside a rain drop of 1 mm diameter will be: [IES-1999]
(a) 0.146N/m2 (b) 73N/m2 (c) 146N/m2 (d) 292 N/m2
IES-19. What is the pressure inside a soap bubble, over the atmospheric
pressure if its diameter is 2 cm and the surface tension is 01 N/m?
[IES-2008]
(a) 04 N/m2 (b) 40 N/m2 (c) 40.0 N/m2 (d) 400.0 N/m2
CapillarityIES-20. The capillary rise at 200C in clean glass tube of 1 mm diameter
containing water is approximately [IES-2001]
(a) 15 mm (b) 50 mm (c) 20 mm (d) 30 mm
IES-21. Which one of the following is correct? [IES-2008]The capillary rise on depression in a small diameter tube is
(a) Directly proportional to the specific weight of the fluid
(b) Inversely proportional to the surface tension
(c) Inversely proportional to the diameter
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(d) Directly proportional to the surface area
IES-22. A capillary tube is inserted in mercury kept in an open container.
Assertion (A): The mercury level inside the tube shall rise above thelevel of mercury outside. [IES-2001]
Reason (R): The cohesive force between the molecules of mercury is
greater than the adhesive force between mercury and glass.
(a) Both A and R are individually true and R is the correct explanation of A
(b) Both A and R are individually true but R is not the correct explanation of A
(c) A is true but R is false
(d) A is false but R is true
IES-23. What is the capillary rise in a narrow two-dimensional slit of width 'w'?
(a) Half of that in a capillary tube of diameter w [IES-2009]
(b) Two-third of that in a capillary tube of diameter 'w'(c) One-third of that in a capillary tube of diameter 'w'
(d) One-fourth of that in a capillary tube of diameter 'w'
IES-24. Assertion (A): A narrow glass tube when immersed into mercury causescapillary depression, and when immersed into water causes capillary
rise. [IES-2009]
Reason (R): Mercury is denser than water.
(a) Both A and R are individually true and R is the correct explanation of A.
(b) Both A and R are individually true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
IES-25. Consider the following statements related to the fluid properties:
1. Vapour pressure of water at 373 K is 1015 103 N/m2.2. Capillary height in cm for water in contact with glass tube and air is
(tube dia)/0268.3. Blood is a Newtonian fluid
Which of the statements given above is/are correct? [IES-2008]
(a) 1 only (b) 1 and 3 (c) 1 and 2 (d) 2 only
Compressibi lity and Bulk ModulusIES-26. Which one of the following is the bulk modulus K of a fluid? (Symbols
have the usual meaning) [IES-1997]
(a)
d
dp(b)
d
dp(c)
dp
d(d)
dp
d
IES-27. When the pressure on a given mass of liquid is increased from 3.0 MPato 3.5 MPa, the density of the liquid increases from 500 kg/m 3 to 501
kg/m3.What is the average value of bulk modulus of the liquid over thegiven pressure range? [IES-2006]
(a) 700 MPa (b) 600MPa (c) 500MPa (d) 250MPa
Vapour PressureIES-28. Which Property of mercury is the main reason for use in barometers?
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(a) High Density (b) Negligible Capillary effect
(c) Very Low vapour Pressure (d) Low compressibility [IES-2007]
IES-29. Consider the following properties of a fluid: [IES-2005]
1. Viscosity 2. Surface tension
3. Capillarity 4. Vapour pressureWhich of the above properties can be attributed to the flow of jet of oil
in an unbroken stream?
(a) 1 only (b) 2 only (c) 1 and 3 (d) 2 and 4
IES-30. Match List-I with List-II and select the correct answer using the code
given below the lists: [IES-2008]List-I (Variable) List-II (Dimensional Expression)
A. Dynamic Viscosity 1. M L2 T-3
B. Moment of momentum 2. M L-1 T-2
C. Power 3. M L-1 T-1D.Volume modulus of elasticity 4. M L2 T-2
5. M L2 T-1
Codes: A B C D A B C D(a) 1 4 2 3 (b) 3 5 1 2
(c) 1 5 2 3 (d) 3 4 1 2
Previous 20-Years IAS Questions
FluidIAS-1. Which one of the following sets of conditions clearly apply to an ideal
fluid? [IAS-1994]
(a) Viscous and compressible (b) Non-viscous and incompressible
(c) Non-viscous and compressible (d) Viscous and incompressible
ViscosityIAS-2. When a flat plate of 0.1 m2 area is pulled at a constant velocity of 30
cm/sec parallel to another stationary plate located at a distance 0.01 cmfrom it and the space in between is filled with a fluid of dynamic
viscosity = 0.001 Ns/m2, the force required to be applied is: [IAS-2004]
(a) 0.3 N (b) 3 N (c) 10 N (d) 16 N
Newtonian Fluid
IAS-3. In a Newtonian fluid, laminar flow between two parallel plates, the
ratio ( ) between the shear stress and rate of shear strain is given by
[IAS-1995]
(a) 2
2
dy
d (b)
dy
du (c)
2
dy
du (d)
21
dy
du
IAS-4. Consider the following statements: [IAS-2000]
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1. Gases are considered incompressible when Mach number is less
than 0.22. A Newtonian fluid is incompressible and non-viscous
3. An ideal fluid has negligible surface tension
Which of these statements is /are correct?
(a) 2 and 3 (b) 2 alone (c) 1 alone (d) 1 and 3
Non-Newtonian Fluid
IAS-5. The relations between shear stress ( ) and velocity gradient for ideal
fluids, Newtonian fluids and non-Newtonian fluids are given below.Select the correct combination. [IAS-2002]
(a) =0; = . ( 2)dy
du; = . ( 3)
dy
du
(b) =0; = . ( )dy
du; = . ( )
dy
du 2
(c) = . ( )dy
du
; = . ( )dy
du 2
; = . (
3
)dy
du
(d) = . ( )dy
du; = . ( )
dy
du 2; =0
IAS-6. Fluids that require a gradually increasing shear stress to maintain a
constant strain rate are known as [IAS-1997]
(a) Rhedopectic fluids (b) Thixotropic fluids
(c) Pseudoplastic fluids (d) Newtonian fluids
Surface TensionIAS-7. At the interface of a liquid and gas at rest, the pressure is: [IAS-1999]
(a) Higher on the concave side compared to that on the convex side
(b) Higher on the convex side compared to that on the concave side
(c) Equal to both sides
(d) Equal to surface tension divided by radius of curvature on both sides.
Vapour PressureIAS-8. Match List-I (Physical properties of fluid) with List-II
(Dimensions/Definitions) and select the correct answer: [IAS-2000]
List-I List-IIA.Absolute viscosity 1. du/dy is constant
B. Kinematic viscosity 2. Newton per metre
C. Newtonian fluid 3. Poise
D. Surface tension 4. Stress/Strain is constant5. Stokes
Codes: A B C D A B C D
(a) 5 3 1 2 (b) 3 5 2 4(c) 5 3 4 2 (d) 3 5 1 2
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Answers with Explanation (Objective)Previous 20-Years GATE Answers
GATE-1. Ans. (a)GATE-2. Ans. (a) Viscosity of gas increases with increasing temperature.
GATE-3. Ans. (c)GATE-4. Ans. (d)
GATE-5. Ans. (c) The property of the liquid surface film to exert a tension is called the surface tension.It is the force required to maintain unit length of the film in equilibrium. In Sl units surface tension is
expressed in2
/ .J
N mm
In metric gravitational system of units it is expressed in kg(f)/cm or kg(f)/m.
Previous 20-Years IES Answers
IES-1. Ans. (a) Both A and R correct and R is correct explanation for A
IES-2. Ans. (a) This question is copied from
Characteristics of fluid
1. It has no definite shape of its own, but conforms to the shape of the containing
vessel.
2. Even a small amount of shear force exerted on a fluid will cause it to undergo a
deformation which continues as long as the force continues to be applied.
3. It is interesting to note that a solid suffers strain when subjected to shear forces
whereas a fluid suffers Rate of Strain i.e. it flows under similar circumstances.
IES-3. Ans. (c) Newton's law of viscosity
where, Shear stress
Rate of strain
du
dy
du
dy
=
IES-4. Ans. (c)
IES-5. Ans. (b) du=2 m/s; dy= 1cm = 0.01 m; = 9.81 poise = 0.981 Pa.s
Therefore ( ) = dy
du= 0.981
01.0
2= 196.2 N/m2
IES-6. Ans. (b)
IES-7. Ans. (c) Specific Gravity = 0.9 therefore Density = 0.9 1000 =900 kg/m3
One Stoke = 10
-4
m
2
/sViscosity ( ) = = 900 0.28 10-4 = 0.0252 Ns/m2
IES-8. Ans. (c) The viscosity of water with increase in temperature decreases and that of air increases.
IES-9. Ans. (d)
IES-10. Ans. (b)
IES-11. Ans. (d)
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IES-12. Ans. (d)
IES-13. Ans. (c)
IES-14. Ans. (d) A is false but R is true.
IES-15. Ans. (d)
IES-16. Ans. (b) Surface tension is due to cohesion between liquid particles at the surface, where as
capillarity is due to both cohesion and adhesion. The property of cohesion enables a
liquid to resist tensile stress, while adhesion enables it to stick to another body.
IES-17. Ans. (b) Pressure inside a water droplet,4
p =d
IES-18. Ans. (d) P =2/292
001.0
073.044mN
d
=
=
IES-19. Ans. (c)
IES-20. Ans. (d) mmgd
h 30001.081.91000
073.044
==
IES-21. Ans. (c) The capillary rise on depression is given by,
=
4 cosh
gd
IES-22. Ans. (d) Mercury shows capillary depression.IES-23. Ans. (a)
IES-24. Ans. (b) Causes of capillary depression: Adhesion is less than cohesion, the wetting tendency is
less and the angle of contact is high.
IES-25. Ans. (a) Vapour pressure of water at 373 K means 100oC is one atmosphere = 1.01325 bar =
101.325 103 N/m2.
Capillary height in cm for water in contact with glass tube =0.3
d
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For water and glass4
h =gd
= 0,
Blood is a pseudoplastic fluid.
Where
n
du; n
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Problem1. A circular disc of diameter D is slowly in a liquid of a large viscosity () at
a small distance (h) from a fixed surface. Derive an expression of torque
(T) necessary to maintain an angular velocity ( )
1. Ans. T =h
D
32
4
2. A metal plate 1.25 m 1.25 m 6 mm thick and weighting 90 N is placedmidway in the 24 mm gap between the two vertical plane surfaces. The
Gap is filled with an oil of specific gravity 0.85 and dynamic viscosity
3.0N.s/m2. Determine the force required to lift the plate with a constantvelocity of 0.15 m/s.
2. Ans. 168.08N
3. A 400 mm diameter shaft is rotating at 200 rpm in a bearing of length 120mm. If the thickness of oil film is 1.5 mm and the dynamic viscosity of the
oil is 0.7 Ns/m2 determine:
(i) Torque required overcoming friction in bearing;(ii) Power utilization in overcoming viscous resistance;
3. Ans. (i) 58.97 Nm (ii) 1.235 kW
4. In order to form a stream of bubbles, air is introduced through a nozzle
into a tank of water at 20C. If the process requires 3.0 mm diameter
bubbles to be formed, by how much the air pressure at the nozzle must
exceed that of the surrounding water? What would be the absolutepressure inside the bubble if the surrounding water is at 100.3 kN/m2?
( = 0.0735 N/m)
4. Ans. Pabs= 100.398 kN/m2 (Hint. Bubble of air but surface tension of water).
5. A U-tube is made up of two capillaries of diameters 1.0 mm and 1.5 mm
respectively. The U tube is kept vertically and partially filled with water
of surface tension 0.0075kg/m and zero contact angles. Calculate thedifference in the level of the menisci caused by the capillarity.
5. Ans. 10 mm
6. If a liquid surface (density) supports another fluid of density, b above
the meniscus, then a balance of forces would result in capillary rise
h=
gd
coc
b )(
4
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Students Note