72
Dynamics
of
the
Vascular System
(3.3.34)
av
av
avwavw
at
az
dr
r 88
r2
a
=-+u-+v-+----
aw
aw
aw
waw vw
a,
=-+u-+v-+--+-
at
dz
dr
r
88
r
These partial derivatives of velocities other than the first terms are
sometimes known as convective accelerations. Notice that acceleration
at a particular instant in time when
z,
r and
0,
are kept constant (i.e.
velocities do not change with
z,
r and
0)
,
one obtains the familiar
equations for acceleration:
dU
a,
=-
at
av
a,
=-
at
(3.3.35)
aw
a,
=-
at
3.3.6 Newtonian Fluid, No-Slip, Boundary Conditions and Entry
Length
3.3.6.1
Newtonian Fluid
The coefficient of viscosity of blood as we have shown earlier, is defined
as the ratio of applied pressure to the velocity gradient. In other words, it
is the shear stress that represents the resisting force of the fluid
deformation along the direction of flow:
dv
z,
=
q-
dz
(3.3.36)
Fluid that behaves in this manner is known as the Newtonian fluid,
attributed to its originator, Newton.
This assumes that the rate
of