Physical Concepts and Basic Fluid Mechanics
vlAl
=
v2A2
69
(3.3.24)
In general,
A1>>A2
and VI<<V~
and assume p1=p2, we have
This results in the Torricelli’s equation describing the velocity speed
of
flow leaving the orifice. Substituting v
=
v2, we obtain
(3.3.26)
The amount
of
flow leaving the orifice with circular cross section
of
radius r is therefore,
Q
=
m2v
=
m2d-
(3.3.27)
3.3.4
The Gorlin Equation
A
popular equation that has been used in the clinical applications is the
Gorlin equation describing the orifice cross-section area. The equation
is
used in calculating valvular cross-sectional area, particularly during
valvular stenostic conditions. The orifice cross-sectional area is given by:
(3.3.28)
Q
1
where
K,
is the contraction coefficient or the ratio
of
the cross-sectional
area of orifice flow jet to the actual opening
of
the orifice
K,
=
A,/A
(3.3.29)
3.3.5
Flow
and
Flow
Acceleration
The Cartesian coordinates in three dimensions, in the x-axis, y-axis and
z-axis together with time is usually represented as:
