Section 4–3 / Pneumatic Systems 107
Resistance
R
Capacitance
C
(a) (b)
P+pi
P+po
0 q
q dq
DP
Slope=R
Figure 4–4 d(DP)
(a) Schematic
diagram of a
pressure system;
(b) pressure-
difference-versus-
flow-rate curve.
fundamental principles, rather than on the details of the operation of the actual
mechanisms.
Pneumatic Systems. The past decades have seen a great development in low-
pressure pneumatic controllers for industrial control systems, and today they are used
extensively in industrial processes. Reasons for their broad appeal include an explosion-
proof character, simplicity, and ease of maintenance.
Resistance and Capacitance of Pressure Systems. Many industrial processes
and pneumatic controllers involve the flow of a gas or air through connected pipelines
and pressure vessels.
Consider the pressure system shown in Figure 4–4(a). The gas flow through the
restriction is a function of the gas pressure difference pi-po. Such a pressure system
may be characterized in terms of a resistance and a capacitance.
The gas flow resistance Rmay be defined as follows:
or
(4–8)
where is a small change in the gas pressure difference and dqis a small change
in the gas flow rate. Computation of the value of the gas flow resistance Rmay be quite
time consuming. Experimentally, however, it can be easily determined from a plot of
the pressure difference versus flow rate by calculating the slope of the curve at a given
operating condition, as shown in Figure 4–4(b).
The capacitance of the pressure vessel may be defined by
or
C= (4–9)
dm
dp
=V
dr
dp
C=
change in gas stored, lb
change in gas pressure, lbfft^2
d(¢P)
R=
d(¢P)
dq
R=
change in gas pressure difference, lbfft^2
change in gas flow rate, lbsec
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