Valve Sizing Calculations (Traditional Method)
626
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 flow, 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 lecting a valve bad upon the size of the pipeline are gone. Selecting the correct valve size for a given application requires a knowledge of proc
ess conditions that the valve will actually e in rvice. The technique for using this information to size the valve is bad upon a combination of theory and experimentation.
Sizing for Liquid Service
Using the principle of conrvation of energy, Daniel Bernoulli found that as a liquid flows through an orifice, the square of the fluid velocity is directly proportional to the pressure differential across the orifice and inverly proportional to the specific gravity of the fluid. The greater the pressure differential, the higher the velocity; the greater the density, the lower the velocity. The volume flow rate for liquids can be calculated by multiplying the fluid velocity times the flow area.
By taking into account units of measurement, the proportionality relationship previously mentioned, energy loss due to friction and turbulence, and varying discharge coefficients for various types of orifices (or valve bodies), a basic liquid sizing equation can be written as follows Q = C V ∆P / G
(1)
斗罗大陆经典语录where: Q = Capacity in gallons per minute
C v = Valve sizing coefficient determined experimentally for
each style and size of valve, using water at standard conditions as the test fluid ∆P = Pressure differential in psi
G = Specific gravity of fluid (water at 60°F = 1.0000)
Thus, C v is numerically equal to the number of U.S. gallons of water at 60°F that will flow through the valve in one minute when the pressure differential across the valve is one pound per square inch. C v varies with both size and style of valve, but provides an index for comparing liquid capacities of different valves under a standard t of conditions.
To aid in establishing uniform measurement of liquid flow capacity coefficients (C v ) 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 C v information for their products, making it relatively easy to compare capacities of competitive products.
To calculate the expected C v for a valve controlling water or other liquids that behave like water, the basic liquid sizing equation above can be re-written as follows
C V = Q
G ∆P
(2)
Viscosity Corrections
Viscous conditions can result in significant sizing errors in using the basic liquid sizing equation, since published C v values are bad on test data using water as the flow medium. Although the majority of valve applications will involve fluids where viscosity corrections can be ignored, or where the corrections are relatively small, fluid viscosity should be considered in each valve lection.Emerson Process Management has developed a nomograph (Figure 2) that provides a viscosity correction factor (F v ). It can be applied to the standard C v coefficient to determine a corrected coefficient (C vr ) for viscous applications.
wait的过去式Finding Valve Size
Using the C v determined by the basic liquid sizing equation and the flow and viscosity conditions, a fluid Reynolds number can be found by using the nomograph in Figure 2. The graph of Reynolds number vs. viscosity correction factor (F v ) is ud 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 C v (C vr ) is found by the equation:
C vr = F V C V
(3)
From the valve manufacturer’s published liquid capacity
information, lect a valve having a C v equal to or higher than the required coefficient (C vr ) found by the equation above.
Figure 1. Standard FCI Test Piping for C v Measurement
∆FLOW
627
U this nomograph to correct for the effects of viscosity. When asmbling data, all units must correspond to tho shown on the nomograph. For high-recovery, ball-type valves, u the liquid flow rate Q scale designated for single-ported valves. For butterfly and eccentric disk rotary valves, u the liquid flow rate Q scale designated for double-ported valves.
Nomograph Equations
1. Single-Ported Valves: N
R
= 17250Q
C V νCS 2. Double-Ported Valves: N
R = 12200Q
C V νCS
1. Lay a straight edge on the liquid sizing coefficient on C v
scale and flow rate on Q scale. Mark interction on index line. Procedure A us value of C vc ; Procedures B and C u value of C vr .
2. Pivot the straight edge from this point of interction with index line to liquid viscosity on proper n scale. Read Reynolds number on N R scale.
3. Proceed horizontally from interction on N R scale to proper curve, and then vertically upward or downward to F v scale. Read C v correction factor on F v scale.
L I q U I D F L O W C O E F F I C I E N T , C V
C
Valve Sizing Calculations (Traditional Method)
628
Predicting Flow Rate
Select the required liquid sizing coefficient (C vr ) from the
manufacturer’s published liquid sizing coefficients (C v ) for the style and size valve being considered. Calculate the maximum flow rate (Q max ) in gallons per minute (assuming no viscosity correction required) using the following adaptation of the basic liquid sizing equation:
Q max = C vr ΔP / G
(4)
Then incorporate viscosity correction by determining the fluid Reynolds number and correction factor F v from the viscosity correction nomograph and the procedure included on it.Calculate the predicted flow rate (Q pred ) using the formula:
Q pred = Q max
F
V
(5)
Predicting Pressure Drop
Select the required liquid sizing coefficient (C vr ) from the published liquid sizing coefficients (C v ) for the valve style and size being considered. Determine the Reynolds number and correct factor F v from the nomograph and the procedure on it. Calculate the sizing coefficient (C vc ) using the formula:
C VC = C vr
F
v
(6)
Calculate the predicted pressure drop (∆P pred ) using the formula:
ΔP pred = G (Q/C vc )2
(7)
Flashing and Cavitation
The occurrence of flashing or cavitation within a valve can have a significant effect on the valve sizing procedure. The two related physical phenomena can limit flow 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 lection of a size or style of valve which can reduce, or compensate for, the undesirable effects of flashing or cavitation.
The “physical phenomena” label is ud to describe flashing and cavitation becau the conditions reprent actual changes in the form of the fluid media. The change is from the liquid state to the vapor state and results from the increa in fluid velocity at or just downstream of the greatest flow restriction, normally the valve port. As liquid flow pass through the restriction, there is a necking down, or contraction, of the flow stream. The minimum cross-ctional area of the flow 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 flow of liquid through the valve, the velocity must be greatest at the vena contracta, where cross ctional area is the least. The increa in velocity (or kinetic energy) is accompanied by a substantial decrea in pressure (or potential energy) at the vena contracta. Farther downstream, as the fluid stream expands into a larger area, velocity decreas and pressure increas. But, of cour, downstream pressure never recovers completely to equal the pressure that existed upstream of the valve. The pressure differential (∆P) that exists across the valve
Figure 3. Vena Contracta
Figure 4. Comparison of Pressure Profiles for
High and Low Recovery Valves
FLOW
FLOW
P P 2
P 2
P
Valve Sizing Calculations (Traditional Method)
is a measure of the amount of energy that was dissipated in the
valve. Figure 4 provides a pressure profile explaining the differing秋天的天气
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 flashing 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 fluid (due to incread fluid velocity at this point) bubbles
will form in the flow stream. Formation of bubbles will increa
greatly as vena contracta pressure drops further below the vapor
pressure of the liquid. At this stage, there is no difference between
flashing and cavitation, but the potential for structural damage to
the valve definitely 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 “flashed.” Flashing can produce
rious 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 at line of the valve plug and at ring.
However, if downstream pressure recovery is sufficient to rai the
outlet pressure above the vapor pressure of the liquid, the bubbles
will collap, or implode, producing cavitation. Collapsing of the
vapor bubbles releas energy and produces a noi similar to what
one would expect if gravel were flowing through the valve. If the
bubbles collap in clo proximity to solid surfaces, the energy
relead 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
带数字的四字词语collap. Obviously, “high recovery” valves tend to be more
subject to cavitation, since the downstream pressure is more likely
to ri above the vapor pressure of the liquid.
Choked Flow
Aside from the possibility of physical equipment damage due to flashing or cavitation, formation of vapor bubbles in the liquid flow stream caus a crowding condition at the vena contracta which tends to limit flow through the valve. So, while the basic liquid sizing equation implies that there is n
o limit to the amount of flow through a valve as long as the differential pressure across the valve increas, the realities of flashing and cavitation prove otherwi. If valve pressure drop is incread slightly beyond the point where bubbles begin to form, a choked flow condition is reached. With constant upstream pressure, further increas in pressure drop (by reducing downstream pressure) will not produce incread flow. The limiting pressure differential is designated ∆P
allow
and the valve recovery coefficient (K
m
) is experimentally determined for each valve, in order to relate choked flow for that particular valve to the basic liquid sizing equation. K
m
is normally published with other valve capacity coefficients. Figures 5 and 6 show the flow vs. pressure drop relationships.
Figure 5. Flow Curve Showing C
v
and K
m
q
(GPM)
ΔP
Figure 6. Relationship Between Actual ∆P and ∆P Allowable q
(GPM)
ΔP
629
Valve Sizing Calculations (Traditional Method)
630
U the following equation to determine maximum allowable pressure drop that is effective in producing flow. Keep in mind, however, that the limitation on the sizing pressure drop, ∆P allow , does not imply a maximum pressure drop that may be controlled y the valve. ∆P allow = K m (P 1 -
r c P v )
(8)
where:
∆P allow = maximum allowable differential pressure for sizing
purpos, psi K m = valve recovery coefficient from manufacturer’s literature P 1 = body inlet pressure, psia
r c = critical pressure ratio determined from Figures 7 and 8
P v = 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 allow , substitute it into the basic liquid sizing equation Q = C V ∆P / G to dete
rmine either Q or C v . If the actual ∆P is less the ∆P allow , then the actual ∆P should be ud in the equation.
The equation ud to determine ∆P allow should also be ud to calculate the valve body differential pressure at which significant 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.Conquently, initial cavitation and choked flow occur nearly simultaneously in globe-style or low-recovery valves.
However, in high-recovery valves such as ball or butterfly valves, significant cavitation can occur at pressure drops below that which produces choked flow. So although ∆P allow and K m are uful in predicting choked flow capacity, a parate cavitation index (K c ) is needed to determine the pressure drop at which cavitation damage will begin (∆P c ) in high-recovery valves.The equation can e expresd:
∆P C = K C (P 1 - P V )
(9)
This equation can be ud anytime outlet pressure is greater than the vapor pressure of the liquid.
Addition of anti-cavitation trim tends to increa the value of K m . In other words, choked flow and incipient cavitation will occur at substantially higher pressure drops than was the ca without the anti-cavitation accessory.
Figure 7. Critical Pressure Ratios for Water Figure 8. Critical Pressure Ratios for Liquid Other than Water
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, R C , ON ThE ORDINATE.
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
RATIO JUST CALCULATED AND PROCEED VERTICALLY TO
INTERSECT ThE CURVE. MOVE hORIzONTALLY TO ThE LEFT AND READ ThE CRITICAL
PRESSURE RATIO, R C , ON ThE ORDINATE.
1.0藏餐
0.90.80.70.60.5C R I T I C A L P R E S S U R E R A T I O —r c
0.20
0.40
0.60
0.80
1.0
VAPOR PRESSURE, PSIA CRITICAL PRESSURE, PSIA
宽容的议论文1.0
0.9
0.8
0.7
0.6
0.5
C R I T I C A L P R E S S U R E R A T I O —r c
500
1000
1500
描写沙漠的句子2000
野苏胶囊
2500
3000
3500
VAPOR PRESSURE, PSIA
