Biomedical Engineering Reference
In-Depth Information
FIGURE 2.3
Distribution of dimensionless velocity according to
Table 2.2
(y*
¼
y/a, z*
¼
z/a): (a) circle; (b) ellipse (a
¼
2b);
(c) concentric annulus (a
¼
2b); and (d) rectangle (a
¼
2b).
the typical sol
ut
ion of the distribution of the dimensionless velocity
u
ð
y
;
z
Þ¼
u
ð
y
;
z
Þ=
u
and the
mean velocity
u
in the channel.
Many micromachining technologies result in microchannels with a rectangular cross section. The
following examples investigate the flows of a single phase as well as multiple phases in rectangular
microchannels.
Example 2.3
(
Single-phase flow in a rectangular microchannel
). A liquid flow in a rectangular
microchannel of width
W
and height
H
. The viscosity of the liquid is
m
. Determine the velocity
distribution in this microchannel and the flow rate if a pressure difference of
D
p
is applied across the
channel length of
L
.
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