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CONTROL VALVE
PRESSURE DROP AND SIZING
1
CONTENT
Chapter Description Page
I Purpose of Control Valve 2
II Type and Main Components of Control Valve 3
III Power 5
IV. Pressure Drop Across Control Valve 7
V. Symbols and Units 10
VI. Unit Conversion 11
Table 1. Typical Flow Factors for single ported C.V. 12
Table 2. Typical flow factor for rotary type C.V. 13
Table 3. Properties of Fluids 14
CONTROL VALVE
PRESSURE DROP AND SIZING
2
I. PURPOSE OF CONTROL VALVE
Control valve is required to control capacity or pressure of fluid where is flowing in piping
system. Pressure control is included liquid level such as in level control. Control valve is
also used as an instrument to control temperature where capacity of mixing fluid in an
equipment or piping is handled by control valve. Figure 1 shows typical application of
control valve.
Temperature control Level control
Flow controller
Figure 1. Typical application of control valve
CONTROL VALVE
PRESSURE DROP AND SIZING
3
Typical pressure controller
Figure 1. (continue) Typical application of control valve
II. TYPE AND MAIN COMPONENTS OF CONTROL VALVE
Figure 2 shows main components of control valve and figure 3 shows several type of
control valves.
Figure 2. Main component of control valve
CONTROL VALVE
PRESSURE DROP AND SIZING
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Figure 3. Types of control valve when divided into number of port, plug & seat type,
number of connection and valve types
CONTROL VALVE
PRESSURE DROP AND SIZING
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Figure 3. (continue) Types of control valve
III. POWER
Control valves are powered by manual, pneumatic system or electric motor. Instrument
air is commonly used for pneumatic power. Figure 4 shows typical of control valve
power system.
Figure 4. Types of actuator and power system for control valve
CONTROL VALVE
PRESSURE DROP AND SIZING
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Figure 4. (continue) Types of actuator and power system for control valve
CONTROL VALVE
PRESSURE DROP AND SIZING
7
2
2..363.1
Cv
QSG
222
72
..
10....3136.2
PoCvY
QnZToMW
IV. PRESSURE DROP ACROSS CONTROL VALVE
The following figure is schematic illustration to show fluid flow at around port and plug of
control valve.
Figure 5. Illustration of fluid flow inside the control valve
Pressure drop of fluid where flows across control valve can be determined as the
following equations.
For liquid,
PLOSS = kg/cm2 (1)
For gas
P/Po = (2)
Or by other method,
P/Po =
2
5.0
.
333..
483.2sin
64.59
1
ToSGPoCg
Qnarc
C (2A)
Where Cv is flow coefficient of valve or valve sizing coefficient given by manufacturers.
Q is volume flow in m3/hr, Qn is volume flow at normal condition in Nm3/hr, Po and To is
fluid pressure and temperature in kg/cm2A and K, MW is fluid and SG is specific gravity.
Y is expansion coefficient, C1 universal flow coefficient, Cg is gas flow coefficient also
given by manufacturers. Typical Y is,
CONTROL VALVE
PRESSURE DROP AND SIZING
8
22
2
.
..364.1
CvmY
QSG
Y =
TXk
PoP
..3
)/(4.11 (3)
k is gas adiabatic exponent, XT is pressure ratio factor when valve is installed without
fitting (elbows or reducers very close to valve). XT is given by manufacturers.
When control valve is installed with fittings, replace XT by XTP,
XTP =
12
24
42
2
2
1147.2071V
VV
T
P
T
d
Cv
Do
d
Do
dX
F
X
(4)
And equation (3) become,
Y =
TPXk
PoP
..3
)/(4.11 (5)
FP is piping construction factor and dV is nominal valve size in mm (it is not port diameter,
d but casing connection size) are given by manufacturers. Do is pipe diameter upstream
fitting in mm. If control valve constructed between identical reducers,
FP =
5.02
2
2
2
2
193.7001V
V
d
Cv
Do
d (6)
If all fittings pressure drop installed in the piping system has been calculated such as in
article “Fluid flow in pipe” in this blog, it will more simple to use equation (3) without XTP
and FP factor.
For liquid-gas mixture
PLOSS = kg/cm2 (7)
Cvm = (Cv+Cg)(1+Fm) (8)
Fm = RQ for RQ < 0.6 and Fm=1.334 RQ – 0.201 for 0.6< RQ <0.9 (9)
RQ = Qg / (QLIQ + Qg)
Qg is gas volume flow, QLIQ is liquid volume flow and RQ is gas-liquid volume ratio.
Limitation and correction
Viscosity correction
For viscous liquid such as oil, Cv in equation (1) shall be corrected become,
CONTROL VALVE
PRESSURE DROP AND SIZING
9
CVR = Cv.Fv (10)
Fv is viscosity correction for Cv. For pressure drop calculation, Fv is given as the following
equations.
If Re < 35, Fv = 18.12 Re-0.517235 . If 35<Re< 3000, Fv = 2.5422 – 0.001843 Re + 4.5572 Re2.10-5
If 3000<Re<60,000, Fv = 1.4683 Re-0.0349125 . If Re > 60,000, Fv = 1 (11)
Choked Flow and Cavitation
High velocity of liquid at vena contracta will reduce static pressure. If static pressure at
the vena contracta is lower than vapor pressure of liquid, vaporation will accour
(flashing) and than cavitation will also accour at downstream of vena contracta or
surrounding valve plug and other parts nearby where vapor bubbles are become liquid
again when static pressure is back to higher than vapor pressure. If bubbles due to
flashing occurrence are so much, these bubbles will crowd space at downstream of
valve port and limit liquid to flow. This occurrence is called choked flow.
To prevent from above condition, design of pressure drop of liquid across control valve
shall be limited at the following equations.
For globe type valve,
PLOSS-MAX-GLOBE =FL2 (Po – rC.Pv ) kg/cm2 (12)
Km (Po – rC.Pv)
FL is valve recovery coefficient given by manufacturers. Po is upstream pressure and Pv
vapor pressure of liquid in kg/cm2A. rC is critical pressure ratio
rC = 0.96 – 0.28 (Pv/Pc)0.5 (13)
where Pc is thermodynamic critical pressure of liquid.
If valve installed with fittings (reducers or elbows), equation (12) become,
PLOSS-MAX-GLOBE = FL 2(Po – rC.Pv )/Fp2 kg/cm2 (14)
For ball and butterfly (ROTARY) type valve,
PLOSS-MAX-ROTARY = FL 2(Po – rC.Pv ) or = FL 2(Po – rC.Pv )/Fp2 kg/cm2 (15)
FL2 can also be replaced by Km. Ball and butterfly valve is more tend to cavitation. Use
following equation to prevent cavitation.
PLOSS-MAX-ROTARY = Kc(Po – Pv ) (16)
Fc is approximately = 0.67 FL2 or see table.
CONTROL VALVE
PRESSURE DROP AND SIZING
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Choked condition will also accour for gas, steam and vapor if velocity at vena
contracta reach the sound velocity. Port pressure drop of gas or steam at 0.8 x sound
velocity is,
P sonic = 0.4 Po.k kg/cm2 (17)
Cg MIN = 0.16585.Qn.(SG To)0.5/Po (18)
V. SYMBOLS AND UNITS
Unless otherwise noted, the following symbols and units are used in this manual.
Symbol Description Unit
Cv Flow coefficient
Cvm Flow coefficient for liquid-gas mixture
Cg Gas sizing coefficient
Cs Steam sizing coefficient
D or Do Inside pipe diameter mm
dV, d Nominal control valve size, port dia. mm
Fm Liquid-gas mixture factor
Fp Installation factor
Fv Viscosity correction factor
g Gravity 9.81 m/s2
FL Valve recovery coefficient
L Pipe length m
Viscosity cP (centipoise)
Po Upstream pipe pressure kg/cm2A
Pv Vapor pressure kg/cm2A
Pc Thermodynamic critical pressure kg/cm2A
P or PLOSS Differential pressure/pressure drop kg/cm2
Q Volume flow (see note) m3/hr
Qg & QLIQ Gas and liquid volume flow m3/hr
CONTROL VALVE
PRESSURE DROP AND SIZING
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RQ Gas-liquid volume ratio
Fluid density kg/m3
Re Reynold Number
rC Critical pressure ratio
SG Specific gravity
T Absolute temperature 0 K
V Fluid velocity m/s
Y Gas net expansion factor
VI. UNIT CONVERSION
Designation Unit to be converted Factor Unit to be used
Length ft 304.8 mm
inch 25.4 mm
Pressure psi 0.07031 kg/cm2
bar 1.0194 kg/cm2
atm. 1.0326 kg/cm2
Pa (Pascal) 1.0194 x 10-5 kg/cm2
Temperature F (Fahrenheit) (tF -32) x (5/9) C
R (Rankin) (5/9) K
C (Celcius) tC + 273 K
Velocity ft/s 0.3048 m/s
ft/min (fpm) 0.00508 m/s
Volume flow GPM (US) 0.227 m3/hr
CFM 1.699 m3/hr
Mass lb 0.4536 kg
Power HP 0.7457 kW
CONTROL VALVE
PRESSURE DROP AND SIZING
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Head ft 0.3048 m
Enthalpy kcal/kg 4.1868 kJ/kg
BTU/lb 2.326 kJ/kg
Gas constant kcal/kg.K 4.1868 kJ/kg.K
Specific heat BTU/lb.R 4.1868 kJ/kg.K
Density lb/ft3 16.0185 kg/m3
Specific volume ft3 /lb 0.06243 m3/kg
Viscosity N.s/m2 1000 cP
lbf.s/ft2 47880.3 cP
Kinematic to absolute viscosity, = SG . in cSt (centistokes), in cP
Note : American Standard State condition is condition where pressure at 1.013 bar A and
temperature at 15.5 C. In volume, is common written as SCF. Normal condition is at 1.0132
bar A and 0 C. In volume, is common written as Nm3 (Symbol for flow in this article is Qn)
Table 1. Typical Cv, FL and XT for Single Ported Globe Style Valve bodies
CONTROL VALVE
PRESSURE DROP AND SIZING
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PRESSURE DROP AND SIZING
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Table 2. Typical Cv, FL and XT for rotary shaft valve
CONTROL VALVE
PRESSURE DROP AND SIZING
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CONTROL VALVE
PRESSURE DROP AND SIZING
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PRESSURE DROP AND SIZING
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Table 3. Properties of some fluids
CONTROL VALVE
PRESSURE DROP AND SIZING
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CONTROL VALVE
PRESSURE DROP AND SIZING
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