Chris Landis
Valve/Vacuum Product
Manager
Parker Hannifin Corp.
Richland, Mich.
In recent years, much discussion
has centered on Cv ratings (also
known as capacity coefficients
or flow factors) and whether or
not American, European, and
Japanese pneumatic-valve manufacturers
rate valves the same
way. With ANSI/NFPA, ISO, and
JIS organizations all specifying
slightly different test methods
and rating criteria, the confusion
is understandable.
Leaving that ongoing discussion
to the respective standards
organizations, here’s a look at the
practical aspects of designing the
most efficient and economical
system without under or oversizing
components. First, we’ll calculate
Cvs for standard pneumatic
cylinders and examine Cv values
for standard ISO valves, including
18 and 26 mm and ISO Sizes
1, 2, and 3. We’ll also chart average
rod speed relative to cylinder
bore size to pinpoint ISO valves
that best match flow demands.
The approach is based on standard Cv calculations:
| Cv= |
Q |
√ |
GT |
22.48 |
(P1-P2)P2 |
where Q = volumetric flow rate
in standard cubic feet per minute
(scfm), based on 14.7-psi atmospheric
pressure and 60°F air
temperature.
To simplify the equation, experts
typically assume a conservative
pressure change between
inlet and outlet ports (P1 – P2) of
5 psi. For time or process-critical
applications, reduce this to 2 psi.
And, in many cases, a pressure
drop of 10 psi is not detrimental
to the application. A 10-psi pressure
drop permits smaller valves
that lower costs and require less
mounting space.
To simplify calculations, let’s
tabulate values for a portion of the equation for 2, 5, and 10-psi
pressure changes. Here, we create
a constant A, defined as
| A= |
1 |
√ |
GT |
22.48 |
(P1-P2)P2 |
and list values for varying inlet
gage pressures in the accompanying
Basic Data table.
This reduces the flow-coefficient
equation to Cv = QA. In terms
of cylinder volume and time,
where atmospheric
pressure, Pa, is assumed
to be 14.7 psi.
Next, calculate values for compression
ratio, Cr = P1/Pa, for various
inlet pressures and also list
values in the Basic Data table.
Restating the volumetric flowrate
equation in terms of compression
ratio results in
Now examine the impact
of cylinder volume and stroke time for known Cv values of ISO
valves. Given that Cv = QA; and V =
(π/4)d2l, we can restate the equation
as:
| Cv= |
( |
(π/4)CrA |
)( |
l |
) |
(d2) |
28.8 |
t |
Here, l/t is a simplified representation
of average rod velocity
in inches per second.
This equation works well for
NFPA cylinders. But because designers
usually specify ISO cylinders
in metric units, apply the
conversion factor 1 in. = 25.4 mm
and revise the equation:
| Cv= |
( |
(π/4)CrA |
)( |
l |
) |
(d2) |
28.8(25.4)3 |
t |
Assuming 80 psig for inlet
pressure — based on a typical
plant operating at 100 psig with
line losses — and using a conservative
5-psi pressure drop
for the constant A, chart average
cylinder rod speed versus
cylinder diameter in terms of
required Cv. The accompanying
tables for two and threeposition
valves highlight areas
where each ISO valve meets Cv
requirements.
Nomenclature
d = Cylinder
diameter, in.
G = Specific gravity
of the fluid (G = 1
for air)
l = Cylinder length,
in.
P1= Absolute pressure
at inlet port
(gage pressure +
14.7), psi
P2 = Absolute
pressure at outlet
port, psi
Pa = Atmospheric
pressure, psi
Q = Volumetric flow
rate, scfm
T = Absolute
temperature
of air, °R
t = Time to fill
cylinder, sec
V = Cylinder
volume, in.3 |