FLUIDS AND THEIR
PROPERTIES
Introduction
• Fluid mechanics is the science that deals with the action of
forces on fluids at rest as well as in motion.
• If the fluids are at rest, the study of them is called fluid
statics.
• If the fluids are in motion, where pressure forces are not
considered, the study of them is called fluid Kinematics
• If the fluids are in motion and the pressure forces are
considered, the study of them is called fluid dynamics.
Fluid
• Matter exists in two states- the solid state and the fluid
state. This classification of matter is based on the spacing
between different molecules of matter as well as on the
behavior of matter when subjected to stresses.
• Because molecules in solid state are spaced very closely,
solids possess compactness and rigidity of form. The
molecules in fluid can move more freely within the fluid
mass and therefore the fluids do not possess any rigidity of
form.
• Thus Fluid exist in two form:– Liquid
– Gas
1.What is Fluid?
• Fluid is a substance that is capable of flowing. It
has no definite shape of its own. It assumes the
shape of its container.
• Both liquids and gases are fluids.
• Examples of fluids are :
i. water
ii. milk
iii. kerosene
iv. petrol
v. emulsions etc.
Hydrostatics
•No relative motion between adjacent layers. Thus, no shear stress
(tangential stress) to deform the fluid.
The only stress in fluid statics is normal stress (perpendicular to surface)
Normal stress is due to pressure (Pressure: gravity field-weight of fluid)
Variation of pressure is due only to the weight of the fluid → fluid
statics is only relevant in presence of gravity fields.
Connected vessels:
A water tower is an elevated structure supporting a water tank constructed at a
height sufficient to pressurize a water supply system for the distribution of potable
water, and to provide emergency storage for fire protection.
Water towers are able to supply water even during power outages, because they
rely on hydrostatic pressure produced by elevation of water (due to gravity) to push
the water into domestic and industrial water distribution systems; however, they
cannot supply the water for a long time without power, because a pump is typically
required to refill the tower. A water tower also serves as a reservoir to help with
water needs during peak usage times. The water level in the tower typically falls
during the peak usage hours of the day, and then a pump fills it back up during the
night.
Atmospheric Pressure
Pressure = Force per Unit Area
Atmospheric Pressure is the weight of the
column of air above a unit area. For example, the
atmospheric pressure felt by a man is the weight
of the column of air above his body divided by
the area the air is resting on
P = (Weight of column)/(Area of base)
Standard Atmospheric Pressure:
1 atmosphere (atm)
14.7 lbs/in2 (psi)
760 Torr (mm Hg)
1013.25 millibars = 101.3 kPascals
1kPa = 1Nt/m2
Variation of Pressure with Depth
• Pressure in a fluid at rest is independent of the
shape of the container.
• Pressure is the same at all points on a horizontal
plane in a given fluid.
Scuba Diving and Hydrostatic Pressure
Scuba Diving and Hydrostatic Pressure
1
• Pressure on diver at 100
ft?
 1m 
kg 
m

Pgage ,2   gz   998 3  9.81 2  100 ft  

m 
s 

 3.28 ft 
100 ft
Pabs ,2
2
1atm


 298.5kPa 
  2.95atm
101.325
kPa


 Pgage ,2  Patm  2.95atm  1atm  3.95atm
• Danger of emergency
ascent?
PV
1 1  PV
2 2
If you hold your breath on ascent, your lung
volume would increase by a factor of 4, which
would result in embolism and/or death.
Boyle’s law
V1 P2 3.95atm
 
4
V2 P1
1atm
Pascal’s Law
• Pressure applied to a
confined fluid increases the
pressure throughout by the
same amount.
• In picture, pistons are at
same height:
F1 F2
F2 A2
P1  P2  


A1 A2
F1 A1
• Ratio A2/A1 is called ideal
mechanical advantage
Pascal’ law
Hydrostatics
The Manometer
P1  P2
P2  Patm   gh
• An elevation change of Dz in
a fluid at rest corresponds
to DP/g.
• A device based on this is
called a manometer.
• A manometer consists of a
U-tube containing one or
more fluids such as
mercury, water, alcohol, or
oil.
• Heavy fluids such as
mercury are used if large
pressure differences are
anticipated.
Mutlifluid Manometer
• For multi-fluid systems
– Pressure change across a fluid column of
height h is DP = gh.
– Pressure increases downward, and
decreases upward.
– Two points at the same elevation in a
continuous fluid are at the same
pressure.
– Pressure can be determined by adding
and subtracting gh terms.
P2  1gh1  2 gh2  3 gh3  P1
Measuring Pressure Drops
• Manometers are well-suited to measure pressure
drops across valves, pipes,
heat exchangers, etc.
• Relation for pressure drop
P1-P2 is obtained by starting
at point 1 and adding or
subtracting gh terms until
we reach point 2.
• If fluid in pipe is a gas,
2>>1 and P1-P2= gh
The Barometer
PC   gh  Patm
Patm   gh
• Atmospheric pressure is
measured by a device called a
barometer; thus, atmospheric
pressure is often referred to as
the barometric pressure.
• PC can be taken to be zero since
there is only Hg vapor above
point C, and it is very low relative
to Patm.
• Change in atmospheric pressure
due to elevation has many
effects: Cooking, nose bleeds,
engine performance, aircraft
performance.
Fluid Statics
• Fluid Statics deals with problems associated with
fluids at rest.
• In fluid statics, there is no relative motion between
adjacent fluid layers.
• Therefore, there is no shear stress in the fluid trying
to deform it.
• The only stress in fluid statics is normal stress
– Normal stress is due to pressure
– Variation of pressure is due only to the weight of the fluid
→ fluid statics is only relevant in presence of gravity fields.
• Applications: Floating or submerged bodies, water
dams and gates, liquid storage tanks, etc.
Buoyancy and Stability
• Buoyancy is due to the fluid displaced by a
body. FB=fgV.
• Archimedes principal : The buoyant force
acting on a body immersed in a fluid is equal
to the weight of the fluid displaced by the
body, and it acts upward through the centroid
of the displaced volume.
Buoyancy and Stability
•
•
Buoyancy force FB is equal
only to the displaced volume
fgVdisplaced.
Three scenarios possible
1. body<fluid: Floating body
2. body=fluid: Neutrally buoyant
3. body>fluid: Sinking body
Example: Galilean Thermometer
• Galileo's thermometer is made of a sealed glass
cylinder containing a clear liquid.
• Suspended in the liquid are a number of weights,
which are sealed glass containers with colored
liquid for an attractive effect.
• As the liquid changes temperature it changes
density and the suspended weights rise and fall to
stay at the position where their density is equal to
that of the surrounding liquid.
• If the weights differ by a very small amount and
ordered such that the least dense is at the top and
most dense at the bottom they can form a
temperature scale.
Example: Floating Drydock
Auxiliary Floating Dry Dock Resolute
(AFDM-10) partially submerged
Submarine undergoing repair work on
board the AFDM-10
Using buoyancy, a submarine with a displacement of 6,000 tons can be lifted!
Example: Submarine Buoyancy and Ballast
• Submarines use both static and dynamic depth
control. Static control uses ballast tanks between the
pressure hull and the outer hull. Dynamic control
uses the bow and stern planes to generate trim
forces.
Examples of Archimedes
Principle
The Golden Crown of Hiero II, King of Syracuse
• Archimedes, 287-212 B.C.
• Hiero, 306-215 B.C.
• Hiero learned of a rumor where the
goldsmith replaced some of the gold
in his crown with silver. Hiero asked
Archimedes to determine whether
the crown was pure gold.
• Archimedes had to develop a
nondestructive testing method
The Golden Crown of Hiero II, King of Syracuse
• The weight of the crown and nugget
are the same in air: Wc = cVc = Wn =
nVn.
• If the crown is pure gold, c=n
which means that the volumes must
be the same, Vc=Vn.
• In water, the buoyancy force is
B=H2OV.
• If the scale becomes unbalanced,
this implies that the Vc ≠ Vn, which in
turn means that the c ≠ n
• Goldsmith was shown to be a fraud!
KONTINUUMOK MECHANIKÁJA Folyadékok mechanikája
Hidrosztatika
A hidrosztatika alaptörvénye (Pascal törvénye) szerint
a folyadékok belsejében bármely dA felületelemet
véve, a rá ható erő merőleges a felületelemre, nagysága
pedig arányos a helyi nyomással (feszültséggel):
Blaise Pascal
1623-1662
KONTINUUMOK MECHANIKÁJA Folyadékok mechanikája
Hidrosztatika
A Föld felszínén nyugvó folyadékokban a nyomás a
folyadékok súlya miatt a magassággal arányosan
változik.
A h magasságú  sűrűségű folyadékoszlop alaplapjának
DA felületére gyakorolt hidrosztatikai nyomását az
alábbiak szerint számíthatjuk ki:
F mg Vg hDAg
p



 hg
DA DA DA
DA
Amennyiben a folyadékra a külső légnyomás (p0) is
hat, úgy a folyadékfelszíntől számított h mélységben
a hidrosztatikai nyomás:
p  p 0  hg
a h mélységben a felület irányítottságától függetlenül
ekkora a nyomás
Pascal’s law
Hydrostatics
F1  pA1
F2  pA2
Hydraulic press
KONTINUUMOK MECHANIKÁJA Folyadékok mechanikája
Hidrosztatika
Merítsünk egy  sűrűségű folyadékba egy
hasáb alakú testet úgy, hogy alaplapja
párhuzamos legyen a folyadék felszínével.
Ekkor, mivel az egymással szemben lévő
oldallapokra ható hidrosztatikai nyomások
kompenzálják egymást, az alap és
fedőlapokra ható hidrosztatikai nyomások
különbsége miatt a testre függőleges irányú
felhajtóerő hat, amelynek nagysága:
F  gV 
Archimedes törvénye szerint a folyadékba mártott test látszólagos súlyveszteséget
szenved, amelynek nagysága egyenlő a test bemerülő része által kiszorított folyadék
súlyával ( F  gV   m g ). Belátható, hogy Archimedes törvénye bármilyen alakú
testre igaz. A felhajtóerő támadáspontja megegyezik a test által kiszorított folyadék
súlypontjával.
KONTINUUMOK MECHANIKÁJA Folyadékok mechanikája
Hidrosztatika
Archimedes törvénye
F  gV 
F  gV   m g
2. Types of Fluids
• Fluids can be classified into five basic types.
They are:
• Ideal Fluid
• Real Fluid
• Pseudo-plastic Fluid
• Newtonian Fluid
• Non-Newtonian Fluid
2.1 Ideal Fluid
• An Ideal Fluid is a fluid that has no viscosity.
• It is incompressible in nature.
• Practically, no ideal fluid exists.
2.2 Real Fluid
• Real fluids are compressible in nature. They
have some viscosity.
• Real fluids implies friction effects.
• Examples: Kerosene, Petrol, Castor oil
What is viscosity?
• Rheology
– Deformation and flow of matter under the
influence of applied stress
– Viscosity, elasticity, and plasticity
• Viscosity
– Measure of the resistance to deformation of a
fluid under shear stress
Shear Stress Experiment
• Internal friction between layers of flow
(Wikipedia 2006)
Molecular Origins
• Gases
• Liquids
– Molecular diffusion
– Additional forces
between layers of flow
between molecules but
– Independent of pressure
exact mechanics
unknown
– Increases with increasing
temperature
– Independent of pressure
except at very high
– Newtonian
pressure
– Decrease with increasing
temperature
– Newtonian and nonNewtonian
Hidrogénkötés a vízben
egy molekula környezetében
szilárd fázisban
folyadék fázisban
Más Példák a Hidrogénkötésre
Characterization of Fluids
• Newtonian Fluid
dV
 
dy
• Non-Newtonian
Fluids are usually
complex mixtures
(de Nevers 2005)
Introduction
• Viscosity is a quantitative measure of a fluid’s resistance to
flow.
Dynamic (or Absolute) Viscosity:
• The dynamic viscosity(η) of a fluid is a measure of the
resistance it offers to relative shearing motion.
η= F/ [A×(u/h)]
η= τ /(u/h) N-s/m²
Kinematic Viscosity :
• It is defined as the ratio of absolute viscosity to the density
of fluid.
ν= η/ρ
m²/s
; ρ= density of fluid
Viscosity Measurements
Capillary Viscometers
• It gives the ‘kinematic viscosity’ of the fluid. It is based on
Poiseuille’s law for steady viscous flow in a pipe.
Viscosity Measurements
Rotational Viscometers
• These viscometer give the value of the ‘dynamic viscosity’.
• It is based on the principle that the fluid whose viscosity is
being measured is sheared between two surfaces.
• In these viscometers one of the surfaces is stationary and the
other is rotated by an external drive and the fluid fills the
space in between.
• The measurements are conducted by applying either a
constant torque and measuring the changes in the speed of
rotation or applying a constant speed and measuring the
changes in the torque.
• There are two main types of these viscometers: rotating
cylinder and cone-on-plate viscometers
Viscosity Measurements
Rotating cylinder viscometer
Viscosity Measurements
Cone-on-plate viscometer
Effects of temperature
• The viscosity of liquids decreases with increase the temperature.
• The viscosity of gases increases with the increase the temperature.
Effects of temperature
• The lubricant oil viscosity at a specific temperature can be
either calculated from the viscosity - temperature equation
or obtained from the viscosity-temperature ASTM chart.
Viscosity-Temperature Equations
Effects of temperature
fig: Viscosity-temperature characteristics of selected oils
Effects of pressure
Viscosity - shear relationship
• For Newtonian fluids, shear stress linearly vary with the
shear rate as shown in Figure.Viscosity is constant for
this kind of fluid.
τ = η (u/h)
• Non Newtonian fluid doesn’t
follow the linear relation
between viscosity and shear rate.
Viscosity – shear relationship
Pseudoplastic Behaviour
• Pseudoplastic or shear thinning and is associated with the thinning
of the fluid as the shear rate increases.
Thixotropic Behaviour
• Thixotropic or shear duration thinning, is associated with a loss of
consistency of the fluid as the duration of shear increases.
• The opposite of this behavior is
known as inverse thixotropic.
Applications
• Selection of lubricants for various purpose.
- we can choose an optimum range of viscosity for engine oil.
- for high load and also for speed operation high viscous lubricants
is required.
• In pumping operation
- for high viscous fluid high power will require.
- for low viscous fluid low power will require.
• In making of blend fuel
- less viscous fuels easy to mix.
• In the operation of coating and printing.
2.3 Pseudo-plastic Fluid
• A fluid whose apparent viscosity or consistenc
y decreases instantaneously with an increase
in shear rate.
• Examples are:
i. quick sand
ii. ketch-up etc.
2.4 Newtonian fluid
• Fluids that obey Newton’s law of viscosity are
known as Newtonian Fluids. For a Newtonian
fluid, viscosity is entirely dependent upon
the temperature and pressure of the fluid.
• Examples: water, air, emulsions
2.5 Non-Newtonian Fluids
• Fluids that do not obey Newton’s law of
viscosity are non-Newtonian fluids.
• Examples: Flubber, Oobleck (suspension of
starch in water), Pastes, Gels & Polymer
solutions.
3. Properties of Fluids
• Properties of fluids determine how fluids can be used in
engineering and technology. They also determine the
behaviour of fluids in fluid mechanics. They are:
•
•
•
•
•
•
Density
Viscosity
Surface Tension
Capillary Action
Specific Weight
Specific Gravity
3.1 density
• Density is the mass per unit volume of a fluid.
In other words, it is the ratio between mass
(m) and volume (V) of a fluid.
• Density is denoted by the symbol ‘ρ’. Its unit is
kg/m3.
3.2 Viscosity
• Viscosity is the fluid property that determines
the amount of resistance of the fluid to shear
stress.
• It is the property of the fluid due to which the
fluid offers resistance to flow of one layer of
the fluid over another adjacent layer.
3.2.1 Dynamic Viscosity
• The Dynamic (shear) viscosity of a fluid
expresses its resistance to shearing flows,
where adjacent layers move parallel to each
other with different speeds.
3.2.2 Kynematic Viscosity
• The kinematic viscosity (also called
"momentum diffusivity") is the ratio of the
dynamic viscosity μ to the density of the fluid
ρ.
3.3 Surface Tension
• The property of fluids to resist tensile stresses
on their surface is called as Surface Tension.
3.4 Capillary Action
• Capillary action is the property of fluid to flow in
a narrow spaces without assistance of and in
opposition to external forces like gravity.
• The effect can be seen in the drawing up of
liquids between the hairs of a paint-brush, in a
thin tube, in porous materials such as paper and
plaster, in some non-porous materials such as
sand or in a cell.
• It occurs because of intermolecular forces
between the liquid and surrounding solid
surfaces.
3.5 Specific Weight
• Specific weight is the weight possessed by unit
volume of a fluid. It is denoted by ‘w’. Its unit
is N/m3.
• Specific weight varies from place to place due
to the change of acceleration due to gravity
(g).
3.6 Specific Gravity
• Specific gravity is the ratio of specific weight
of the given fluid to the specific weight of
standard fluid.
• It is denoted by the letter ‘S’. It has no unit.