II. Properties of II. Properties of FluidsFluids
ContentsContents
1.1. Definition of FluidsDefinition of Fluids
2.2. Continuum HypothesisContinuum Hypothesis
3.3. Density and CompressibilityDensity and Compressibility
4.4. ViscosityViscosity
5.5. Surface TensionSurface Tension
6.6. VaporizationVaporization
7.7. Forces Acting on FluidsForces Acting on Fluids
1. Definition of Fluids1. Definition of Fluids
Definition of FluidsDefinition of Fluids
A fluid is a substance that deforms
continuously when subjected to a shear stress, no
matter how small that the shear stress may be
Flows
Solid Fluid
Fixed Plate
F U
Fluid
Definition of FluidsDefinition of Fluids
A fluid is a substance that cannot support
any shear stress in static state
Fluids
Liquids (water)
Gases (air)
Classification of FluidsClassification of Fluids
Liquids and GasesLiquids and Gases
Liquid has definite volume;
gas has no definite volume.
2. Continuum Hypothesis2. Continuum Hypothesis
The Sensitive VolumeThe Sensitive Volume
The minimal volume in which the
number of fluid molecule is big
enough so that the average of any
physical quantity over this volume is
essentially independent of the volume
itself
V
B
V 0
Physical quantity
Sensitive volume
Micro effect
Macro effect
The Sensitive VolumeThe Sensitive Volume
FACT: There are 2.71016
molecules in 1 mm3 air of 0 C at 1
atm
The sensitive volume is usually
very small (infinitesimally small)
from a macroscopic view
Fluid ParticleFluid Particle
A mass of fluid that has a
spatial dimension equivalent
to the sensitive volume
Mathematical point of view:
Fluid particle = Moving point
with no size
with no
orientation
Continuum HypothesisContinuum Hypothesis
At any point in a fluid we can find a
fluid particle which occupies that
point
The fluid is a continuum
formed by fluid particles
3. Density and Compressibility3. Density and Compressibility
DensityDensity
Vm 0
limV
mV
rD ®
D=
D
DensityDensity
Density is the mass per unit
volume
Unit: kg / m3
Specific WeightSpecific Weight
Unit: N / m3
W mg=
gg r=
( )29.8m sg =
Specific VolumeSpecific Volume
1v
r=
Specific Volume is the volume
occupied by a unit mass of fluid
Compressibility of FluidCompressibility of Fluid
vp K
vD
D = -
pK
vvD
= -D
(Bulk modulus)
Compressibility of WaterCompressibility of Water
0
0. 5
1
1. 5
2
2. 5
3
0 10 20 30 40 50 60 70 80 90 100
K
T
910´
Incompressible FluidIncompressible Fluid
pK
vvD
= - ® ¥D
Incompressible FluidIncompressible Fluid
The bulk modulus of liquid is usually
very large, or the compressibility of
liquid is usually very small
Water can be assumed as
incompressible fluid in hydraulics
Incompressible FluidIncompressible Fluid
A fluid can be assumed to be
incompressible if the variation of
density within the flow is not large
Air can be assumed as
incompressible fluid when
velocity is much smaller than the
speed of sound
4. Viscosity 4. Viscosity
ViscosityViscosity
EXPERIMENTEXPERIMENT
A measurement on stickiness of
fluids
ViscosityViscosity
A measurement on the ability
of a fluid to resist shearing
F U
u
y
x
Fixed Plate
Moving Plate
Measured ResultsMeasured Results
The flow is nearly parallelThe flow is nearly parallel
The fluid near the lower plate does not moveThe fluid near the lower plate does not move
The fluid near the upper plate moves with the plateThe fluid near the upper plate moves with the plate
The velocity distribution in The velocity distribution in yy direction is linear direction is linear
F
UAd
µ
F U
u
y
x
ViscosityViscosity
F U duA dy
td
= µ =
dudy
t m=
Viscosity
Shear stress
Rate of strain
Udtd Udt
ViscosityViscosity
Coefficient of ViscosityCoefficient of Viscosity
Absolute ViscosityAbsolute Viscosity
Dynamic ViscosityDynamic Viscosity
du dyt
m=
Unit of : N s /
m2
Dynamic Viscosity of FluidsDynamic Viscosity of Fluids
Viscosity is a function of temperatureViscosity is a function of temperature
T
G a s e s
Liq
uid
s
Newtonian and Non-Newtonian FluidNewtonian and Non-Newtonian Fluid
I d e a l F l u id
N e w t o n i a n F l u i d
I de a
l Pl a
s ti c
N o n - Ne w
t o n i a n Fl u i d
Inviscid Fluid ( Inviscid Fluid ( ) )
The viscosity of water is very small
and may be omitted depends on the
problem of interest
Water can be assumed as
inviscid fluid in many
situations
Kinematic ViscosityKinematic Viscosity
mn
r=
Unit of : m2 / s
Kinematic Viscosity of FluidsKinematic Viscosity of Fluids
ProblemProblem
A journal bearing consists of a shaft and a sleeve as
shown in the following figure. The clearance space is filled
with oil. The sleeve is fixed. The shaft turns at a known
speed. Calculate the rate of heat generation at the
bearing.
Diameter of shaft: d (m)
Diameter of sleeve: d
(m)
Length of sleeve: l (m)
Viscosity of oil: (N s/m2)
Speed of shaft: n (rpm)Shaft
Sleeve
Oil
SolutionSolution
Angular velocity of the shaft:
Shear stress on the surface of the shaft:
Torque to keep rotation of the shaft:
Heat generation rate (= Power):
2 60nv p=
( )12 60
U d n dv pmt m m
d d d= = =
2 2 60T A n l dt mp d= =
( )2 3 2 1800 J sQ T n l dv mp d= =
5. Surface Tension 5. Surface Tension
Capillary RiseCapillary Rise
h
Surface TensionSurface Tension
= Surface tension per unit length
Unit of : N / m
6. Vaporization6. Vaporization
ICE
WATER VAPOR
Te m p e ra t u re
Pre
ss
ure
T P
C P
S o l i d L iq u i d
G a s
S u b l i m a t i o n
Va po r i za ti o
nFusio n
Vapor PressureVapor Pressure
hp
Water
Vapor
Vapor PressureVapor Pressure
0
2000
4000
6000
8000
10000
0 20 40 60 80 100
2kg m
Co
6. Forces Acting on Fluids6. Forces Acting on Fluids
Two Types of ForcesTwo Types of Forces
• Body forceBody force
Forces acting on fluid mass, e.g. gravity Forces acting on fluid mass, e.g. gravity
forceforce
• Surface forceSurface force
Contact force acting on fluid surfaceContact force acting on fluid surface
Description of Body ForceDescription of Body Force
Vm
0limV
Ff
mD ®
D=
D
rr
FDr
(Force per unit mass)
In case of gravity,
f gk= -r r
Description of Surface ForceDescription of Surface Force
0limA
nn
Pp
AD ®
D=
D
rr
Fr
(Force per unit area = Stress)
nPDr
nr
AD• Normal stress
• Shear Stress
END OF CHAPTER IIEND OF CHAPTER II