66
Dynamics
of
the
Vascular
System
This
is
sometimes referred to as the centerline velocity
or
axial velocity.
The velocity
is
zero at the vessel wall, when r=ri.
Equation
(3.3.10)
is that of a parabola, hence the velocity profile
across the vessel wall is
known
as a parabolic velocity profile. This is
shown
in
Fig.
3.3.2.
Fig.
3.3.2:
Illustration
of
the parabolic velocity profile. The velocity is maximal at
the
centerline and decreases progressively towards the vessel wall in a parabolic fashion.
The amount of flow,
or
volume flow, is obtained as,
which results in the well-known Poiseuille equation
(3.3.12)
(3.3.13)
The average velocity across the velocity profile is simply the amount
of
flow divide
by
the cross-sectional area
of
the vessel lumen, xr?,
(3.3.14)
