Physical Concepts and Basic Fluid Mechanics
67
3.3.2
Bernoulli’s Equation and Narrowing Vessel
Lumen
For a vessel with a narrowed segment or stenosis, as shown in Fig.
3.3.3,
the total volume flow through all segments must be the same, by the
conservation
of
mass. The
flow
is
given by the product
of
the cross-
sectional area and the flow velocity:
Q
=
A,v,
=
A2v2
=
A3v3
(3.3.15)
Fig. 3.3.3:
A
cylindrical vessel with
a
narrowed segment
or
stenosis.
The familiar kinetic energy equation
is
given as
1
2
K.E.
=
-mv2
and the corresponding potential energy is
P.E.
=
pQ
The total energy
is
their sum:
W
=
P.E.+
K.E.
This gives rise to
(3.3.16)
(3.3.17)
(3.3.18)
(3.3.1
9)
