88
4
if r = 0 (velocity at the centre).
The velocity profile is given as
V V
r R
z =
−(
)




max
/
1
2
(4.24)
V
r R
z
= =
0 at
V V
r
z
= = max at
0
Then,
V
r R
V
z at =
(
)=
/
/ max
2 3 4
(4.25)
5 Drag Force—The other driving force in rheology is the drag
force (e.g. shear driven flow) that could be well understood
by the model of flow between parallel plates using a linear
coordinate system (x, y, z). The flow between parallel plates
is shown schematically in . Fig. 4.4. The width and
thickness of the plate are w and t, respectively.
The velocity profile for flow between parallel plates may be formulated as
V V
y H
z =
(
)
max
/
(4.26)
The volumetric flow rate for flow through a circular pipe using
Eq. 4.24 is given by
Q
R
P
L
=
∆
( )
π
η
4
32
(4.27)
where
5 Q = Volumetric flow rate
5 R = Radius of pipe
5 ∆P = Pressure difference
5 L = Length of Pipe
5 η = Viscosity of fluid
Flow
Stationary
L
H
V max = V Plate
y = H
y = 0
. Fig. 4.4 Flow between parallel plates
Chapter 4 · Rheology in Processing of Polymeric Composites