Fluid properties

Fluid and Fluid
properties
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

Fluid Concept
Fluid mechanics is a division in applied
mechanics related to the behaviour of liquid
or gas which is either in rest or in motion.
The study related to a fluid in rest or
stationary is referred to fluid static,
otherwise it is referred to as fluid dynamic.
Fluid can be defined as a substance which
can deform continuously when being
subjected to shear stress at any magnitude.
In other words, it can flow continuously as
a result of shearing action. This includes
any liquid or gas.

DEFINE FLUIDS
(a) Solid (b) Liquid (c) Gas
k
kk
k
Free surface

A fluid is a substance that flows under the action of
shearing forces. If a fluid is at rest, we know that the
forces on it are in balance.
A gas is a fluid that is easily compressed. It fills any
vessel in which it is contained.
A liquid is a fluid which is hard to compress. A
given mass of liquid will occupy a fixed volume,
irrespective of the size of the container.
A free surface is formed as a boundary between a
liquid and a gas above it.

• Define “characteristics” of a specific fluidDefine “characteristics” of a specific fluid
•Properties expressed by basic “dimensions”Properties expressed by basic “dimensions”
– length, mass (or force), time, temperaturelength, mass (or force), time, temperature
• Dimensions quantified by basic “units”Dimensions quantified by basic “units”
We will consider systems of units, important fluidWe will consider systems of units, important fluid
properties (not all), and the dimensions associated withproperties (not all), and the dimensions associated with
those properties.those properties.A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR

Classification of fluids
Ideal fluid and Real fluid
Newtonian fluid and Non- newtonian fluid
Compressible and incompressible fluid.

…
Elastic
solid
Ideal
plastic
Non
New
tonian
fluid
Newtonian
fluid
Ideal fluid
(dU/
dY)
τ=Shear
stress

IDEAL FLUID
The fluid in which there is no friction; it is INVISCID
(it’s viscosity is zero).
The internal forces at any section within it are always
normal to the section, even during motion.
 So, these forces are purely pressure forces.
This does not exist in reality, many fluids approximate frictionless
flow at sufficient distances from solid boundaries and hence we
can analyze their behavior by assuming an ideal fluid.

In real fluids, either liquid or gas, tangential or
shearing forces are developed always whenever there
is motion relative to a body, thus creating fluid
friction, because these forces oppose the motion of
one particle past another.
These frictional forces give rise to a fluid property
called Viscosity.
Real fluids

Non Newtonian fluids
Non Newtonian fluids are relatively uncommon in
engineering use (examples are paints, printer’s ink,
gels and emulsions, sludges and slurries, and certain
plastics).
So, we will use fluids that obey Newton’s equation of
viscosity under normal conditions.

• Length = meters (m)Length = meters (m)
• Mass = kilograms (kg)Mass = kilograms (kg)
• Time = second (s)Time = second (s)
• Force = Newton (N)Force = Newton (N)
– Force required to accelerate 1 kg @ 1 m/sForce required to accelerate 1 kg @ 1 m/s22
– Acceleration due to gravity (g) = 9.81 m/sAcceleration due to gravity (g) = 9.81 m/s22
– Weight of 1 kg at earth’s surface = W = mg = 1 kg (9.81 m/sWeight of 1 kg at earth’s surface = W = mg = 1 kg (9.81 m/s22
) =) =
9.81 kg-m/s9.81 kg-m/s22
= 9.81 N= 9.81 N
• Temperature = Kelvin (Temperature = Kelvin (oo
K)K)
– 273.15273.15 oo
K = freezing point of waterK = freezing point of water
– oo
K = 273.15 +K = 273.15 + oo
CC

• Work and energy = Joule (J)Work and energy = Joule (J)
J = N*m = kg-m/sJ = N*m = kg-m/s22
* m = kg-m* m = kg-m22
/s/s22
• Power = watt (W) = J/sPower = watt (W) = J/s
• SI prefixes:SI prefixes:
G = giga = 10G = giga = 1099
c = centi = 10c = centi = 10-2-2
M = mega = 10M = mega = 1066
m = milli = 10m = milli = 10-3-3
k = kilo = 10k = kilo = 1033
µµ = micro = 10= micro = 10-6-6

• Mass per unit volume (e.g., @ 20Mass per unit volume (e.g., @ 20 oo
C, 1 atm)C, 1 atm)
– WaterWater ρρwaterwater = 1,000 kg/m= 1,000 kg/m33
(62.4 lbm/ft(62.4 lbm/ft33
))
– MercuryMercury ρρHgHg = 13,500 kg/m= 13,500 kg/m33
– AirAir ρρairair = 1.205 kg/m= 1.205 kg/m33
• Densities of gases = strong f (T,p) =compressibleDensities of gases = strong f (T,p) =compressible
• Densities of liquids are nearly constantDensities of liquids are nearly constant
(incompressible) for constant temperature(incompressible) for constant temperature
• Specific volume = 1/density = volume/massSpecific volume = 1/density = volume/mass

The density of a fluid is defined as its mass per
unit volume. It is denoted by the Greek
symbol, ρ.
ρ =
V m3
kgm-3
If the density is constant (most liquids), the flow is
incompressible.
If the density varies significantly (eg some gas flows), the
flow is compressible.
(Although gases are easy to compress, the flow may be treated
as incompressible if there are no large pressure fluctuations)
ρ water= 998 kgm-3
ρair =1.2kgm-3
kg
m

2 kg, 4000 cm3
Wood
177 cm3
45.2 kg
;
mass m
Density
volume V
ρ= =
Lead: 11,300 kg/mLead: 11,300 kg/m33
Wood: 500 kg/mWood: 500 kg/m33
4000 cm3
Lead
Same volume
2 kg
Lead
Same mass

4 kg
3
4 kg
;
7800 kg/m
m m
V
V
ρ
ρ
= = =
V = 5.13 x 10-4
m3V = 5.13 x 10-4
m3
What is the mass if the volume is 0.046 m3
?
3 3
(7800 kg/m )(0.046 m );m Vρ= =
m = 359 kgm = 359 kg

]/[]/[ 33 ftlbformNgργ =
• Weight per unit volume (e.g., @ 20Weight per unit volume (e.g., @ 20 oo
C, 1 atm)C, 1 atm)
γγwaterwater = (998 kg/m= (998 kg/m33
)(9.807 m)(9.807 m22
/s)/s)
= 9,790 N/m= 9,790 N/m33
[= 62.4 lbf/ft[= 62.4 lbf/ft33
]]
γγairair = (1.205 kg/m= (1.205 kg/m33
)(9.807 m)(9.807 m22
/s)/s)
= 11.8 N/m= 11.8 N/m33
[= 0.0752 lbf/ft[= 0.0752 lbf/ft33
]]

Ratio of fluid density to density of water @ 4o
C
3
/1000 mkg
SG
liquid
water
liquid
liquid
ρ
ρ
ρ
==
Water SGwater = 1
Mercury SGHg = 13.55
Note: SG is dimensionless and independent of system of units

Specific Gravity
STPwater
liquid
STPwater
liquid
SG
@@ γ
γ
ρ
ρ
==
A.N.KHUDAIWALA
(L.M.E) G.P.PORBANDAR
The specific gravity (or relative density) can be defined in two ways:
Definition 1: A ratio of the density of a liquid to the density of
water at standard temperature and pressure (STP)
(20°C, 1 atm), or
Definition 2: A ratio of the specific weight of a liquid to the
specific weight of water at standard temperature
and pressure (STP) (20°C, 1 atm),
Unit: dimensionless.

The specific gravity (or relative density) of a
material is the ratio of its density to the density of
water (1000 kg/m3
).
Steel (7800 kg/m3
) ρr = 7.80
Brass (8700 kg/m3
) ρr = 8.70
Wood (500 kg/m3
) ρr = 0.500
Steel (7800 kg/m3
) ρr = 7.80
Brass (8700 kg/m3
) ρr = 8.70
Wood (500 kg/m3
) ρr = 0.500
Examples:Examples:
3
1000 kg/m
x
r
ρ
ρ =

• Viscosity,Viscosity, µµ,, is a measure of resistance to fluid flow as ais a measure of resistance to fluid flow as a
result of intermolecular cohesion. In other words, viscosityresult of intermolecular cohesion. In other words, viscosity
can be seen as internal friction to fluid motion which cancan be seen as internal friction to fluid motion which can
then lead to energy loss.then lead to energy loss.
• Different fluids deform at different rates under the sameDifferent fluids deform at different rates under the same
shear stress. The ease with which a fluid pours is anshear stress. The ease with which a fluid pours is an
indication of its viscosity. Fluid with a high viscosity such asindication of its viscosity. Fluid with a high viscosity such as
syrup deforms more slowly than fluid with a low viscositysyrup deforms more slowly than fluid with a low viscosity
such as water. The viscosity is also known as dynamicsuch as water. The viscosity is also known as dynamic
viscosity.viscosity.
 Units:Units: N.s/m2 or kg/m/sN.s/m2 or kg/m/s
 Typical values:Typical values:
Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/sWater = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s

• Proportionality constant = dynamic (absolute)Proportionality constant = dynamic (absolute)
viscosityviscosity
• Newton’s Law of ViscosityNewton’s Law of Viscosity
• ViscosityViscosity
• UnitsUnits
• Water (@ 20Water (@ 20oo
C):C): µµ = 1= 1xx1010-3-3
N-s/mN-s/m22
• Air (@ 20Air (@ 20oo
C):C): µµ = 1.8= 1.8xx1010-5-5
N-s/mN-s/m22
• Kinematic viscosityKinematic viscosity
V
V+d
v
dy
dV
µτ =
dydV /
τ
µ =
2
2
//
/
m
sN
msm
mN ⋅
=
ρ
µ
ν =
Kinematic viscosity: m2
/s
1 poise = 0.1 N-s/m2
1 centipoises = 10-2
poise = 10-3
N-s/m2

Viscosity
From Newton’s equation of viscosity we have,
µ = τ / (dU/dY)
This is known as Coefficient of viscosity, the
absolute viscosity, the dynamic viscosity or simply
the viscosity of fluid.
The distinction between solids and fluid lies in the
manner in which each can resist SHEARING
STRESS.
Further distinction among various kinds of fluids
and solids is as:

Viscosity
In case of solids, shear stress depends on magnitude
of deformation but according to Newton’s equation of
viscosity the shear stress is proportional to time rate
of (angular) deformation.
A fluid for which absolute viscosity does not change with rate
of deformation is called NEWTONIAN FLUID.
The slope of this line is “Absolute Viscosity”
A fluid for which absolute viscosity changes with rate of
deformation is called NON-NEWTONIAN FLUID.

Viscosity
Kinematic Viscosity = Absolute Viscosity / Density
ν = µ / ƿ
Is called so because force is not involved, the only
dimensions being length and time, as in Kinematics.
UNITS:
In BG: ft2
/sec
In S.I: m2
/s
In Metric system it had units
cm2
/s, also known as
STOKE(St).
Name given after Sir George Stoke, an
English Physicist and pioneering investigator
of viscosity.
-6 2

Kinematic viscosity, ν
A.N.KHUDAIWALA
Definition: is the ratio of the viscosity to the density;
• will be found to be important in cases in which significant viscous and
gravitational forces exist.
Units: m2
/s
Typical values:
Water = 1.14x10-6 m2/s; Air = 1.46x10-5 m2/s;
In general,
viscosity of liquids with temperature, whereas
viscosity of gases with in temperature.
ρµ=ν /

Viscosity
DISTINCTION BETWEEN µ & ν :
 µ of most fluids is virtually INDEPENDENT of
pressures encountered ordinarily in engineering work.
ν of gases varies strongly with pressure because of
change in density.

Example 1.2
A reservoir of oil has a mass of 825 kg. The reservoir has a
volume of 0.917 m3
. Compute the density, specific weight, and
specific gravity of the oil.
Solution:


A.N.KHUDAIWALA
3
/900
917.0
825
mkg
m
volume
mass
oil ==
∀
==ρ
3
oil m/N882981.9x900g
mg
volume
weight
==ρ=
∀
==γ
9.0
998
900
@
===
STPw
oil
oilSG
ρ
ρ

Surface Tension
Surface tension coefficient s can be defined as the intensity of
intermolecular traction per unit length along the free surface of a
fluid, and its SI unit is N/m.
The surface tension effect is caused by unbalanced cohesion
forces at fluid surfaces which produce a downward resultant force
which can physically seen as a membrane.
The coefficient is inversely proportional to temperature and is
also dependent on the type of the solid interface.

For example, a drop of water on a glass surface will have a
different coefficient from the similar amount of water on a wood
surface.

Surface Tension
The effect may be becoming significant for small fluid system such
as liquid level in a capillary, as depicted in Fig. 1.6, where it will
decide whether the interaction form by the fluid and the solid
surface is wetted or non-wetted.
If the adhesion of fluid molecules to the adjacent solid surface is
stronger than the intermolecular cohesion, the fluid is said to wet
on the surface. Otherwise, it is a non-wetted interaction.

Surface Tension
 The pressure inside a drop of fluid can be calculated using a free-body
diagram of a spherical shape of radius R cut in half, as shown in Fig. 1.7,
and the force developed around the edge of the cut sphere is 2πRσ.
 This force must be balance with the difference between the internal
pressure pi and the external pressure pe acting on the circular area of the
cut. Thus,
2πRσ = ∆pπR2
∆p = pi –pe =
2σ
R

Properties of Fluids
Density = ρ (decreases with rise in T)
 mass per unit volume ( lbs/ft3
or kg/m3
)
for water density = 1.94 slugs/ft3
or 1000 kg/m3
Specific Weight = γ (Heaviness of fluid)
 weight per unit volume γ = ρg
for water spec wt = 62.4 lbs/ft3
or 9.81 kN/m3
Specific Gravity = SG
 Ratio of the density of a fluid to the density of water
SG = ρf / ρw SG of Hg = 13.55

Differences between adhesive &
Cohesive
A distinction is usually made between an
adhesive force, which acts to hold two
separate bodies together (or to stick one
body to another) and a cohesive force,
which acts to hold together the like or
unlike atoms, ions, or molecules of a
single body.

Capillarity
Rise and fall of liquid in a capillary tube is caused by surface tension.
Capillarity depends on the relative magnitudes of the cohesion of the liquid to
walls of the containing vessel.
When the adhesive forces between liquid and solid are larger than the liquid's
cohesive forces, the meniscus in a small diameter tube will tend to be concave
If adhesive forces are smaller than cohesive forces the meniscus will tend to be
convex, for example mercury in glass.
water
mercury
concave
convex

Compressibility of Liquids
Compressibility is the change in volume due to
change in pressure.
The compressibility of liquid is inversely related to its
volume modulus of elasticity (also known as bulk
modulus).
Eν = - ν(dp/dν) = - (ν/dν)dp
Where; ν = Specific Volume.
(ν/dν) = Dimensionless
ratio

In most engineering problems, the bulk modulus at
or near atmospheric pressure is one of the interest.
The BULK MODULUS is a property of fluid.
And for liquids, is a function of temperature and
pressure.
Eν is directly related to temperature. It
minimum compressibility at this
temperature.

We often specify applied pressures in terms of
absolute terms, because atmospheric pressure varies.
Absolute pressure is the actual pressure on fluid
relative to absolute zero.
The standard atmospheric pressure at sea level is
about 14.7 psia or 101.3 kn/m2
abs or 1013 mb.

• Different behavior of liquids and gases to an increase of pressure.
Bulk modulus and the compressibility modulus
FLUID. Pressure
V
V
P
∆
∆
Β −=
The pressure due to a fluid pressing in on an object tends to compress the object.
The ratio of the increase in pressure ΔP to the fractional decrease in volume -
(ΔV/V) is called the bulk modulus.
Liquids and solids are relatively incompressible, they have large values of B.
On the other way, the density of liquid and solids is relatively constant with
pressure changes
Gases are easily compressed and the values of B are strongly dependent on
pressure changes. The density of gases depends strongly of pressure changes,
besides of changes in temperature.
The compressibility modulus is the
reciprocal of bulk modulus (1/B)

Vapour Pressure
Vapour pressure is the partial pressure produced by fluid vapour
in an open or a closed container, which reaches its saturated
condition or the transfer of fluid molecules is at equilibrium along
its free surface.
In a closed container, the vapour pressure is solely dependent on
temperature. In a saturated condition, any further reduction in
temperature or atmospheric pressure below its dew point will
lead to the formation of water droplets.
On the other hand, boiling occurs when the absolute fluid
pressure is reduced until it is lower than the vapour pressure of
the fluid at that temperature.
For a network of pipes, the pressure at a point can be lower than
the vapour pressure, for example, at the suction section of a
pump. Otherwise, vapour bubbles will start to form and this
phenomenon is termed as cavitation.

Basic Unit System & Units
Derived Units
There are many derived units all obtained from combination of the above
primary units. Those most used are shown in the table below:
The SI system consists of six primary units, from which
all quantities may be described but in fluid mechanics we
are generally only interested in the top four units from this
table.

Derived Units

Table summarizes these unit systems.

A.N.KHUDAIWALA (L.M.E) G.P.PBR

Fluid properties

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