Valve Sizing Calculations (Traditional Method)
626
Te c h n i c a l
Introduction
Fisher® regulators and valves have traditionally been sized using
equations derived by the company. There are now standardized
calculations that are becoming accepted worldwide. Some product
literature continues to demonstrate the traditional method, but
the trend is to adopt the standardized method. Therefore, both
methods are covered in this application guide.
Improper valve sizing can be both expensive and inconvenient.
A valve that is too small will not pass the required ow, and
the process will be starved. An oversized valve will be more
expensive, and it may lead to instability and other problems.
The days of selecting a valve based upon the size of the pipeline
are gone. Selecting the correct valve size for a given application
requires a knowledge of process conditions that the valve will
actually see in service. The technique for using this information
to size the valve is based upon a combination of theory
and experimentation.
Sizing for Liquid Service
Using the principle of conservation of energy, Daniel Bernoulli
found that as a liquid ows through an orice, the square of the
uid velocity is directly proportional to the pressure differential
across the orice and inversely proportional to the specic gravity
of the uid. The greater the pressure differential, the higher the
velocity; the greater the density, the lower the velocity. The
volume ow rate for liquids can be calculated by multiplying the
uid velocity times the ow area.
By taking into account units of measurement, the proportionality
relationship previously mentioned, energy losses due to friction
and turbulence, and varying discharge coefcients for various
types of orices (or valve bodies), a basic liquid sizing equation
can be written as follows
where:
Q = Capacity in gallons per minute
Cv = Valve sizing coefcient determined experimentally for
each style and size of valve, using water at standard
conditions as the test uid
∆P = Pressure differential in psi
G = Specic gravity of uid (water at 60°F = 1.0000)
Thus, Cv is numerically equal to the number of U.S. gallons of
water at 60°F that will ow through the valve in one minute when
the pressure differential across the valve is one pound per square
inch. Cv varies with both size and style of valve, but provides an
index for comparing liquid capacities of different valves under a
standard set of conditions.
Q = CV ∆P / G
(1)
∆P ORIFICE
METER
FLOW
INLET VALVE TEST VALVE LOAD VALVE
Figure 1. Standard FCI Test Piping for Cv Measurement
To aid in establishing uniform measurement of liquid ow capacity
coefcients (Cv) among valve manufacturers, the Fluid Controls
Institute (FCI) developed a standard test piping arrangement,
shown in Figure 1. Using such a piping arrangement, most
valve manufacturers develop and publish Cv information for
their products, making it relatively easy to compare capacities of
competitive products.
To calculate the expected Cv for a valve controlling water or other
liquids that behave like water, the basic liquid sizing equation
above can be re-written as follows
CV = Q
G
(2)
∆P
PRESSURE
INDICATORS
Viscosity Corrections
Viscous conditions can result in signicant sizing errors in using
the basic liquid sizing equation, since published Cv values are
based on test data using water as the ow medium. Although the
majority of valve applications will involve uids where viscosity
corrections can be ignored, or where the corrections are relatively
small, uid viscosity should be considered in each valve selection.
Emerson Process Management has developed a nomograph
(Figure 2) that provides a viscosity correction factor (Fv). It can
be applied to the standard Cv coefcient to determine a corrected
coefcient (Cvr) for viscous applications.
Finding Valve Size
Using the Cv determined by the basic liquid sizing equation and
the ow and viscosity conditions, a uid Reynolds number can be
found by using the nomograph in Figure 2. The graph of Reynolds
number vs. viscosity correction factor (Fv) is used to determine
the correction factor needed. (If the Reynolds number is greater
than 3500, the correction will be ten percent or less.) The actual
required Cv (Cvr) is found by the equation:
C
From the valve manufacturer’s published liquid capacity
information, select a valve having a Cv equal to or higher than the
required coefcient (Cvr) found by the equation above.
= FV CV (3)
vr
627
Te c h n i c a l
Valve Sizing Calculations (Traditional Method)
3000
3,000
4,000
6,000
8,000
10,000
20,000
30,000
40,000
60,000
80,000
100,000
200,000
300,000
400,000
600,000
800,000
C
INDEX
1 2 3 4 6 8 10 20 30 40 60 80 100 200
2000
2,000
1,000
2,000
2,000
3,000
3,000
4,000
4,000
6,000
6,000
8,000
8,000
10,000
10,000
800
600
400
300
200
100
80
60
40
30
20
10
8
6
4
3
2
1
1,000
1,000
2,000
2,000
3,000
3,000
4,000
4,000
6,000
6,000
8,000
8,000
10,000
10,000
20,000
20,000
30,000
30,000
40,000
40,000
60,000
60,000
80,000
80,000
100,000
100,000
200,000
300,000
400,000
800
800
600
600
400
400
300
300
200
200
100
100
80
80
60
60
40
40
35
32.6
30
20
10
8
6
4
3
2
1
0.8
0.6
0.4
0.3
0.2
0.1
0.08
0.06
0.04
0.03
0.02
0.01
1,000
1,000
800
600
800
600
400
300
200
100
80
60
40
30
20
400
300
200
100
80
60
40
30
20
10
10
8
8
6
6
4
4
3
3
2
2
1
0.8
0.6
0.4
0.2
0.1
0.3
1
0.8
0.6
0.4
0.3
0.2
0.1
0.08
0.06
0.04
0.04
0.06
0.08
0.03
0.03
0.02
0.02
0.01
0.01
0.008
0.008
0.006
0.006
0.004
0.004
0.003
0.003
0.002
0.002
0 .001
0.001
0.0008
0.0008
0.0006
0.0006
0.0004
0.0004
0.0003
0.0003
0.0002
0.0002
0.0001
0.0001
1000
800
600
400
300
200
100
80
60
40
30
20
10
8
6
4
3
2
1
0.8
0.6
0.4
0.3
0.2
0.1
0.08
0.06
0.04
0.03
0.02
0.01
3,000
4,000
6,000
8,000
10,000
20,000
30,000
40,000
60,000
80,000
100,000
200,000
300,000
400,000
600,000
800,000
1,000,000
1 2 3 4 6
8 10 20 30 40 60 80 100 200
1 2 3 4 6 8 10 20 30 40 60 80 100 200
2,000
1,000
1,000
2,000
2,000
3,000
3,000
4,000
4,000
6,000
6,000
8,000
8,000
10,000
10,000
20,000
20,000
30,000
30,000
40,000
40,000
60,000
60,000
80,000
80,000
100,000
100,000
200,000
300,000
400,000
800
800
600
600
400
400
300
300
200
200
100
100
80
80
60
60
40
40
35
32.6
30
20
10
8
6
4
3
2
1
1,000
800
600
400
300
200
100
80
60
40
30
20
10
8
6
4
3
2
1
0.8
0.6
0.4
0.2
0.1
0.3
0.04
0.06
0.08
0.03
0.02
0.01
3,000
4,000
6,000
8,000
10,000
20,000
30,000
40,000
60,000
80,000
100,000
200,000
INDEX
1 2 3 4 6 8 10 20 30 40 60 80 100 200
2,000
1,000
1,000
2,000
2,000
3,000
3,000
4,000
4,000
6,000
6,000
8,000
8,000
10,000
10,000
20,000
20,000
30,000
30,000
40,000
40,000
60,000
60,000
80,000
80,000
100,000
100,000
200,000
300,000
400,000
800
800
600
600
400
400
300
300
200
200
100
100
80
80
60
60
40
40
35
32.6
30
20
10
8
6
4
3
2
1
1,000
800
600
400
300
200
100
80
60
40
30
20
10
8
6
4
3
2
1
0.8
0.6
0.4
0.2
0.1
0.3
0.04
0.06
0.08
0.03
0.02
0.01
Q
C
V
V
INDEX
H
R
FOR SELECTING VALVE SIZE
FOR PREDICTING PRESSURE DROP
C
CORRECTION FACTOR, F
V
V
F
V
R
- CENTISTOKES
CS
LIQUID FLOW COEFFICIENT, C
KINEMATIC VISCOSITY V
LIQUID FLOW RATE (SINGLE PORTED ONLY), GPM
LIQUID FLOW RATE (DOUBLE PORTED ONLY), GPM
REYNOLDS NUMBER - N
VISCOSITY - SAYBOLT SECONDS UNIVERSAL
Nomograph Instructions
Use this nomograph to correct for the effects of viscosity. When
assembling data, all units must correspond to those shown on the
nomograph. For high-recovery, ball-type valves, use the liquid
ow rate Q scale designated for single-ported valves. For buttery
and eccentric disk rotary valves, use the liquid ow rate Q scale
designated for double-ported valves.
Nomograph Equations
1. Single-Ported Valves:
2. Double-Ported Valves:
NR = 17250
NR = 12200
Figure 2. Nomograph for Determining Viscosity Correction
Q
C
V νCS
Q
C
V νCS
Nomograph Procedure
1. Lay a straight edge on the liquid sizing coefcient on C
scale and ow rate on Q scale. Mark intersection on index
line. Procedure A uses value of Cvc; Procedures B and C use
value of Cvr.
2. Pivot the straight edge from this point of intersection with
index line to liquid viscosity on proper n scale. Read Reynolds
number on NR scale.
3. Proceed horizontally from intersection on NR scale to proper
curve, and then vertically upward or downward to Fv scale.
Read Cv correction factor on Fv scale.
C
CORRECTION FACTOR, F
V
FOR PREDICTING
FLOW RATE
V
v
Valve Sizing Calculations (Traditional Method)
628
Te c h n i c a l
Predicting Flow Rate
Select the required liquid sizing coefcient (Cvr) from the
manufacturer’s published liquid sizing coefcients (Cv) for the
style and size valve being considered. Calculate the maximum
ow rate (Q
correction required) using the following adaptation of the basic
) in gallons per minute (assuming no viscosity
max
liquid sizing equation:
Q
= Cvr ΔP / G (4)
max
Then incorporate viscosity correction by determining the uid
Reynolds number and correction factor Fv from the viscosity
correction nomograph and the procedure included on it.
Calculate the predicted ow rate (Q
Q
pred
=
) using the formula:
pred
Q
max
(5)
F
V
Predicting Pressure Drop
Select the required liquid sizing coefcient (Cvr) from the published
liquid sizing coefcients (Cv) for the valve style and size being
considered. Determine the Reynolds number and correct factor Fv
from the nomograph and the procedure on it. Calculate the sizing
coefcient (Cvc) using the formula:
C
CVC =
Calculate the predicted pressure drop (∆P
ΔP
pred
vr
(6)
F
v
) using the formula:
pred
= G (Q/Cvc)2 (7)
Flashing and Cavitation
The occurrence of ashing or cavitation within a valve can have a
signicant effect on the valve sizing procedure. These two related
physical phenomena can limit ow through the valve in many
applications and must be taken into account in order to accurately
size a valve. Structural damage to the valve and adjacent piping
may also result. Knowledge of what is actually happening within
the valve might permit selection of a size or style of valve which
can reduce, or compensate for, the undesirable effects of ashing
or cavitation.
P
2
P
2
2
P
2
FLOW
FLOW
P
1
RESTRICTION
Figure 3. Vena Contracta
P
1
P
1
Figure 4. Comparison of Pressure Profiles for
High and Low Recovery Valves
VENA CONTRACTA
P
HIGH RECOVERY
LOW RECOVERY
The “physical phenomena” label is used to describe ashing and
cavitation because these conditions represent actual changes in
the form of the uid media. The change is from the liquid state
to the vapor state and results from the increase in uid velocity at
or just downstream of the greatest ow restriction, normally the
valve port. As liquid ow passes through the restriction, there is a
necking down, or contraction, of the ow stream. The minimum
cross-sectional area of the ow stream occurs just downstream of
the actual physical restriction at a point called the vena contracta,
as shown in Figure 3.
To maintain a steady ow of liquid through the valve, the velocity
must be greatest at the vena contracta, where cross sectional
area is the least. The increase in velocity (or kinetic energy) is
accompanied by a substantial decrease in pressure (or potential
energy) at the vena contracta. Farther downstream, as the uid
stream expands into a larger area, velocity decreases and pressure
increases. But, of course, downstream pressure never recovers
completely to equal the pressure that existed upstream of the
valve. The pressure differential (∆P) that exists across the valve
629
Te c h n i c a l
Valve Sizing Calculations (Traditional Method)
is a measure of the amount of energy that was dissipated in the
valve. Figure 4 provides a pressure prole explaining the differing
performance of a streamlined high recovery valve, such as a ball
valve and a valve with lower recovery capabilities due to greater
internal turbulence and dissipation of energy.
Regardless of the recovery characteristics of the valve, the pressure
differential of interest pertaining to ashing and cavitation is the
differential between the valve inlet and the vena contracta. If
pressure at the vena contracta should drop below the vapor pressure
of the uid (due to increased uid velocity at this point) bubbles
will form in the ow stream. Formation of bubbles will increase
greatly as vena contracta pressure drops further below the vapor
pressure of the liquid. At this stage, there is no difference between
ashing and cavitation, but the potential for structural damage to
the valve denitely exists.
If pressure at the valve outlet remains below the vapor pressure
of the liquid, the bubbles will remain in the downstream system
and the process is said to have “ashed.” Flashing can produce
serious erosion damage to the valve trim parts and is characterized
by a smooth, polished appearance of the eroded surface. Flashing
damage is normally greatest at the point of highest velocity, which
is usually at or near the seat line of the valve plug and seat ring.
However, if downstream pressure recovery is sufcient to raise the
outlet pressure above the vapor pressure of the liquid, the bubbles
will collapse, or implode, producing cavitation. Collapsing of the
vapor bubbles releases energy and produces a noise similar to what
one would expect if gravel were owing through the valve. If the
bubbles collapse in close proximity to solid surfaces, the energy
released gradually wears the material leaving a rough, cylinder
like surface. Cavitation damage might extend to the downstream
pipeline, if that is where pressure recovery occurs and the bubbles
collapse. Obviously, “high recovery” valves tend to be more
subject to cavitation, since the downstream pressure is more likely
to rise above the vapor pressure of the liquid.
Q
(GPM)
Q
(GPM)
K
m
C
v
Figure 5. Flow Curve Showing Cv and K
ACTUAL
FLOW
C
v
Figure 6. Relationship Between Actual ∆P and ∆P Allowable
∆P (ALLOWABLE)
ΔP
PREDICTED FLOW USING
ACTUAL ∆P
ACTUAL ∆P
∆P (ALLOWABLE)
ΔP
PLOT OF EQUATION (1)
CHOKED FLOW
P1 = CONSTANT
m
Choked Flow
Aside from the possibility of physical equipment damage due to
ashing or cavitation, formation of vapor bubbles in the liquid ow
stream causes a crowding condition at the vena contracta which
tends to limit ow through the valve. So, while the basic liquid
sizing equation implies that there is no limit to the amount of ow
through a valve as long as the differential pressure across the valve
increases, the realities of ashing and cavitation prove otherwise.
If valve pressure drop is increased slightly beyond the point where
bubbles begin to form, a choked ow condition is reached. With
constant upstream pressure, further increases in pressure drop (by
reducing downstream pressure) will not produce increased ow.
The limiting pressure differential is designated ∆P
recovery coefcient (Km) is experimentally determined for each
and the valve
allow
valve, in order to relate choked ow for that particular valve to the
basic liquid sizing equation. Km is normally published with other
valve capacity coefcients. Figures 5 and 6 show these ow vs.
pressure drop relationships.
Valve Sizing Calculations (Traditional Method)
630
Te c h n i c a l
1.0
1.0
0.9
c
0.8
0.7
0.6
CRITICAL PRESSURE RATIO—r
0.5
0 500 1000 1500 2000 2500 3000 3500
VAPOR PRESSURE, PSIA
USE THIS CURVE FOR WATER. ENTER ON THE ABSCISSA AT THE WATER VAPOR PRESSURE AT THE
VALVE INLET. PROCEED VERTICALLY TO INTERSECT THE
CURVE. MOVE HORIZONTALLY TO THE LEFT TO READ THE CRITICAL
PRESSURE RATIO, RC, ON THE ORDINATE.
Figure 7. Critical Pressure Ratios for Water Figure 8. Critical Pressure Ratios for Liquid Other than Water
c
0.9
0.8
0.7
0.6
CRITICAL PRESSURE RATIO—r
0.5
0 0.20 0.40 0.60 0.80 1.0
USE THIS CURVE FOR LIQUIDS OTHER THAN WATER. DETERMINE THE VAPOR
PRESSURE/CRITICAL PRESSURE RATIO BY DIVIDING THE LIQUID VAPOR PRESSURE
AT THE VALVE INLET BY THE CRITICAL PRESSURE OF THE LIQUID. ENTER ON THE ABSCISSA AT THE
INTERSECT THE CURVE. MOVE HORIZONTALLY TO THE LEFT AND READ THE CRITICAL
RATIO JUST CALCULATED AND PROCEED VERTICALLY TO
PRESSURE RATIO, RC, ON THE ORDINATE.
VAPOR PRESSURE, PSIA
CRITICAL PRESSURE, PSIA
Use the following equation to determine maximum allowable
pressure drop that is effective in producing ow. Keep in mind,
however, that the limitation on the sizing pressure drop, ∆P
does not imply a maximum pressure drop that may be controlled y
allow
,
the valve.
∆P
= Km (P1 - rc P v) (8)
allow
where:
∆P
= maximum allowable differential pressure for sizing
allow
purposes, psi
Km = valve recovery coefcient from manufacturer’s literature
P1 = body inlet pressure, psia
r
= critical pressure ratio determined from Figures 7 and 8
c
Pv = vapor pressure of the liquid at body inlet temperature,
psia (vapor pressures and critical pressures for
many common liquids are provided in the Physical
Constants of Hydrocarbons and Physical Constants
of Fluids tables; refer to the Table of Contents for the
page number).
After calculating ∆P
equation
Q = CV ∆P / G
actual ∆P is less the ∆P
, substitute it into the basic liquid sizing
allow
to determine either Q or Cv. If the
, then the actual ∆P should be used in
allow
the equation.
The equation used to determine ∆P
calculate the valve body differential pressure at which signicant
should also be used to
allow
cavitation can occur. Minor cavitation will occur at a slightly lower
pressure differential than that predicted by the equation, but should
produce negligible damage in most globe-style control valves.
Consequently, initial cavitation and choked ow occur nearly
simultaneously in globe-style or low-recovery valves.
However, in high-recovery valves such as ball or buttery valves,
signicant cavitation can occur at pressure drops below that which
produces choked ow. So although ∆P
predicting choked ow capacity, a separate cavitation index (Kc) is
and Km are useful in
allow
needed to determine the pressure drop at which cavitation damage
will begin (∆Pc) in high-recovery valves.
The equation can e expressed:
∆PC = KC (P1 - PV) (9)
This equation can be used anytime outlet pressure is greater than
the vapor pressure of the liquid.
Addition of anti-cavitation trim tends to increase the value of Km.
In other words, choked ow and incipient cavitation will occur at
substantially higher pressure drops than was the case without the
anti-cavitation accessory.
631
Te c h n i c a l
Valve Sizing Calculations (Traditional Method)
Liquid Sizing Equation Application
EQUATION APPLICATION
1
2 Use to calculate expected Cv for valve controlling water or other liquids that behave like water.
Q = Cv ΔP / G
CV = Q
G
∆P
Basic liquid sizing equation. Use to determine proper valve size for a given set of service conditions.
(Remember that viscosity effects and valve recovery capabilities are not considered in this basic equation.)
3
4 Use to nd maximum ow rate assuming no viscosity correction is necessary.
5 Use to predict actual ow rate based on equation (4) and viscosity factor correction.
6 Use to calculate corrected sizing coefcient for use in equation (7).
7
8
9
C
= FV C
vr
Q
= Cvr ΔP / G
max
Q
Q
=
pred
C
CVC =
F
ΔP
= G (Q/Cvc)
pred
∆P
= Km (P1 - rc P v)
allow
∆PC = KC (P1 - PV)
V
max
F
V
vr
v
2
Liquid Sizing Summary
The most common use of the basic liquid sizing equation is
to determine the proper valve size for a given set of service
conditions. The rst step is to calculate the required Cv by using
the sizing equation. The ∆P used in the equation must be the actual
valve pressure drop or ∆P
step is to select a valve, from the manufacturer’s literature, with a
Cv equal to or greater than the calculated value.
Accurate valve sizing for liquids requires use of the dual
coefcients of Cv and Km. A single coefcient is not sufcient
to describe both the capacity and the recovery characteristics of
the valve. Also, use of the additional cavitation index factor Kc
is appropriate in sizing high recovery valves, which may develop
damaging cavitation at pressure drops well below the level of the
choked ow.
, whichever is smaller. The second
allow
Use to nd actual required Cv for equation (2) after including viscosity correction factor.
Use to predict pressure drop for viscous liquids.
Use to determine maximum allowable pressure drop that is effective in producing ow.
Use to predict pressure drop at which cavitation will begin in a valve with high recovery characteristics.
∆P = differential pressure, psi
∆P
= maximum allowable differential pressure for sizing
allow
purposes, psi
∆Pc = pressure differential at which cavitation damage
begins, psi
Fv = viscosity correction factor
G = specic gravity of uid (water at 60°F = 1.0000)
Kc = dimensionless cavitation index used in
determining ∆P
c
Km = valve recovery coefcient from
manufacturer’s literature
P1 = body inlet pressure, psia
Pv = vapor pressure of liquid at body inlet
temperature, psia
Liquid Sizing Nomenclature
Cv = valve sizing coefcient for liquid determined
experimentally for each size and style of valve, using
water at standard conditions as the test uid
Cvc = calculated Cv coefcient including correction
for viscosity
Q = ow rate capacity, gallons per minute
Q
Q
= designation for maximum ow rate, assuming no
max
viscosity correction required, gallons per minute
= predicted ow rate after incorporating viscosity
pred
correction, gallons per minute
rc = critical pressure ratio
Cvr = corrected sizing coefcient required for
viscous applications
Valve Sizing Calculations (Traditional Method)
632
Te c h n i c a l
Sizing for Gas or Steam Service
A sizing procedure for gases can be established based on adaptions
of the basic liquid sizing equation. By introducing conversion
factors to change ow units from gallons per minute to cubic
feet per hour and to relate specic gravity in meaningful terms
of pressure, an equation can be derived for the ow of air at
60°F. Because 60°F corresponds to 520° on the Rankine absolute
temperature scale, and because the specic gravity of air at 60°F
is 1.0, an additional factor can be included to compare air at 60°F
with specic gravity (G) and absolute temperature (T) of any other
gas. The resulting equation an be written:
520
Q
SCFH
= 59.64 CVP
∆P
1
GT
P
1
The equation shown above, while valid at very low pressure
drop ratios, has been found to be very misleading when the ratio
of pressure drop (∆P) to inlet pressure (P1) exceeds 0.02. The
deviation of actual ow capacity from the calculated ow capacity
is indicated in Figure 8 and results from compressibility effects and
critical ow limitations at increased pressure drops.
Critical ow limitation is the more signicant of the two problems
mentioned. Critical ow is a choked ow condition caused by
increased gas velocity at the vena contracta. When velocity at the
vena contracta reaches sonic velocity, additional increases in ∆P
by reducing downstream pressure produce no increase in ow.
So, after critical ow condition is reached (whether at a pressure
drop/inlet pressure ratio of about 0.5 for glove valves or at much
lower ratios for high recovery valves) the equation above becomes
completely useless. If applied, the Cv equation gives a much higher
indicated capacity than actually will exist. And in the case of a
high recovery valve which reaches critical ow at a low pressure
drop ratio (as indicated in Figure 8), the critical ow capacity of
the valve may be over-estimated by as much as 300 percent.
The problems in predicting critical ow with a Cv-based equation
led to a separate gas sizing coefcient based on air ow tests.
The coefcient (Cg) was developed experimentally for each
type and size of valve to relate critical ow to absolute inlet
pressure. By including the correction factor used in the previous
equation to compare air at 60°F with other gases at other absolute
temperatures, the critical ow equation an be written:
(A)
∆P
= 0.5
P
1
Q
C
∆P
= 0.15
P
1
v
∆P / P
Figure 9. Critical Flow for High and Low Recovery
Valves with Equal C
LOW RECOVERY
HIGH RECOVERY
1
v
Universal Gas Sizing Equation
To account for differences in ow geometry among valves,
equations (A) and (B) were consolidated by the introduction of
an additional factor (C1). C1 is dened as the ratio of the gas
sizing coefcient and the liquid sizing coefcient and provides a
numerical indicator of the valve’s recovery capabilities. In general,
C1 values can range from about 16 to 37, based on the individual
valve’s recovery characteristics. As shown in the example, two
valves with identical ow areas and identical critical ow (Cg)
capacities can have widely differing C1 values dependent on the
effect internal ow geometry has on liquid ow capacity through
each valve. Example:
High Recovery Valve
Cg = 4680
Cv = 254
C1 = Cg/Cv
= 4680/254
= 18.4
Low Recovery Valve
Cg = 4680
Cv = 135
C1 = Cg/C
= 4680/135
= 34.7
v
Q
= CgP1 520 / GT (B)
critical
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