Changes in gas density directly related to changes in pressure and
temperature through following equation
Ideal or perfect gas law or the equation of state for an ideal gas
Where
p is absolute pressure (it is a measured relative to absolute zero pressure;
a pressure that would only occur in a perfect vacuum; standard sea
level atmospheric pressure is 14.696 psi (abs) or 101.33 kPa (abs))
density,
T the absolute temperature and
R is a gas constant
RT
p
51
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Viscosity: another very significant property
Viscosity is a measure of a fluid's resistance to flow
Newtonian
Fluids:
A fluid
that
behaves
according
to
Newton's law, with a viscosity
μ
(absolute or dynamic or
simply viscosity)
that is independent of the stress, is said to
be Newtonian.
Gases, water and many common liquids can be considered
Newtonian in ordinary conditions and contexts.
Most of the common fluids (water, air, oil, etc.)
Also called
“
Linear
”
fluids
52
Viscosity contd
…
NonNewtonian Fluids:
There are many fluids that
significantly deviate from that law in some way or
other. For example:
Special fluids (e.g., most biological fluids, toothpaste, some paints, etc.)
Also called “Non

linear” fluids
53
Viscosity
Kinematic viscosity
,
Shear thinning fluids
–
the apparent viscosity decreases
with increasing shear rate; the harder the fluid is sheared,
the less viscous it becomes.
Examples

many
colloidal
suspensions
and
polymer
solutions are shear thinning. For example, latex paint does
not drip from the brush because the shear rate is small and
the apparent viscosity is large. However, it flows smoothly
onto the wall because the thin layer of paint between the
wall and the brush causes a large shear rate and a small
apparent viscosity.
54
Viscosity
Shear thickening fluids
–
the apparent viscosity increases
with increasing shear rate; the harder the fluid is sheared,
the more viscous it becomes
Examples 
watercorn starch mixture and watersand
mixture (quicksand). Thus, the difficulty in removing an
object from quicksand increases dramatically as the speed
of removal increases
Bingham plastic
–
neither a fluid nor a solid; such
material can withstand a finite shear stress without motion,
but once the yield stress is exceeded it flows like a fluid
Examples
–
toothpaste and mayonnaise
55
Characteristic of Real Fluid in presence of a
solid boundary
56
Real fluids, even though
they
may
be
moving,
always
“
stick
”
to
the
solid
boundaries
that
contain them.
THIS IS KNOWN AS
NOSLIP CONDITION
Compressibility of fluids
57
Bulk modulus.
Compression and expansion of gases.
Speed of sound.
Compressibility of fluids
Bulk
Modulus (
):
How compressible is the fluid?
Change in volume (or density) of a fluid with change
in pressure
Since decrease in volume of a given mass, (
)
will result in an increase in density. Thus, we can
write
The bulk modulus (also referred to as the bulk
modulus of elasticity) has dimensions of pressure
(FL
2
) [lb/in
2
or psi; N/m
2
or Pa]
/
d
dp
E
v
m
/
d
dp
E
v
58
v
E
Compression and Expansion of Gases