INTRODUCTION TO FLUID DYNAMICS
With few exceptions, a material can be characterized as a fluid if it deforms
continuously under the action of shear stress. Conversely, a fluid at rest cannot have
a shearing stress.
For our applications, we will treat a fluid as a continuum even
though both liquids and gases are made up of molecules.
On a macroscopic scale,
fluid properties such as density, viscosity, etc. are continuous.
Intrinsic Fluid Properties
The intrinsic properties of a fluid are its: Density, Viscosity, Compressibility,
and Surface Tension.
We will discuss and define each one individually.
Density (
ρ
):
Density is defined as the mass per unit volume of a fluid and has units of
[M/L
3
].
In the MKS system, this would be represented by (kg/m
3
) or (g/cm
3
) in the
CGS system where 1 g/cm
3
= 10
3
kg/m
3
.
Values of density for several common
biofluids are:
ρ
water
=
999 kg / m
3
at 15
°
C
ρ
air
= 1.22 kg / m
3
at Standard atmospheric temperature and pressure
ρ
whole
= 1060 kg / m
3
at 20
°
C (6% higher than water)
blood
A related property of a fluid is its Specific Gravity, SG, which is defined as
its density divided by the density of water.
Thus, for whole blood, SG = 1.06.
Viscosity (
µ
):
As we said earlier, a fluid is defined as a material which deforms under the
action of a shear stress.
The viscosity of a fluid (or its ‘stickiness’) is related to the
amount of deformation that a fluid experiences when a shear stress is applied to it.
Just as with a solid, fluid shear stress is defined as a force per unit area applied
tangential to a surface and is denoted by
τ
.
To illustrate this, consider two parallel plates each of crosssectional area
A cm
2
, with fluid of viscosity
µ
between them as shown in Figure 1.
Figure 1. Fluid subjected to simple shearing stress.
1
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View Full DocumentIf a tangential force P is applied to the top plate as shown, it will result in
the plate moving with a velocity u cm/s relative to the lower plate. The fluid
adjacent to the top plate will move with the same velocity as that of the plate
since the fluid is assumed to stick to the plate (known as the ‘no slip’ condition).
Similarly, the fluid adjacent to the bottom plate will be at rest since it sticks to a
stationary surface.
Thus, a velocity gradient is produced within the fluid as
shown. The shearing force P divided by the area A over which it acts is defined
as the
shearing stress
,
τ,
having the units [ML
1
T
2]
. The velocity gradient, also
referred to as the
rate of shear
,
γ
±
,
is the ratio u/h where h is the distance
between the two parallel plates. The rate of shear thus has the dimensions of sec

1
.
In general, the rate of shear is defined as du/dy where y is the distance
perpendicular to the direction of shear as shown in the figure. The viscous
properties of all fluids are defined by the relationship between the shear stress
and rate of shear over a range of shear rates.
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 Spring '12
 prof.sumanchakrobarty
 Fluid Dynamics, Shear, Stress

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