Physical Concepts and Basic Fluid Mechanics
75
3.3.6.4
Entry Length
Entry length is defined as the distance from the entrance or inlet
of
a
vessel
at
which point the flow is fully developed.
In
the case of
Poiseuille flow, this means that the centerline velocity reaches its
maximum with the velocity profile becomes fully parabolic.
But
Poiseuille flow assumes
a
tube that is long enough for such flow to
occur.
However, under pulsatile flow conditions, flow does not fully
develop and hence the accuracy in the determination of entry length
becomes an issue. This is normally circumvented by assuming that the
flow is almost fully developed in analyzing flow in blood vessels.
A
common criterion that
is
used assumes that the centerline velocity is
within
1
or
2%
of the centerline velocity according to Poiseuille’s flow,
i.e.
98%
or
99%.
The determined entry length is of course determined also by the
manner in which flow enters the vessel.
A
general rule of thumb used
follows the following formulation:
=0.O4Re
1
d
-
(3.3.39)
This assumes that the entry length
1,
in a vessel of diameter d
as
a flow
with uniform velocity v.
R,
is Reynolds number, as defined above.
Because
of
the finite geometry of the vascular segments, i.e. finite
length
and
diameter, there are situation where the entry
length
requirement for an almost fully developed flow is not met. Thus, flow is
frequently accepted as partially developed.
A
lower Reynolds number,
such as those occurring
at
smaller vessels, with much smaller lumen
diameters, the requirement
of
the entry length becomes much less
stringent.
