68
Dynamics
of the
Vascular System
associated with the pre-stenotic section, with
p=hpg
due to gravity or
static pressure difference.
We have also, for the stenotic section:
(3.3.20)
From the conservation of energy, equating these
2
equations, we have
For the case when gravity is ignored or when hl=h2, we have the familiar
Bernoulli equation
122
P1
=P2+-P(vI
-v2
)
2
(3.3.22)
The commonly known phrase that the faster the
flow
velocity, the lower
the pressure, i.e. v2>v1, then p2<p1. This
is
cIearIy seen from the
illustration in the figure. The well-known Bernoulli equation described
above is for
a
steady, inviscid (non-viscous) and incompressible fluid
flow.
3.3.3
Orifice
Flow
and
Torricelli’s Equation
The problem of flow through an orifice small in dimension compared
with the reservoir was considered by Torricelli in the
17’
century. The
pressure and velocity at the surface of the reservoir are p1 and v1 and
those at the orifice are p2 and
v2,
respectively.
We have for the
velocities,
(3.3.23)
From continuity equation that flow entering equals flow leaving, we have