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DEPARTMENT OF CIVIL ENGINEERING
BITS PILANI , RAJASTHAN
BY
DR. SHIBANI K HANRA JHA
AUGUST 2013
Transport Phenomena
Course: CE F212 Transport Phenomena 3 0 3
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Course: CE F212 Transport Phenomena 3 0 3
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Overview of the Course
Course: CE F212 Transport Phenomena 3 0 3
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Basic Properties of Fluids (Lecture 1-2)
Fluid at Rest-Pressure and its Effect (Lecture 3-7)
Study of fundamentals of fluid flow and Kinematics of FluidMotion (Lecture 8-15)
Flow Analysis using Control Volumes (Lecture 16-21) Fluids in MotionThe Bernoulli Equation (Lecture 22-25)
Flow Analysis using Differential Methods (Lecture 26-29)
Dimensional Analysis, modeling, and similitude (Lecture 30-33)
Study of flow pattern through orifices and mouthpieces (Lecture34-36)
Study of flow pattern over notches and weirs (Lecture 37-39)
Study of flow pattern through pipes (Lecture 40-43)
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Evaluation of your performance in this course
Course: CE F212 Transport Phenomena 3 0 3
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1. Mid-semester30%
2. Comprehensive45%
3. Tutorial/Assignment25%
1. 6 evaluative tutorials with 2 surprised tutorials (best 5 for finalgrading);
2. 2 evaluative assignments
***IMPLICITLY ON YOUR REGULARITY IN THE CLASS
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D EPA R TM EN T O F C I V I L EN G I N EER I N G
B I T S P I L A N I , R A J A S T H A N
B Y
D R . S H I B A N I K H A N R A J H A
A U G U S T 2 0 1 3
Basic Properties of Fluids
Lecture 1, 2
Course: CE F212 Transport Phenomena 3 0 3
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Course: CE F212 Transport Phenomena 3 0 3
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Topics to be Covered
Characteristics of Fluids Dimensions, Dimensional Homogeneity and Units Systems of Units
Measures of Fluid Mass and Weight Density
Specific Weight Specific Gravity
Ideal Gas Law
Viscosity
Compressibility of Fluids Bulk Modulus
Compression and Expansion of Gases
Speed of Sound
Vapor Pressure
Surface Tension.
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Objectives (Lecture 1-2)
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1. Identify the units for the basic quantities of time,length, force and mass.
2. Properly set up equations to ensure consistency of
units.
3. Define the basic fluid properties.
4. Identify the relationships between specific weight,
specific gravity and density, and solve problems usingtheir relationships.
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What is Fluid?
By definition, a fluid is any material that is unable to withstand a staticshear stress.
Unlike an elastic solid which responds to a shear stress with arecoverable deformation, a fluid responds with an irrecoverable flow.
Examples of fluids include gases and liquids.
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Concepts and Definitions- fluids (liquid and gas)
A liquid takes the shape of thecontainer it is in and forms a freesurface in the presence of gravity
A gas expands until it encountersthe walls of the container and fillsthe entire available space. Gasescannot form a free surface
Gas and vapor are often used assynonymous words
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Concepts and Definitions
Intermolecular bonds are strongest in
solids and weakest in gases. One
reason is that molecules in solids are
closely packed together,
Whereas in gases they are separated
by relatively large distances
On a microscopic scale, pressure is
determined by the interaction ofindividual gas molecules.
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Formation of drops:
depends on basic properties of fluid
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The ubiquity of drops is
beautifully illustrated by
this picture of a dolphin,jumping out of the water
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Formation of drops:
Depends on basic properties of fluid
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Some observations from everyday
life indicate that even the formation
of an individual drop is more
complicated than one might think
What are the
parameters on which
this drop formation
depends???
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Why is fluid so useful in engineering applications?
Typically, liquids are considered to be incompressible.
That is once you place a liquid in a sealed container you can DOWORK on the FLUID as if it were an object.
The PRESSURE you apply is transmitted throughout the liquidand over the entire length of the fluid itself.
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Civil Engineering Applications
Fluid mechanics is involved in nearly all areas of CivilEngineering either directly or indirectly. Some examples ofdirect involvement are those where we are concerned withmanipulating the fluid:
Sea and river (flood) defences; Water distribution / sewerage (sanitation) networks;
Hydraulic design of water/sewage treatment works;
Dams;
Irrigation;
Pumps and Turbines;
Water retaining structures.
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Civil Engineering Applications
And some examples where the primary object is construction -yet analysis of the fluid mechanics is essential:
Flow of air in / around buildings; Bridge piers in rivers;
Ground-water flow.
Notice how nearly all of these involve water. The following course, although introducing general fluid flow ideas and
principles, will demonstrate many of these principles through exampleswhere the fluid is water.
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Characteristics of Fluids
Although the differences between solids and
fluids can be explained qualitatively on the
basis of molecular structure; a more specificdistinction is based on how they deform under
the action of an external load
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Concepts and Definitions
A solid can resist an applied shear stress by deforming,whereas a fluid deforms continuously under the influenceof shear stress, no matter however small is the stress.
In solids stress is proportional tostrain, but in fluids stressis proportional tostrain rate.
When a constant shear force is applied, a solid eventuallystops deforming, at some fixed strain angle, whereas afluid never stops deforming and approaches a certain rateof strain.
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Concepts and Definitions
Difference between solid and fluid behaviour Solid:
It can resist an applied shear by deforming
Stress is proportional to strain
Fluid: Deforms continuously under applied shear
Stress is proportional to strain rate
F
A
F V
A h
Solid Fluid
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Concepts and Definitions
Stress is defined as the
force per unit area.
Normal component:normal stress
In a fluid at rest, the
normal stress is called
pressure Tangential component:
shear stress
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Concepts and Definitions
In the analysis of fluids, we often take small volumes(elements) and examine the forces on these
Forces acting along edges (faces), such as F, are know as
shearing forces
A fluid is a substance which deforms continuously,
or f lows, when subjected to shearing forces of any magni tude.
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Shear Stress in moving fluid
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If fluid is in motion, shear stress are developed if the particles ofthe fluid move relative to each other. Adjacent particles havedifferent velocities, causing the shape of the fluid to becomedistorted
On the other hand, the velocity of the fluid is the same at everypoint, no shear stress will be produced, the fluid particles are atrest relative to each other.
Moving plate Shear force
Fluid particles New particle position
Fixed surface
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Dimensions
Fluid characteristics can be described qualitatively in terms of certain basic(primary) quantities such as length [L], time [T], mass [M] and
temperature []
Quantitative description requires both a number and a standard by whichvarious quantities can be compared
A standard for length might be a meter or foot, for time an hour or second,and for mass a slug or kilogram; such standards are called units,
The primary quantities can be used to describe any other secondary quantity.Example:
A[L2], Velocity[LT-1], Density[ML-3]
Systems of Dimensions
[M], [L], [T], and []
[F], [L], [T], and []
[F],[M], [L], [T], and []
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Dimensional homogeneity
Dimensionally homogeneous equations: All theoretically derived equations are dimensionallyhomogeneous
Dimensions of the left side of the equation must be the same as those on the right side, and alladditive separate terms must have the same dimensions. Example
V=V0+at
(LT-1=LT-1+LT-2 T)
Restricted homogeneous equations: equations that are restricted to a particular system of units.Example
d=gt2/2
d=4.9t2
General homogeneous equations: valid in any system of units. ExampleF=ma
Concept of dimensions is basis for the powerful tool of dimensional analysis(which wi l l be discussed in later par t of this cour se)
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Systems of Units
Qualitative vs quantitative measure of any given quantity Units gives the quantitative measure of a quantity British Gravitational (BG) system
International system (SI)
English Engineering (EE) system
Two systems of unit that are widely used in engineering systems of unitare BG and SI
Systems of Units
MLT SI (kg, m, s, K)
FLT British Gravitational (lbf, ft, s, oR)
FMLT English Engineering (lbf, lbm, ft, s, oR)
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Systems of Units: Primary Units
In SI system six primary units
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Systems of Units: Derived Units
In SI system derived units
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Analysis of Fluid Behaviour
The study of transport phenomenon involves some fundamentallaws you must have encountered in physics and mechanicsbefore, like Newtons laws of motion
Conservation of mass
Conservation of energy Hence, this is indeed helpful since many of the concepts and
techniques of analysis used in this subject will be ones you haveencountered before
The broad aspects of transport phenomenon can be subdivided
into fluid statics (fluid at rest) and fluid dynamics (fluid inmotion)
However before moving towards the broader aspects, it isnecessary to review certain fluid properties that are intimatelyrelated to fluid behaviour
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Measures of fluid mass and weight
Density: mass per unit volume (BG- slugs/ft3; SI- kg/m3)
liquid density varies less with pressure and temperaturewhereas for gas this variation is quite high
Specific volume: volume per unit mass ( this property is
mainly used in thermodynamics)
volume
mass
mass
Volumev
1
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Measures of fluid mass and weight
Specific Weight: weight per unit volume (BG- lb/ft3, SI- N/m3)
g acceleration due to gravity (32.174 ft/s2
; 9.807 m/s2)
Water at 60 o F has a specific weight of 62.4 lb/ft3 and 9.80 kN/m3)
Specific Gravity: ratio of densities
= 1.94 slugs/ft3 or 1000 kg/m3
gvolume
weight
COHO
SG4@2
)2.39(4@2 FCOHOO
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Hydrostatic Pressure
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Suppose a Fluid (such as a liquid) is atREST, we call this HYDROSTATICPRESSURE
Two important points
A fluid will exert a pressure in alldirections
A fluid will exert a pressureperpendicular to any surface it contacts
Notice that
The arrows on TOP of the objects are smallerthan at the BOTTOM.
This is because pressure is greatly affected by theDEPTH of the object.
Since the bottom of each object is deeper than thetop, the pressure is greater at the bottom.
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Pressure vs. Depth
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Suppose we had an object submerged in
water with the top part touching the
atmosphere. If we draw an FBD for this
object, we would have three forces
1. The weight of the object
2. The force of the atmosphere pressing
down
3. The force of the water pressing up
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Pressure vs. Depth
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But recall, pressure is force per unit area.So if we solve for force; we can insert
our new equation
Note: The initial
pressure in this
case is atmospheric
pressure, which is aCONSTANT.
Po=1x105 N/m2
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A closer look at Pressure vs. Depth
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ghPP 0
ghP
Depth below surface
Initial PressureMay or MAY NOT beatmospheric pressure
GAUGE PRESSURE = CHANGE inpressure or the DIFFERENCE in the initial and
absolute pressure
ABSOLUTE PRESSURE
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Pressure Transmission
Hydraulic Lift
In a closed system, pressure changes from one point are
transmitted throughout the entire system (Pascals Law).
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Ideal gas law
Gases are highly compressible compared to liquids Changes in gas density directly related to changes in pressure and
temperature through following equation
Ideal or perfect gas law or the equation of state for an ideal gas
Where
p is absolute pressure (it is a measured relative to absolute zero pressure;a pressure that would only occur in a perfect vacuum; standard sea-level atmospheric pressure is 14.696 psi (abs) or 101.33 kPa (abs))
density,
T the absolute temperature and
R is a gas constant
RTp
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Viscosity
Viscosity is a measure of a fluid's resistance to flow
Newtonian Fluids: A fluid that behaves according toNewton's law, with a viscosity (absolute or dynamic orsimply viscosity) that is independent of the stress, is said to
be Newtonian.
Gases, water and many common liquids can be considered
Newtonian in ordinary conditions and contexts. Most of the common fluids (water, air, oil, etc.) Also called Linear fluids
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Viscosity
non-Newtonian Fluids: There are many fluids thatsignificantly deviate from that law in some way orother. For example:
Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.)
Also called Non-linear fluids
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Viscosity
Kinematic viscosity , Shear thinning fluids the apparent viscosity decreases
with increasing shear rate; the harder the fluid is sheared,the less viscous it becomes.
Examples - many colloidal suspensions and polymersolutions are shear thinning. For example, latex paint doesnot drip from the brush because the shear rate is small and
the apparent viscosity is large. However, it flows smoothlyonto the wall because the thin layer of paint between thewall and the brush causes a large shear rate and a smallapparent viscosity.
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Viscosity
Shear thickening f luidsthe apparent viscosity increaseswith increasing shear rate; the harder the fluid is sheared,the more viscous it becomes
Examples - water-corn starch mixture and water-sand
mixture (quicksand). Thus, the difficulty in removing anobject from quicksand increases dramatically as the speedof removal increases
Bingham plastic neither a fluid nor a solid; such
material can withstand a finite shear stress without motion,but once the yield stress is exceeded it flows like a fluid
Examplestoothpaste and mayonnaise
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Real Fluid
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Real fluids, even though
they may be moving,
always stick to the
solid boundaries thatcontain them.
THIS IS NO-SLIP
CONDITIONS
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Compressibility of fluids
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Bulk modulus.
Compression and expansion of gases.
Speed of sound.
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Compressibility of fluids
Bulk Modulus ( ): How compressible is the fluid?Change in volume (or density) of a fluid with changein pressure
Since decrease in volume of a given mass, ( )will result in an increase in density. Thus we canwrite
The bulk modulus (also referred to as the bulkmodulus of elasticity) has dimensions of pressure(FL-2) [lb/in2 or psi; N/m2 or Pa]
/d
dpE
v
m
/d
dpE
v
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vE
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Compression and Expansion of Gases
When gases are compressed (or expanded) the relationshipbetween pressure and density depends on the nature of the
process
At constant temperature conditions (isothermal process), the following
condition holds
If compression or expansion is frictionless and no heat is exchanged
with the surroundings (isentropic process), then
Where k is the ratio of the specific heat at constant pressure (cp), to the
specific heat at constant volume, (cv) (i.e., )
Two specific heats are related to the gas constant R, through the equation
Course: CE F212 Transport Phenomena 3 0 3
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tconsp
tan
tconsp
k tan
v
p
c
ck
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Compression and Expansion of Gases
Two specific heats are related to the gasconstant R, through the equation
With explicit equations relating pressure
and density the bulk modulus for gases canbe determined by obtaining the derivative
for either of the two processes
discussed before and substituting the
results into the equation for bulk modulus.
Thus, for and isothermal process
Thus, for an isentropic process
Course: CE F212 Transport Phenomena 3 0 3
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vpccR
ddp /
pEv
kpEv
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Compression and Expansion of Gases
It is to be noted that in both the cases, the bulk modulusvaries directly with pressure
For air under standard atmospheric conditions with p=14.7psi (abs) and k=1.40, the isentropic bulk modulus is Ev=20.6
psi For water under the same conditions shows Ev=312,000 psi.
comparing the both, it shows that air is approximately15,000 times as compressible as water
NOTE: dealing with gases needs greater attention becauseof the significant effect of compressibility on fluidbehaviour; however under small pressure changes, gasescan also be treated as incompressible
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Example of some application of compressibility of
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Example of some application of compressibility of
a liquid
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Water pulse generator using compressed water has beendeveloped foruse in mining operation
It can fracture rock by producing an effect comparable toa conventional explosive such as gunpowder
At the ultrahigh pressures used (300 to 400 Mpa, or 3000 to4000 atmospheres), the water is compressed by about 10 to15%
When a fast opening valve within the pressure vessel isopened, the water expands and produces a jet of water thatupon impact with the target material produces an effectsimilar to the explosive force from conventional explosives.
Mining with water jet prevents various hazards
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Speed of Sound
Speed of sound (c): the velocity at which the smalldisturbances propagate in a fluid is called the acoustic
velocity or the speed of sound, c
Or in terms of the bulk modulus the speed can be defined as
Since the disturbance is small, there is negligible heat
transfer and the process is assumed to be isentropic
Course: CE F212 Transport Phenomena 3 0 3
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ddpc
vEc
CHECK THE DIMENSION.
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Speed of Sound
For gases undergoing isentropic process, , so that
Using the ideal gas law, one can write
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kpc
kpEv
kRTc
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Vapor pressure
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If liquids are simply placed in a container open tothe atmosphere, some liquid molecules willovercome the intermolecular cohesive forces andescape into the atmosphere.
If the container is closed with small air space leftabove the surface, and this space evacuated to form avacuum, a pressure will develop in the space as aresult of the vapor that is formed by the escapingmolecules.
When an equilibrium condition is reached, thevapor is said to be saturated and the pressure thatthe vapor exerts on the liquid surface is termed theVAPOR PRESSURE, pv.
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Vapor pressure
Since this depends upon molecular activity, which is afunction of temperature, the vapor pressure of a fluid alsodepends on its temperature and increases with it.
If the pressure above a liquid reaches the vapor pressureof the liquid, boiling occurs; for example if the pressureis reduced sufficiently, boiling may occur at roomtemperature.
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NOTE: it can be observed that liquids like waterand gasoline will evaporate if they are simply
placed in a container open to the atmosphere
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Vapor pressure
Cavitation: when vapor bubblesare formed in a flowing fluidthey are swept along into regionsof higher pressure where they
suddenly collapse withsufficient intensity to actuallycause structural damage. Theformation and subsequentcollapse of vapor bubbles in aflowing fluid called cavitation isan important transportphenomena
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Cavitation Bubbles
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Engineering significance of vapor pressure
In a closed hydraulic system, Ex. in pipelines orpumps, water vaporizes rapidly in regions wherethe pressure drops below the vapor pressure.
Cavitationscan affect the performance of hydraulicmachinery such as pumps, turbines and propellers,and the impact of collapsing bubbles can causelocal erosion of metal surface.
Cavitationsin a closed hydraulic system can beavoided by maintaining the pressure above thevapor pressure everywhere in the system.
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Surface tension
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At the interface between a liquid and a gas, or betweentwo immiscible liquids, forces develop in the liquid
surface which cause the surface to behave as if it were a
skin ormembrane stretched over the fluid mass.
Although such a skin is actually not present, this
conceptual analogy allows us to explain several commonly
observed phenomena.
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Surface tension
The cohesive forcesbetween liquid molecules are responsible for the phenomenon known
as surface tension.The molecules at the surface do not have other like molecules on all sides of them and
consequently they cohere more strongly to those directly associated with them on the
surface.
This forms a surface "film" which makes it more difficult to move an object through the
surface than to move it when it is completely submersed.
The cohesive forces between
molecules down into a liquid areshared with all neighboring atoms.
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Surface tension
Wetting fluid: if the adhesion of the molecules to the solid surface is strong compared to thecohesion between molecules, the liquid will wet the surface and the level in a tube placed in a
wetting liquid will actually be rised
Non-wetting fluid: if the adhesion of the molecules to the solid surface is weak compared to
the cohesion between molecules, the liquid will not wet the surface and the level in a tube
placed in a non-wetting liquid will actually be depressed
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Surface tension
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Surface tension: the intensityof the molecular attraction per
unit length along any line in
the surface and is designated
by the Greek symbol .
The force due to surface tension = The force due to pressure difference
Where pi is the internal pressure
and pe is the external pressure
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Surface Tension Effects
Surface tension effects play a role in many fluid mechanics problems
including the
movement of liquids through soil and other porous media,
flow of thin film,
formation of drops and bubbles, andthe breakup of liquid Jets.
Surface phenomena associated with liquid-gas, liquid-liquid or
liquid-gas-solid interfaces are exceedingly complex.
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NOTE: THESE COMPLEX
PHENOMENON ARE BEYOND THE
SCOPE OF THIS COURSE
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Rise or fall of a liquid in a capillary tube
Wettability of fluid: MEASUREMENT
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A l f i f i l i
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A common example of interfacial tension
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Measurement of Surface Tension
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Wetting or non-wetting ???Which one is more wetting/non-wetting
fluid ???
Example: use of surface tension property
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Example: use of surface tension property
Walking on water
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Typical body length is 0.4 in
Cover 100 body length in 1 sec
It is Surface tension that keeps
water strider
How they propel themselves atsuch a high speed???
Each stroke creates dimples on the surface with
underwater swirling vortices sufficient to propel itforward
It is the rearward motion of the vortices that propels
water strider forward
Water Striders walk on water
Example: use of surface tension property
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Example: use of surface tension property
Spreading of oil spills
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Oil spills are frequent occurrence and creates a disastrousenvironmental problem
Most oils tend to spread horizontally into a smooth and slipperysurface called slick
Spread of oil slick is influenced by size of spill, wind speed-direction
and the physical properties of oil These properties include surface tension, specific gravity and
viscosity
Higher the surface tension, more likely the spread will remain in theplace
Oil (with Sp Gr less than one), increases its Sp Gr, if the lightercomponent evaporates from the oil
Higher the viscosity of the oil, greater the tendency to stay in one place
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Oil Rainbow
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An example of combined effect of Sp. Gr, surfacetension (interfacial tension) and Viscosity
S f th l t 1 2
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Summary of the lecture 1-2
At the end of these lectures one should be able know thefollowings concepts
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Fluid
Units
Basic dimensions
Dimensionally
homogeneous
Density
Specif ic weight
Specif ic gravity
I deal gas law
Absolute pressure
Gage pressure
No-slip condition
Rate of shearing strain
Absolute viscosity
Newtonian f lu id
non-Newtonian f lu id
Kinematic viscosity
Bulk modulus
Speed of sound
Vapor pressure
Surface tension
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Questions to be answered
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1. Which one is more viscous???2. Which one is more viscous among water, air,
oil, coal-tar ???
3. Does a fluid deform if there is no shearingstress???
4.Does the motion of fluid confirms the
deformation5. If same size balls are dropped in two liquids
with different viscosity, which liquid will show
higher splashes???
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Questions to be answered
68
6. Which among wood, steel and glass surface will show higherwetting by water???
7. Which among water, oil and magma is most compressible
fluid???
8.What is the dimension of specific gravity and specific weight???9.Which among air, mercury and water is most wetting and most
non-wetting???
10. When is the force that acts on oil kept in a rectangular tank at
rest? Which part of the tank experiences maximum pressure???
11. Which among gasoline, mercury and seawater shows higher
speed of sound???