Basic Prop Fluids

7/27/2019 Basic Prop Fluids

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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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Overview of the Course


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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


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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


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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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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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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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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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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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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


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tconsp

tan

tconsp

k tan

v

p

c

ck


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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


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vpccR

ddp /

pEv

kpEv


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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


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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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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



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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

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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???

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Basic Prop Fluids