Biomedical Engineering Reference
In-Depth Information
FIGURE 2-58
Flow through an
inclined tapered
pipe.
FIGURE 2-59
Using a restriction in
a piece of pipe to
measure flow.
and the conservation of mass requires that
v
1
A
1
ρ
=
v
2
A
2
ρ
(2.61)
Rearranging and substituting for
v
2
in equation (2.61) gives the volumetric flow rate,
Q
,
in terms of the drop in pressure across the restriction in the pipeline
2
(
p
1
−
p
2
)
ρ
A
2
Q
=
v
1
A
1
=
(2.62)
A
2
A
1
2
1
−
The assumption of incompressibility is reasonable for a liquid but not a gas, but the
assumption that the fluid has no viscosity, resulting in a flat velocity profile, is generally
not justified. This requires the application of correction factors to compensate.
The orifice plate, shown in Figure 2-60b, is the simplest and cheapest type of differ-
ential pressure flowmeter. It is simply a plate with a hole of the specified diameter that is
clamped into the pipe. Unfortunately, after passing through the plate the jet continues to
contract until it reaches a minimum diameter before expanding again. Because
A
2
should
be this diameter, which is unknown, correction factors must be applied to equation (2.62).
This modified equation is
4
ε
4
d
2
2
C
(
p
1
−
p
2
)
Q
=
1
(2.63)
ρ
−
β
