1. No category

Chapter 2: Fluid Properties
By
y
Dr Ali Jawarneh
1
Outline
In this chapter we will
• Discuss the following properties of a fluid:
– Density,
Density specific weight
weight, specific gravity
gravity.
– Specific heat, Internal energy and enthalpy.
• Present the equation of state
state.
• Discuss in detail the physical meaning of
viscosity, its definitions, variation, and
applications.
• Present newtonian versus Non-Newtonian
Fluids
• Discuss the properties of elasticity and surface
t
tension.
i
• Discuss the considerations of vapour pressure.
2
2.1: Basic Units
• SI (International system):
Length (m), time (s), temperature (K), work &
energy (J) or (N.m), Power (W) or (J/s).
• English system:
Mass: 1slug=14.59 kg, or Ibm=0.4536 kg, or 1
slug=32.2
slug
32.2 Ibm
Length: foot (ft)=30.48 cm
pound force {{Ibf}=4.448
}
N
Force: p
Temperature: Rankine{oR}=460+oF
)
T((oC)+32
)
T((oF)=1.8
3
2.2: System; Extensive & Intensive
Properties
• A system is defined as a given quantity of
matter.
• The total mass of a given system is constant,
since it always consists of the same matter.
• Extensive p
properties
p
are p
properties
p
related to
the total mass of the system,example: M, W.
properties
p
are p
properties
p
• Intensive p
independent of the amount of fluid, example: p,
T, ρ.
4
5
2.3: properties Involving the Mass or Weight of
the Fluid
- Mass Density, ρ
• The mass density (or simply density) is the
mass per unit volume.
• It is represented by the symbol (ρ) and has a
unit of kg/m3.
• Density of water at 4°C = 1000 kg/m3.
• Density of air at 20°C and standard pressure
= 1.2
1 2 kg/m3.
• Values densities of common fluids are given
in tables A.2 – A.5 in the textbook.
6
- Specific Weight
• The specific weight is simply the weight per
unit
nit volume.
ol me
• It is represented by the symbol (γ) and has a
unit of N/m3.
γ =ρ g
• The specific weight of water at 20°C = 9.79
9 79
kN/m3.
20°C
C and
• The specific weight of air at 20
standard pressure = 11.8 N/m3.
• See tables A-3 to A-5
7
- Specific Gravity
• Specific gravity is the ratio of the specific
weight
g of a given
g
fluid to the specific
p
weight
g
of water at a standard reference temperature.
p
gravity
g
y is represented
p
by
y the symbol
y
• Specific
(S) or sp.gr. or SG and is dimensionless.
γ fluid ρ fluid
S=
=
γ water ρ water
• At standard reference temp
p of 4 oC,,
γwater=9810 N/m3
8
- The Equation of State
• The equation of state for an ideal gas
can be
b expressed
d as:
p = ρ RT
• The value of (R) is the gas constant
which is characteristic of the gas itself.
• Values of (R) are given in Table A.2.
• Although
g no gas
g is ideal, most gases
g
that we deal with behave like ideal
gases.
9
Variation of Density
y
10
Density {at standard atm press and
15 oC,
C Table A
A-2}
2}
11
Density
y (Air)
( ) {{Table A.3}}
12
Density
y ((Water,, Table A.5))
13
2.4: Properties Involving the Flow of Heat
- Specific Heat
• The specific heat (c) is the amount of thermal
energ that must
energy
m st be transferred to a unit
nit
mass of a substance to raise its temperature
by
y one degree.
g
• It is a measure of the capacity of a substance
to store thermal energy.
• It is given in units of J/kg.K.
• Specific heat can be given at constant
pressure (cp)or
) att constant
t t volume
l
(cv).
)
• The ratio cp/cv.is given by the symbol (k) and
is always constant for a given gas
gas.
14
- Specific Internal Energy
• The specific internal energy (u) is the energy
that a substance possesses per unit mass
because of the state of the molecular activity
in the substance
substance.
- Specific Enthalpy
• Specific
S
ifi enthalpy
th l (h) iis given
i
as h=
h u + p/ρ
/
• Both of u and h are given in J/kg.
• For
F an ideal
id l gas u and
d h are function
f
ti
off
temperature alone.
15
2.5: Viscosity
• A fl
fluid
id is
i a substance
b t
that
th t deforms
d f
continuously when subjected to a
shear stress
stress.
• Shear stress in a viscous fluid is
proportional to the time rate of the of
strain as follows:
dV
τ =μ
dy
• τ: shear
h
stress,
t
μ: dynamic
d
i viscosity,
i
it
dV/dy: velocity gradient, or time rate of
strain or shear strain
strain,
16
Viscosity
y
• μ is the viscosity of the fluid, referred to at
times as dynamic viscosity or absolute
viscosity.
• It is basically defined as the ratio of the
yg
gradient.
shear stress to the velocity
• Thus, the unit used for viscosity is: N.s/m2
• Another unit used for the viscosity is the
poise, which is 0.1 N.s/m2.
17
Viscosity
y
• Viscosity and density are inter-related in
many equations used in fluid mechanics.
• The quantity μ/ρ is commonly used and
y ((ν).
)
termed the kinematic viscosity
ν= μ/ρ
• The units of the kinematic viscosity are
m2/s.
18
Viscosity
y
• The velocity distribution in a fluid near a
boundary can be given as follows:
19
Viscosity
y
• The previous distribution implies the
following:
– The velocity
y of the fluid is zero at the
boundary (no-slip condition).
– The velocity gradient at the boundary is
finite.
– The velocity gradient becomes less steep
with distance from the boundary; the
maximum shear stress is at the boundary.
20
Viscosity
y
• The viscosity of a gas increases with
temperature as given by the
Sutherland’s equation:
μ ⎛T ⎞
= ⎜⎜ ⎟⎟
μo ⎝ To ⎠
3/ 2
To + S
T +S
• The value of (S) is characteristic of the
gas itself
itself. Values of (S) are given for
different gases in table A.2
21
Viscosity
y
• In contrast, the viscosity of a liquid
decreases with temperature, according to the
equation:
b /T
μ = Ce
• Where C and b are empirical constants
determined from at least two data points.
• The
Th variation
i ti off viscosity
i
it (dynamic
(d
i and
d
kinematic) for different fluids are given in
figures A.2
A 2 and A.3.
A3
22
23
Dynamic or absolute Viscosity
{Fig A 2}
{Fig.A.2}
24
Kinematic Viscosity
y {{Fig.
g A.3}}
25
Example: Two plates are separated by 1/4 inch
space. The lo
space
lower
er plate is stationar
stationary, the upper
pper
plate moves at a velocity of 10 ft/s. Oil (SAE
10W-30
10W
30, 150 oF) which fills the space
space. The
variation in velocity of the oil is linear. What is
the shear stress in the oil?
26
Solution:
From Figure A.2: μ = 5 .2 x 10 −4 Ib.s/ft 2
dV ΔV
10
=
=
= 480
dy
Δy ( 1 / 4 ) / 12
dV
τ=μ
= 5 .2 x 10
0 − 4 x 480
80 = 0 .250
50 Ib/ft
b/ft 2
dy
Another way to find dV/dy since the relation is linear:
V=a y+b
@y=0, V=0
@y
0=0+b
b=0
@y=(1/4)/12, V=10
10=a [(1/4)/12]+0
a=480
dV/dy=480
y
V=480 y
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Example: A block weighing 1 kN and having
dimensions 200 mm on an edge is allo
allowable
able to
slide down an incline on a film of oil having a
thickness of 0.005
0 005 mm.
mm If we use a linear
velocity profile in the oil. What is the terminal
speed
p
of the block. The viscosity
y of the oil is
7x10-3 N.s/m2
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Solution:
μ = 7 x10 −3 N.s/m 2
W sin 20o = Fshear
τ =μ
dV
dy
dV
VT
=
= 200 000VT
dy ( 0.005 / 1000 )
τ = 1400VT
Fshear
200 200
= τ A = 1400VT )(
x
) = 56VT
1000 1000
W sin 20o = Fshear
1 x1000 x sin 20o = 56 VT
VT = 6 .11 m/s
29
Viscosity
y
- Newtonian versus Non-Newtonian Fluids
• Not in all fluids,, the relationship
p between the
shear stress and the rate of strain is directly
proportional, as discussed earlier.
• In some fluids, these relationship is not
directly proportional. These are called “nonN
Newtonian”
i ” fluids.
fl id
• Examples of non-Newtonian fluids are shearthi i [ paints,
thinning[
i t ink],
i k] shear
h
thickening
thi k i
[mixture of glass particles in water, and
Bingham plastic [toothpaste].
[toothpaste]
30
Viscosity
y
31
2.6: Elasticity
• Elasticity (also often called compressibility)
of the fluid
fl id is related to the amo
amount
nt of
deformation (expansion or contraction) for a
given pressure
g
p
change,
g , quantitatively
q
y
described by the bulk modulus of elasticity
Eν :
dp
dp
Eν =
=−
dρ ρ
dV V
• Th
The bulk
b lk modulus
d l off water
t is
i around
d 2.2
22
GN/m2, corresponding to a change of 0.05%
in volume for a change
g of 1 MPa.
32
Elasticity
y
• The elasticity of an ideal gas is
proportional to pressure.
• For an isothermal process:
p
Eν = ρ R T = p
• For and adiabatic process:
Eν =
cp
cv
p
33
2.7- Surface Tension, σ
• Theory of molecular attraction: molecules of
liquid below the surface act on each other by
f
forces
th
thatt are equall in
i all
ll direction.
di
ti
However, molecules near the surface have a
greater attraction for each other than they
g
y do
for molecules below the surface.
• This produces in effect a surface on the
liquid where each portion exerts tension on
adjacent portions.
• Surface
S f
tension
t
i (σ)
( ) is
i usually
ll referred
f
d to
t in
i
units of N/m.
• At room temperature,
p
, surface tension for a
water-air surface is 0.073 N/m.
34
Capillary Action:
• Th
The phenomenon
h
off capillary
ill
effect
ff t can be
b
explained microscopically by considering cohesive
forces ((forces between like molecules,, such as
water & water) and adhesive forces (forces
between unlike molecules such as water & glass).
The liquid
liq id molecules
molec les at solid-liquid
solid liq id interface are
subjected to both cohesive & adhesive forces. The
relative magnitude
g
determine whether a liquid
q
wets a solid surface or not. Obviously, the water
molecules are more strongly attracted to the glass
molecules than they are to other water molecules,
molecules
and thus water tends to rise along the glass
surface. The opposite occurs for mercury, which
causes the liquid surface near the glass wall to
35
suppressed.
36
2.8: Vapour Pressure
• Vapour pressure is the pressure at which a
liq id will
liquid
ill boil.
boil
• The vapour pressure increases with
temperature.
temperature
• When the temperature of a liquid increases,
its vapour pressure increases to the point at
which it is equal to atmospheric pressure,
and thus boiling occurs.
• Similarly, boiling can occur at low
temperatures if the pressure in the liquid is
decreased to its vapour pressure
pressure.
37
Vapour
p
Pressure
• The effect of vapour pressure can be noticed
in flowing liquids when vapour bubbles start
growing in local regions of very low pressure
and collapse in regions of high pressure.
This phenomenon is known as cavitation.
38
Cavitation
• As these bubbles
move to the higher
pressure region they
collapse.
collapse
• This can cause
excessive intermittent
pressures that can
cause severe damage
g
to moving parts.
39