II. Properties of Fluids
Contents
1.
Definition of Fluids
2.
Continuum Hypothesis
3.
Density and Compressibility
4.
Viscosity
5.
Surface Tension
6.
Vaporization
7.
Forces Acting on Fluids
1. Definition of Fluids
Definition of Fluids
Flows
A fluid is a substance that deforms continuously
when subjected to a shear stress, no matter how
small that the shear stress may be
Solid
Fluid
F
Fluid
Fixed Plate
U
Definition of Fluids
A fluid is a substance that cannot support
any shear stress in static state
Classification of Fluids
Liquids
(water)
Fluids
Gases
(air)
Liquids and Gases
Liquid has definite volume;
gas has no definite volume.
2. Continuum Hypothesis
The 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
Physical quantity
B
Micro effect
Macro effect
Sensitive volume
V0
V
The Sensitive Volume
FACT: There are 2.71016 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 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 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 Compressibility
Density
V
m
Dm
r = lim
DV ® 0 D V
Density
Density is the mass per unit volume
Unit:
kg / m3
Specific Weight
W = mg
(g =
9.8 m s2 )
g = rg
Unit: N / m3
Specific Volume
Specific Volume is the volume occupied by a unit
mass of fluid
1
v =
r
Compressibility of Fluid
Dv
Dp = - K
v
Dp
K = Dv v
(Bulk modulus)
Compressibility of Water
´ 109
3
2.5
2
K
1.5
1
0.5
0
0
10
20
30
40
50
T
60
70
80
90
100
Incompressible Fluid
Dp
K = ® ¥
Dv v
Incompressible 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 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
Viscosity
A measurement on stickiness of fluids
EXPERIMENT
Viscosity
A measurement on the ability of a fluid
to resist shearing
y
F
U

Moving Plate
u
Fixed Plate
x
y
F
Measured Results

U
u

The flow is nearly parallel

The fluid near the lower plate does not move

The fluid near the upper plate moves with the plate

The velocity distribution in y direction is linear

Fd
U µ
A
x
Viscosity
F
U
du
t =
µ
=
A
d
dy
Shear stress
du
t = m
dy
Viscosity
Rate of strain
Udt
d
Udt
t
m=
du dy
Viscosity
Coefficient of Viscosity
Absolute Viscosity
Dynamic Viscosity
Unit of m :
N  s / m2
Dynamic Viscosity of Fluids
Viscosity is a function of temperature
Li
qu
id
s
m
G as es
T
Id

ea
lP
la
st
ic
Newtonian and Non-Newtonian Fluid
N
n
o
N
ew
n
o
t
i
an
F
i
lu
d
lu
F
ian
n
o
wt
e
N
id
Ideal Fluid

Inviscid Fluid ( m = 0 )
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 Viscosity
m
n =
r
Unit of n :
m2 / s
Kinematic Viscosity of Fluids
Problem
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.
Oil
Diameter of shaft: d (m)
Diameter of sleeve: d +  (m)
Sleeve
Length of sleeve: l (m)
Viscosity of oil: m (N  s/m2)
Speed of shaft: n (rpm)
Shaft
Solution

Angular velocity of the shaft:
v = 2pn 60

Shear stress on the surface of the shaft:
U
v d 1 n pmd
t = m = m
=
d
2 d
60d
( )

Torque to keep rotation of the shaft:
T = t A = n ml p 2d 2 60d

Heat generation rate (= Power):
Q = T v = n 2 ml p 3d 2 1800d
(J s )
5. Surface Tension
Capillary Rise

h
Surface Tension
 = Surface tension per unit length
Unit of  : N / m
6. Vaporization
ICE
WATER
VAPOR
F u s io n
n
io
at
po
r iz
Liq u i d
S o l id
Va
Pre s s u re
CP
Ga s
TP
S u b lim a tio
n
Te m p e ra t u re
Vapor Pressure
Vapor
Water
p
h
Vapor Pressure
kg m 2
10000
8000
6000
4000
2000
0
0
20
40
60
80
100
o
C
6. Forces Acting on Fluids
Two Types of Forces
•
Body force

•
Forces acting on fluid mass, e.g. gravity force
Surface force

Contact force acting on fluid surface
Description of Body Force
r
r
DF
f = lim
DV ® 0 D m
V
m
(Force per unit mass)
r
DF
In case of gravity,
r
r
f = - gk
Description of Surface Force
r
r
D Pn
pn = lim
DA ® 0 D A
(Force per unit area = Stress)
r
DA F
r
n
r
D Pn
• Normal stress
• Shear Stress
END OF CHAPTER II